UNIVERSITY OF CALIFORNIA Los Angeles. Seismic Investigations of Core-Mantle Boundary Structure. and Source Properties of Deep-Focus Earthquakes

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1 UNIVERSITY OF CALIFORNIA Los Angeles Seismic Investigations of Core-Mantle Boundary Structure and Source Properties of Deep-Focus Earthquakes A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Geophysics and Space Physics by Steven Eric Persh 2002

2 ccopyright 2002 by Steven Eric Persh

3 The dissertation of Steven Eric Persh is approved. Gerald Schubert Jonathan P. Stewart Paul J. Tackley Heidi Houston, Committee Co-chair John E. Vidale, Committee Co-chair University of California, Los Angeles 2002 ii

4 For Mom and Dad and For Jenny iii

5 TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES viii xi 1 Introduction Stacking seismograms Seismographic networks I Reflection properties and fine-scale structure of the core-mantle boundary 7 2 Introduction Core-mantle boundary The core-mantle boundary region Ultra-low velocity zones PcP and ScP Core-mantle boundary reflection coefficients Data and Processing Computing envelope stacks Measuring amplitude ratios Calculating reflection coefficients Globally-averaged reflection properties Stacks Amplitude ratios Mapping reflection properties Discussion ULVZprecursor search Introduction ULVZ studies using PcP and ScP Data NCSN and SCSN LASA Japan array iv

6 4.3 Observations Coherent stacks Envelope stacks Modeling Discussion Diminished core-grazing P -waves Introduction Data and Observations ISC amplitudes GSN stacks Discussion Conclusion Core-mantle boundary Summary of results Reflection properties of the CMB Search for ULVZ precursors Diminished core-grazing P -waves Implications for structure at the CMB Future work II Source properties of deep-focus earthquakes 83 7 Introduction Deep earthquakes Proposed mechanisms Source time functions Data and Processing Earthquakes Computation of source time functions Scaling relationships Moment- and duration-scaling Frequency-domain stacking Depth dependence Source time functions Duration Shape Stress drop Circular crack model Energy Apparent stress v

7 9.5.2 Seismic efficiency Summary Subduction zone variation Duration Shape Thermal parameter Summary Initiation, Termination, and Aftershocks Initiation Termination Aftershocks Mainshocks: Source time functions Mainshocks: Harvard CMT catalog Summary Conclusion Deep earthquakes Summary of results Implications for mechanism of deep earthquakes Future work A Acronyms 193 B Review of core-mantle boundary properties 194 B.1 Overview B.2 Seismological results B.2.1 Velocity structure B.2.2 D 00 discontinuity B.2.3 Anisotropy B.2.4 Ultra-low velocity zones B.3 Geodynamical properties C Core-mantle boundary supplemental information 203 C.1 Selection criteria D Transformational faulting 207 D.1 Thermo-kinetic modeling D.2 Experimental results E Deep earthquakes supplemental information 213 E.1 Earthquake selection and data processing E.1.1 Selection criteria vi

8 E.1.2 Measuring durations E.1.3 Events common to other studies E.2 Depth dependence Bibliography 226 vii

9 LIST OF FIGURES 1.1 Examples of coherent and envelope stacking Seismic networks used Map of ULVZ detections Travel time curves Raypaths of P, P cp, and ScP Global coverage of PcP bounce points Global coverage of ScP bounce points PcP-aligned envelope stacks of GSN seismograms Hz bandpass ScP-aligned envelope stacks of GSN seismograms Hz bandpass PcP=P vs. distance from GSN stacks ScP=P vs. distance from GSN stacks PcP/P by bounce point location ScP/P by bounce point location PcP/P vs. distance at three bounce point locations Correlation of PcP/P in different bandpasses Correlation of ScP/P in different bandpasses Earthquakes, networks, and CMB bounce point locations Northern and Southern California Seismographic Networks Large Aperture Seismic Array configuration Subarray stacks for an event recorded at LASA Japan array station locations PcP and ScP stacks NCSN and SCSN PcP stacks LASA PcP and ScP stacks J-array Envelope stacks of ScP Slowness stack of an event recorded at SCSN Slowness stack of an event recorded at LASA Slowness stack of an event recorded at Japan array Stack amplitudes at predicted ULVZ precursor times Raypaths for core-grazing P -waves Map of attenuated P di arrivals at LASA viii

10 5.3 Average spectra of anomalous and normal events ISC amplitude at LASA vs. magnitude Recent focal mechanisms from the New Hebrides region Map of corrected ISC amplitudes Comparison of envelope stacks of core-grazing P from GSN and LASA Locations of deep earthquakes Depth distribution of seismicity Map of earthquake and station locations Computation of a source time function Velocity stacks Velocity stacks, continued Comparison with others source time functions Initiation picks and pre-event noise Scaling relationships Moment vs. depth Velocity-corrected duration vs. moment Effects of moment-scaling Scaled duration vs. moment Moment-scaled source time functions Moment-scaled source time functions, continued Scaled duration vs. depth Bootstrap resampling of scaled durations Least-squares fits to scaled duration vs. depth Comparison of depth dependence of scaled duration from several studies Average source time functions by depth range First and second moments of time functions vs. depth Average zero-crossings by depth range Static stress drop vs. depth Energy vs. moment Apparent stress vs. depth Apparent stress vs. static stress drop Maximum seismic efficiency vs. depth Map of earthquakes grouped by subduction zone Scaled duration vs. depth by subduction zone Average scaled duration by subduction zone and depth range Average source time functions by subduction zone and depth range Average zero-crossings by subduction zone and depth range Scaled duration vs. thermal parameter ix

11 11.1 Initial moment-rate vs. moment and depth Average nucleation rates by moment and depth Moment-rates at four times before termination Average termination rates by moment and depth Number of aftershocks vs. scaled duration Number of aftershocks vs. static stress drop Number of aftershocks vs. moment Number of aftershocks vs. depth Number of aftershocks compared with overall seismicity Bootstrap resampling of number of aftershocks Number of aftershocks vs. thermal parameter C.1 Choosing minimum signal-to-noise values for P cp C.2 Choosing minimum signal-to-noise values for ScP D.1 P T diagram for olivine-spinel system D.2 Metastable olivine wedge in a subducting slab E.1 Effects of minimum seismogram criterion on number of earthquakes E.2 Number of seismograms stacked vs. moment E.3 Number of seismograms stacked vs. depth E.4 Scaled duration vs. number of seismograms stacked E.5 Check for directivity effects E.6 Comparison of auto-picked and hand-picked durations E.7 Comparison of durations of common events E.8 Scaled duration vs. depth using auto-picked durations E.9 Scaled duration vs. depth using best-fit scaling exponent x

12 LIST OF TABLES 3.1 Q model used to correct for attenuation Earthquakes used in ULVZ precursor search NCSN and SCSN Earthquakes used in ULVZ precursor search LASA Earthquakes used in ULVZ precursor search Japan array Earthquakes studied for diminished core-grazing P -waves Deep earthquakes studied A.1 List of acronyms xi

13 ACKNOWLEDGEMENTS When I began graduate school at UCLA, I knew virtually nothing about geophysics or seismology and was somewhat unsure about my ability to negotiate the many trials that lay ahead. Now that I have reached the conclusion, I realize how fortunate I have been not to face these challenges alone, but with the assistance of many people who generously and patiently tutored and supported me over the years. My co-advisors John Vidale and Heidi Houston fostered my initial interest in the class projects that developed into my dissertation research. The encouraged me to continue by suggesting interesting and important lines of investigation. They furnished the freedom to find my own solutions to scientific and technical problems, but never left me entirely without guidance. I have benefitted especially from their deep knowledge of seismology and quick recognition of the important aspects of an observation. Conversations with John and Heidi provided perspective and direction, especially valuable during the many times I reached a state of high alarm about my progress. I must also acknowledge Heidi as the professor in my first-ever seismology course, Introduction to Earthquakes, which I audited before enrolling as a graduate student and which captured my interest enough to enter the field. The other members of my committee Gerald Schubert, Paul Tackley, and Jonathan Stewart raised important issues that I continued to ponder long after each exam and helped me consider more carefully the implications of my results. Two other mentors deserve special mention: Paul Earle arrived as a postdoc at just the right time for me to absorb all I could from him about science, seismology, and programming. Without his assistance, I might still be figuring out how to read data files. xii

14 I count Paul as not only a colleague but a good friend as well. Paul Davis accepted me as a novice student of geophysics, and graciously allowed me to follow my interests as they developed. My fellow grad students and friends shared the frustrations and successes of graduate school and opened my eyes to all there is to experience in LA outside my office. Thanks to Fei Xu, Ann-Sophie Provost, Shirley Baher, Allen Husker, Elizabeth Cochran, Heather Lin, Janet Green, Bill Akers, and Mervi Eeva for many hours of commiseration and mostly guiltless recreation. The opportunities to spend time with friends outside UCLA have been all too infrequent, but more special when they arise. The fortuitous residences of Steve Lin, Ken Wang, Mimi Kao, Sarah Oh, and Mike Huang in or near San Francisco during most of my graduate career made the city more hospitable during AGU, particularly with our annual visit to Napa Valley after the end of (okay, sometimes during) the conference. My family provided a comfortable home to which to return when I needed to recuperate. Mom and Dad have always expressed their unconditional love regardless of what I chose to do or how well I performed in school. That is the greatest support parents can give. My brother Barry motivated me by often noting that I was still in school after all these years. I think he also paid for more than his share of long-distance phone calls that never failed to leave me feeling better. My greatest fortune has been to come home every day to Jenny, my sweetie, and receive her beautiful smile and exuberant greeting. I am afraid I caused her to re-experience the anxieties of grad school as she saw me through its stages. Jenny deserves more thanks than xiii

15 I can express for so many things, but especially for reading the roughest of drafts of each chapter, for bringing me dinner when I worked late, and for bringing me back to reality when I started stressing about the point size of the figure captions. I could not have finished without Jenny s love, support, and frequent hugs. Chapter 4 is based in part on Absence of short-period ULVZ precursors to PcP and ScP from two regions of the CMB by Steven E. Persh, John E. Vidale, and Paul S. Earle, Geophys. Res. Lett., 28, , xiv

16 VITA December 15, 1971 Born, Silver Spring, Maryland 1994 B. S., Physics Stanford University Palo Alto, California 1996 M. S., Physics Yale University New Haven, Connecticut 1998 M. S., Geophysics and Space Physics University of California, Los Angeles PUBLICATIONS AND PRESENTATIONS Houston, H. and S. E. Persh, How do big earthquakes get their start?, Eos Trans. AGU, 80 (46), F718, Persh, S. E. and P. M. Davis, Modeling the earthquake cycle with dynamic rupture followed by viscoelastic relaxation, Eos Trans. AGU, 78 (46), F476, Persh, S. E., H. Houston, and P. S. Earle, Source time functions of deep earthquakes from global stacks of broadband seismograms, Eos Trans. AGU, 80 (46), F669, Persh, S. E. and J. E. Vidale, Global mapping of core-mantle boundary reflection amplitudes, Eos Trans. AGU, 82 (47), F1130, Persh, S. E., J. E. Vidale, and P. S. Earle, Fine-scale structure at the core-mantle boundary from reflected phases, Eos Trans. AGU, 79 (45), F617, Persh, S. E., J. E. Vidale, and P. S. Earle, CMB structure from a global survey of Global Seismographic Network and LASA PcP and ScP phases, Eos Trans. AGU, 81 (48), F906, Persh, S. E., J. E. Vidale, and P. S. Earle, Absence of short-period ULVZ precursors to PcP and ScP from two regions of the CMB, Geophys. Res. Lett., 28, , Persh, S. E., J. E. Vidale, and P. S. Earle, Searching for evidence of ultralowvelocity zones at Earth s core-mantle boundary, Eos Trans. AGU, 82 (20), S260, xv

17 ABSTRACT OF THE DISSERTATION Seismic Investigations of Core-Mantle Boundary Structure and Source Properties of Deep-Focus Earthquakes by Steven Eric Persh Doctor of Philosophy in Geophysics and Space Physics University of California, Los Angeles, 2002 Professor Heidi Houston, Co-chair Professor John E. Vidale, Co-chair This dissertation investigates geophysical problems concerning the structure of the Earth s interior and the physics of the earthquake source by stacking seismograms recorded at global and regional networks. The core-mantle boundary (CMB) region contains thermal and compositional heterogeneities at different length-scales, including thin layers at the base of the mantle with large P -wave velocity reductions (ULVZs). Core-reflected seismic phases P cp and ScP are sensitive to velocity and density changes within ULVZs, discontinuity sharpness, and CMB variability on short length-scales. Amplitudes of globally-recorded PcP and ScP reveal a sharp average CMB with no more than 10% velocity reductions in the mantle for P - and S-waves. The amplitudes do not support proposed 30% S-wave velocxvi

18 ity reductions or core-mantle transition zones. No precursor arrivals to P cp and ScP are visible on regional network stacks at times and amplitudes predicted for ULVZ properties. This suggests ULVZs transition gradually from the lower mantle. Diminished core-grazing P -waves sampling the CMB in a localized region of the mid-pacific provide evidence for short length-scale variation, possibly reflecting dynamical processes. Time histories of moment release provide insight into rupture processes of deep earthquakes, whose physical mechanism remains unknown. We compare source time functions computed from stacks of teleseismic P -waves of 111 deep earthquakes with MW 6:4 and depth 100 km. An abrupt change in character occurs at 550 km. Earthquakes deeper than 550 km have shorter durations and simpler time functions. Shallow events have longer durations, and the km range averages more subevents. Radiated energy-to-moment ratios are lower than for large shallow earthquakes and maximum seismic efficiency decreases slightly with depth. Initiations and terminations are consistent with self-similar rupture, although large events tend to begin more rapidly. Aftershock productivity declines significantly km, then rises below 550 km. Individual subduction zones generally demonstrate similar depth dependence, but differences suggest thermal or structural properties of slabs influence rupture. If transformational faulting of metastable olivine operates km, these observations suggest a change in mechanism occurs around 550 km, possibly involving another metastable mineral. xvii

19 Chapter 1 Introduction Seismology is concerned with the structure of the Earth s interior and the physics of the earthquake source. Seismic waves carry information about the slip histories that generate them and the properties of Earth materials through which they propagate. Seismograms originating from globally-distributed sources and recorded by regional and global networks can be used to measure properties of earthquakes and Earth materials and map their variations. In this dissertation, we follow this strategy in the study of two geophysical problems: Part I investigates fine-scale structure at Earth s core-mantle boundary by measuring its reflection properties, searching for basal mantle layering, and documenting evidence for variations on small length-scales. Part II studies source characteristics of deep-focus earthquakes by comparing their properties as functions of depth, subduction zone, and seismic moment. The results have implications for our understanding of the composition and dynamics of Earth s interior. We will place constraints on the origins of low-velocity layers at the base of the mantle and find variation of core-mantle boundary structure over short dis- 1

20 tances, which may derive from thermal and compositional heterogeneity arising from geodynamical processes. Differences in the manner in which moment release occurs during deep earthquakes may indicate changes in the failure mechanism with depth and convey information about internal properties of the subducting lithosphere and the complexity of the rupture process. Although the two geophysical problems are not directly related, the methods used here to study them have much in common. They take advantage of improvements in the ability to store and process large volumes of seismic data. In particular, different forms of stacking seismograms recorded by global and regional networks are central to the processing techniques applied in this dissertation. 1.1 Stacking seismograms Stacking involves combining multiple seismograms in order to improve the ability to detect and measure particular seismic phases. It is generally accomplished by aligning an arrival based on travel time, or an identifiable feature, and summing. In the work in this dissertation, we stack arrivals from source-receiver pairs with common midpoints as well as from single events recorded at multiple stations. In coherent stacking, velocity seismograms are linearly averaged: Coherent features sum constructively, and incoherent features (such as background noise) sum destructively. Coherent stacking thus provides a simple method to enhance the signal-to-noise ratio (Fig- 2

21 p ure 1.1). If noise is uncorrelated, the signal-to-noise improves by a factor of N if N seismograms are stacked. This signal enhancement is particularly useful in the work presented in this dissertation, where the seismic phases of interest are often small and difficult to identify on individual seismograms or where the termination time of the earthquake rupture is lost in the noise of individual seismograms but emerges from the stack. Another form of stacking, envelope stacking, sums the aligned envelope functions of seismograms (Figure 1.1). This procedure sums all arriving energy, regardless of whether it is coherent. This is useful for combining waveforms from multiple earthquakes or for measuring scattered energy. Several variations on these techniques exist: Stacking can be performed in the timeor frequency-domain. N-th root and logarithmic stacking dampen large spikes to reduce their influence [McFadden et al., 1986]. And, stacking in slowness-time space resolves an arrival s incidence angle at an array. 1.2 Seismographic networks Seismic networks are a central element of stacking. The growth of large networks of high-quality seismographic instruments has enabled progressively more detailed investigations of the Earth s interior [Benz et al., 1994]. Regional-scale seismic networks such as the Northern and Southern California Seismic Networks ([N/S]CSN), the Large Aperture Seismic Array (LASA) and the Japan Array (J-array) contain hundreds of short-period in- 3

22 Coherent stacking ScP station: EMS station: IND station: FOX station: PSH Stack of 145 seismograms Time [s] Envelope stacking station: EMS ScP station: IND station: FOX station: PSH Stack of 145 envelopes Time [s] Figure 1.1: (upper panel) Four individual seismograms and a 145-seismogram coherent stack of ScP recorded at the Southern California Seismic Network from a MW 6.0 earthquake in the Aleutian Islands ( in Table 4.1). The pre-arrival noise is significantly reduced, enabling a search for precursor arrivals. (lower panel) Envelopes and envelope stack of the same data. Incoherent arrivals do not cancel, so this procedure can reveal whether scattered energy precedes ScP. 4

23 Networks Global Seismographic Network NCSN / SCSN LASA Japan array 60 o 30 o 0 o -30 o -60 o Figure 1.2: Locations of networks used in the research presented here. Over 100 Global Seismographic Network (GSN) stations are shown by gray triangles; Northern and Southern California Seismic Networks ([N/S]CSN) by blue triangles; Large Aperture Seismic Array (LASA) by green triangle; and Japan array by red triangle. GSN are broadband stations; others are short-period. struments spread over hundreds of kilometers. These networks enable sensitive mapping of particular regions in the Earth. Their wide apertures provide the ability to detect arrivals at different incidence angles as well as off-azimuth arrivals. The Global Seismographic Network (GSN) consists of over 100 three-component stations deployed worldwide, recording continuously at 20 samples per second. It has improved coverage of seismicity in traditionally remote regions, and its broadband instruments allow recovery of long-period information from seismograms. The coverage enables global averaging and mapping of Earth structure and earthquake properties. It also ensures that events are detected in many azimuthal directions, reducing problems from nodal moment tensor orientations that can occur when recording in a single location. Figure 1.2 shows the networks used in the research in this dissertation. We apply stack- 5

24 ing techniques to data recorded by these networks to address two outstanding problems in seismology and geophysics: (I) the character of Earth s core-mantle boundary region; and (II) properties and origins of deep-focus earthquakes. 6

25 Part I Reflection properties and fine-scale structure of the core-mantle boundary 7

26 Chapter 2 Introduction Core-mantle boundary 2.1 The core-mantle boundary region The core-mantle boundary (CMB) region has long been of interest due to its significance as a seismological discontinuity and importance in geodynamical processes, such as thermal mantle convection, core formation and cooling, chemical mixing in the mantle, magnetic field behavior, and the effects of core-mantle coupling on the Earth s rotation rate [Loper and Lay, 1995]. The CMB region acts as a thermal and chemical boundary layer [Lay et al., 1998], and the D 00 layer of the mantle overlying it has been associated with with reduced or negative velocity gradients and increased heterogeneity [Lay et al., 1998], discontinuities [e.g., Lay and Helmberger, 1983], and anisotropy [e.g., Kendall and Silver, 1996]. Seismological results from the CMB present a complicated picture with unresolved issues. There is evidence for chemical and thermal heterogeneities, partial melt, volumetric scattering, and discontinuities (Appendix B). We expect some connections between the patterns detected by seismology, the dynamics of mantle convection and heat flow, and mantle 8

27 composition and physical state, but the lateral variation of CMB region properties, especially at short length-scales, is still being mapped. Fine-scale structure is implicated in many of the major questions about the dynamics and composition of the CMB region and the interaction between the core and mantle: the causes of layering; the extent of core-mantle chemical reactions; the fate of subducted lithosphere; the role of the CMB in the generation of mantle plumes; and the extent to which velocity heterogeneities in D 00 have thermal versus compositional origins. Thus, resolving the finescale structure near the CMB is important for understanding the physics of the Earth s deep interior. 2.2 Ultra-low velocity zones Recently, several lines of evidence have indicated the existence of fine-scale structure in the form of a thin layer at the base of the mantle with large velocity reductions relative to average material at those depths. These ultra-low velocity zones (ULVZs) have been modeled with thicknesses 5-50 km and velocity reductions ln V P = -0.1 to -0.2 and ln V S = -0.1 to -0.5 [Garnero and Jeanloz, 2000], although tradeoffs exist between the thickness and velocity reduction [Garnero and Helmberger, 1998] and there is only limited evidence for the V S reduction. Density increases in ULVZs have also been suggested, but they are poorly constrained [Garnero and Helmberger, 1998]. Seismic arrivals used to identify such ultra-low velocity zones (ULVZs) include delayed core phases (SP di KS [Garnero and 9

28 Helmberger, 1996]); scattered core phases (P KP [Vidale and Hedlin, 1998; Wen and Helmberger, 1998b]); and precursors to core-reflected phases (PcP [Mori and Helmberger, 1995; Revenaugh and Meyer, 1997]; and ScP [Garnero and Vidale, 1999]). Possible explanations for ULVZs include partial melting [Williams and Garnero, 1996; Holland and Ahrens, 1997], phase transitions [Garnero et al., 1998], layering associated with subducted lithosphere or primordial differentiation [Tackley, 1998], reactions with core material [Manga and Jeanloz, 1996], partitioning of iron from mantle melt [Knittle, 1998], and a thin layer of finite rigidity at the top of the outer core [Buffett et al., 2000; Garnero and Jeanloz, 2000]. Appendix B discusses these explanations in more detail. With about half the CMB sampled (44%), ULVZs cover about 12% of the surface [Williams et al., 1998] (Figure 2.1). The zones vary laterally in their thickness and velocity contrast [Garnero et al., 1998], which may account for the lack of observation in some regions. ULVZ locations correlate with surface hotspots [Williams et al., 1998], and ULVZs have been located under regions of presumed mantle upwelling [Wen, 2000; Helmberger et al., 2000]. Cataloging the extent of ULVZs and the character of lateral heterogeneity is an important task for integrating them into our understanding of core-mantle interactions, the origin of mantle upwellings and the fate of subducted lithosphere. In addition, several important characteristics of ULVZs remain poorly understood: (i) the length-scales over which variations exist; (ii) magnitudes of V S reduction and density increase within ULVZs; (iii) sharpness of boundary between ULVZ and overlying mantle; and (iv) degree of attenuation and scattering of seismic waves. Determining these properties 10

29 regions studied Locations of ULVZs ULVZ no ULVZ 60 o 30 o 0 o -30 o -60 o 0 o 60 o 120 o 180 o -120 o -60 o 0 o Figure 2.1: Map of ULVZ detections, adapted from Garnero et al. [1998]. Circum-Pacific boxes indicate regions searched for ULVZ-generated precursors in Chapter 4. Box near Hawaii indicates region studied in Chapter 5. will allow us to further constrain proposed explanations for ULVZs and advance our understanding of the major questions regarding the CMB region in general. Two seismic phases that could serve to address these issues are the short-period core-reflections P cp and ScP. 2.3 P cp and ScP P cp and ScP are core-reflected phases: the former is the compressional-wave reflection off the CMB, and the latter is a shear-to-compressional conversion upon reflection. P cp arrives at source-receiver distances up to 98. Beyond 83, however, the separation between P and P cp is less than five seconds, and it can be difficult to distinguish the two phases (Figure 2.2). ScP arrives in a relatively quiet time window between about

30 Time [seconds] ScP PcP P S PP Distance [degrees] Figure 2.2: Travel time as function of source-receiver distance (from the iasp91 [Kennett and Engdahl, 1991] velocity model). and 720 seconds after P, depending on distance (Figure 2.2). ScP has an asymmetric raypath (Figure 2.3). In a standard reflection such as PcP, the downgoing incidence angle and the upgoing takeoff angle are equal. In the case of ScP, the upgoing P -wave departs with a greater angle from the vertical than that of the incident S-wave (from applying Snell s law with V P >V S ). Therefore ScP s bounce point is closer to the source than the receiver, and the critical angle is reached at a source-receiver distance of 62, when the takeoff angle of the upgoing P -wave exceeds 90 from the vertical. We utilize PcP and ScP for several reasons. As short-period (1-4 second) phases they are sensitive to fine structure. Thus they are useful phases with which to investigate the sharpness of the ULVZ upper boundary and the lateral variability of ULVZ occurrence and CMB properties on short length-scales. At teleseismic distances (30 ), their arrivals are contaminated only by the crossing phases PP and S (Figure 2.2), both of which are 12

31 6371 km * PcP P ScP CMB ICB 0 km Figure 2.3: Raypaths of P, PcP, and ScP for source-receiver distance of 45. Star: source. Triangle: receiver. Generated using the TauP raypath utility [Crowell et al., 1999]. diminished at higher frequencies. P cp and ScP can easily be stacked in network data, allowing us to take advantage of noise reduction to search for precursor arrivals or measure reflection coefficients. PcP and ScP also offer advantages over other seismic phases for studying the CMB. Many observations of ULVZs have been made with long-period phases such as SP di KS, which integrate the velocity structure over a large distance (P di segments can be over 1000 km long [Garnero and Helmberger, 1996]). The smaller Fresnel zones of PcP and ScP ( km at the CMB) enable us to seek possible variations over shorter length-scales, which are unconstrained by the long-period data. Although PKP samples the CMB at high frequencies [Vidale and Hedlin, 1998; Wen and Helmberger, 1998b], its usefulness is hampered by the ambiguity over whether scattering occurs at the core entry or exit point, which is not an issue for PcP and ScP. 13

32 Amplitudes of P cp and ScP are sensitive to both velocity and density contrasts at the CMB. ScP in particular can potentially yield information about ln VS, which remains somewhat unconstrained thus far, but whose predicted values play a crucial role in the presumption of partial melt at the base of the mantle. Garnero and Vidale [1999] demonstrate the potential utility of ScP for identifying ULVZs and measuring ln VS. ScP interactions with aulvz can produce three arrivals: SdP, aprecursor, where the conversion occurs at the ULVZ upper boundary; SpcP, aprecursor which converts to P upon entering the ULVZ and then reflects at the CMB; and ScsP, apostcursor which reflects from the CMB as an S-wave and converts to P upon exiting the CMB. Detections of these arrivals would provide better constraints on ln VS and ln in ULVZs [Reasoner and Revenaugh, 2000]. Three projects are described in this part of the dissertation: (i) measuring and mapping reflection properties of the CMB with GSN stacks of PcP and ScP (Chapter 3); (ii) searching for ULVZ-associated precursor arrivals on regional network stacks of PcP and ScP (Chapter 4); and (iii) observation of diminished core-grazing P -waves as evidence for short length-scale variation in CMB region properties (Chapter 5). The results address some of the outstanding questions about ULVZ characteristics and the nature of the CMB. 14

33 Chapter 3 Core-mantle boundary reflection coefficients If basal layers exist with extreme velocity reductions or a high degree of heterogeneity and/or partial melt, they would affect amplitudes of CMB-reflected phases by changes in the impedance contrast or reduced sharpness of the boundary and by losses due to attenuation and precursor reflections. The work in this chapter assesses these effects by mapping global properties of the CMB in short-period reflection. We first stack GSN-recorded seismograms to measure globally-averaged CMB reflection amplitudes and compare with predictions for basal layering. We next map lateral variations of CMB-reflection properties to compare with patterns of tomography and ULVZ observations. 3.1 Data and Processing Seismograms from many different earthquakes will not sum constructively so we cannot coherently stack the GSN database. Instead, we employ envelope stacking, in which the envelope functions of the seismograms are summed. Since envelope functions are strictly positive, incoherent noise does not cancel out; rather, all arriving energy contributes to the 15

34 stack. We do not interpret precursory scattered energy to the core-reflections since it will likely be too small and inconsistent (geographically) to appear above the noise envelope in a global averaging. Instead, we characterize the CMB by computing the amplitude ratios P cp -to-p and ScP-to-P. The data come from the Fast Archive Recovery Method (FARM) database of GSN waveforms maintained by the Incorporated Research Institutions for Seismology (IRIS) Data Management Center. We have downloaded the database between 1988 and 2000, which consists of over 535,000 seismograms from over 3000 earthquakes, and decimated the waveforms to five samples per second. To select the seismograms to stack, we impose several selection criteria. We take events with moment magnitudes (MW) between 6.0 and 7.0. The lower bound serves to reject traces of insufficient signal-to-noise; the upper bound is chosen so that the earthquake time functions are relatively compact. Source depths between 0 and 100 km are used. The seismograms are taken at teleseismic distances (30 to 80 for PcP and 30 to 65 for ScP). The lower bound avoids complicated P arrivals from upper mantle triplications and the upper bound for PcP recognizes that the travel time difference from P is often less than the expected source duration at large epicentral distances. We only use vertical components, since CMB reflections are nearly vertically-incident. We also apply signal-to-noise criteria. We measure the amplitude of PcP or ScP on the velocity seismograms and compute the ratio to the pre-event noise level. To counter the bias from selecting for large PcP or ScP,weimpose a second requirement that each seis- 16

35 PcP coverage 15 o x15 o bins Hz 30 o < < 70 o 60 o o o o o # samples Figure 3.1: Number of PcP bounce points in bins for source-receiver distances between 30 and 70 degrees. Number in each grid element is given. Note that the scale is logarithmic. mogram meets a minimum P -to-noise ratio as well as the P cp - (or ScP-)to-noise levels. Further discussion of the procedure for imposing signal-to-noise criteria is included in Appendix C. For PcP the procedure yields between 5549 and 5728 seismograms, depending on the bandpass, from about 21,000 seismograms matching the source-property criteria. For ScP the procedure yields between 3769 and 3956 seismograms, depending on the bandpass, from about 15,000 seismograms matching the source-property criteria. The extent of global coverage is shown in Figure 3.1 (PcP) and Figure 3.2 (ScP). The configuration of sources and stations is clearly uneven over the globe. About 30% of the CMB surface is sampled by PcP, and 25% is sampled by ScP (counting grid elements with at least 10 hits). Nevertheless, this represents the best global sampling of the CMB so far achieved with core-reflected phases. 17

36 ScP coverage 15 o x15 o bins Hz 30 o < < 65 o 60 o o o o o # samples Figure 3.2: Number of ScP bounce points in bins for source-receiver distances between 30 and 65 degrees. Number in each grid element is given. Note that the scale is logarithmic. 18

37 3.1.1 Computing envelope stacks The selected seismograms are demeaned, bandpass filtered ( Hz, Hz, or Hz), and grouped in three-degree-wide distance bins. We compute the envelope function of each seismogram, align at the iasp91 predicted P cp or ScP arrival time, subtract the background noise, and apply a series of amplitude corrections to account for source and path effects. We repeat these steps for the P -wave on every seismogram to compute a separate P -aligned stack corresponding to each core-reflection-aligned stack. This is necessary because the source and path amplitude corrections are different for P, P cp, and ScP. It also avoids the broadening of P arrivals that would result from misalignment of P on corereflection-aligned stacks because we combine earthquakes from a range of source depths and distances. Because noise and signal sum in a root-mean-square sense, we compute the square of the envelope function in order to subtract noise properly [e.g., Earle and Shearer, 2001]. The observed amplitude of PcP (A obs )isaconvolution of the amplitude leaving the PcP source as compressional waves (A P ) with several factors: the radiation pattern (), geometrical spreading (G), attenuation (Q), the instrument response (I), and the reflection coefficient (R PcP )atthe CMB. A obs PcP = A P G Q I R PcP (3.1) We can write similar expressions for A obs P and A obs ScP. The processing of each seismogram involves stripping away the factors other than R PcP or R ScP. Then, the amplitude ratio 19

38 P cp /P or ScP/P will yield the reflection coefficient at the CMB. To account for radiation pattern we compute the initial takeoff angle of the rays (based on source depth and epicentral distance) and use the event s Harvard CMT catalog moment tensor solution to calculate a correction factor [Aki and Richards, 1980]. Similarly, we can multiply the seismograms by a correction factor for geometrical spreading [Lay and Wallace, 1995]. For ScP,wemultiply by an additional factor of five in amplitude to account for the difference in amplitude in shear and compressional waves at the source. We do not remove the instrument response, which is too computationally intensive given the number of seismograms we process. The broadband GSN seismographs have relatively flat response curves in the bandpasses we use, so this does not have a large effect. Attenuation is calculated at the peak of the spectrum in each bandpass, as determined from frequency-domain stacks of a subset of the data. The peaks occur at about 0.3 Hz ( Hz bandpass), 0.55 Hz ( Hz bandpass), and 1.0 Hz ( Hz bandpass). There can be a tradeoff between attenuation in the deep mantle and reflection coefficient at the CMB. Greater attenuation at the base of the mantle mimics a smaller reflection coefficient. Unfortunately, depth dependence of mantle attenuation is not determined precisely, so the correction for attenuation is the most uncertain of the amplitude factors. For P waves in the mantle, we use Warren and Shearer [2000] s two-layer Q model, with the division between the upper and lower mantle at 660 km. We use the expression Q = 4 9 Q (3.2) to obtain attenuation for the S leg of ScP. Table 3.1 gives Q and Q as a function of fre- 20

39 Table 3.1: Q model used to correct for attenuation [Warren and Shearer, 2000] Frequency Depth 1.0 Hz 0.5 Hz 0.25 Hz Q km km Q km km quency and depth. In the frequency range we consider, Warren and Shearer [2000] present frequency-independent and frequency-dependent versions of their model; the latter is obtained by requiring their model to match Durek and Ekstrom [1996] s QL6 model at long periods (>100 s). Their frequency-independent Q values are somewhat large and the longperiod constraint forces Q in the frequency-dependent model to be lower. For PcP, the choice does not seem to make much difference. However, initial tests of ScP amplitudes require frequency-dependent attenuation, and the very high Q in the frequency-independent case does not generate enough shear attenuation to match our data. Bock and Clements [1982] found that frequency-dependent attenuation in the lower mantle was required to match their ScP data sampling the CMB between Tonga and Australia. In general, mantle attenuation is most likely frequency-dependent [e.g., Anderson and Given, 1982; Choy and Cormier, 1986]. One drawback of Warren and Shearer [2000] s model is its limited resolution in the lower mantle, but an advantage is that it was derived within the same frequency range we use. After the applying the amplitude corrections, we take the logarithm of the envelope functions and sum them. After stacking, we divide by the number of seismograms and compute 21

40 the antilog. Since we cannot check each corrected trace individually, stacking logarithms guards against any anomalous seismograms dominating the stack Measuring amplitude ratios To compute amplitude ratios (P cp=p or ScP=P), we must subtract background noise on the envelope stacks at each signal phase. We measure the background noise by fitting a linear function to the noise before the signal phase and extrapolating into the signal window. In practice for the core-reflections, this is a somewhat difficult procedure, since contamination from crossing phases such as pp, sp, PP, and S, can affect the background noise. Accordingly, we have to adjust the window in which we perform the fittoavoid these phases. The signal amplitude (P cp, ScP, orp ) isthe total envelope minus the extrapolated noise function. We measure the total envelope by finding the peak within a wide search window and then averaging the envelope in a four-second window surrounding it. This provides a more stable value than simply taking the peak. We then divide to obtain the amplitude ratio PcP=P or ScP=P. 3.2 Calculating reflection coefficients The amplitude ratios measure the reflection coefficients at the CMB, which depend on the impedance contrast and incidence angle. In this section, we calculate reflection coefficients at the CMB by solving the boundary-value problem for a solid-fluid interface. 22

41 We follow Aki and Richards [1980] s derivation for a solid-solid interface, setting V S = 0 in the core and adapting the boundary conditions to those that apply at a solid-fluid interface. The incident waves displacement amplitudes are given by P d S d P u, where the superscript indicates whether the ray is downgoing (d) orupgoing (u) relative to the CMB. There is no S u since shear-waves do not propagate in the core. Each of these incident rays can produce three outgoing waves: P u S u P d (no S d ). For example, P d! P u represents PcP, while S d! S u represents ScP. Intotal, there are nine possible scattering coefficients. We assume here steady-state plane waves incident on a flat boundary. The resulting reflection coefficients are independent of frequency [Aki and Richards, 1980]. These conditions are realistic because the CMB is locally flat, with no apparent major topography [e.g., Earle and Shearer, 1997], and curvature is unimportant. To find the partitioning of energy between the resultant outgoing waves, we must consider the continuity of displacements and stresses across the boundary. In the case of solidfluid interface, the horizontal displacements will be discontinuous because shear waves cannot propagate in the fluid. Likewise, horizontal tractions must equal 0. However, normal displacements and tractions must still be continuous. The boundary conditions are: continuity of normal displacements: cos(i m )(P d m P u m ) sin(j m)(s d m S u m )=cos(i c)(p d c P u c ) (3.3) 23

42 continuity of normal tractions: m V Pm (1 2V 2 Sm p2 )(P d m + P u m ) 2 mv 2 Sm p cos(j m)(s d m + Su m )= cv Pc (P d c + P u c ) horizontal tractions vanish: (3.4) 2 m V 2 Sm p cos(i m)(p d m P u m )+ mv Sm (1 2V 2 Sm p2 )(S d m S u m )=0 (3.5) where the subscript m indicates values in the mantle and c indicates values in the core. The angles i are the angles from normal for P waves, while j are those for S waves, given by Snell s law. The constant p is the ray parameter. With this system of equations, we can fix one of the three possible incident waves (Pm d Sd m Pu c )toamplitude 1 and set the other two to 0, leaving three unknowns (the scattered amplitudes Pm u Su m Pd c )inthree equations. In matrix form: M 0 P u m S u m 1 C A = N 0 P d m S d m 1 C A (3.6) P d c P u c where the incident waves are on the right-hand side and the scattered waves are on the lefthand side and M = 0 B cos(i m ) sin(j m ) cos(i c ) m V Pm (1 2V 2 Sm p2 ) 2 m V 2 Sm p cos(j m) c V Pc 2 m V 2 Sm p cos(i m) m V Pm (1 2V 2 Sm p2 ) 0 1 C C A (3.7) 24

43 and N = 0 Thus, the scattering matrix is 0 cos(i m ) sin(j m ) cos(i c ) m V Pm (1 2V 2 Sm p2 ) 2 m V 2 Sm p cos(j m) c V Pc 2 m V 2 Sm p cos(i m) m V Pm (1 2V 2 Sm p2 ) 0 B P d P u S d P u P u P u P d S u S d S u P u S u P d P d S d P d P u P d 1 C C A 1 C A (3.8) = M 1 N (3.9) where the notation is incident wave-scattered wave. Matrix elements (1,1) and (1,2) are PcP and ScP, respectively. We can vary the elastic parameters above the CMB to determine their effects on reflection coefficients. Velocity reductions and density increases in the mantle bring its values closer to those of the core, so the reflected amplitudes are reduced. The range-dependence changes slightly, as well. This is particularly noticeable for ScP at greater distances. In PREM, the reflection coefficient rises sharply near the critical distance due to the increasingly vertical polarization of the downgoing S leg. In the ULVZ models, this effect is sharply reduced. In computing the reflection coefficients, we ignore potential scattering of the incident wave due to reflections at the upper boundary of a ULVZ or scattering within it. Since both effects would reduce the predicted amplitudes of PcP or ScP, our calculations represent upper bounds. Observed amplitudes lower than the predictions could result from a combination of reduced reflection coefficient and losses due to scattering. 25

44 3.3 Globally-averaged reflection properties Stacks Stacks aligned on P cp and ScP are shown in Figures 3.3 and 3.4, respectively. The envelope of the P -generated coda is clearly a significant source of noise, even 100 seconds after the P arrival. The coda results from scattering of seismic waves near the source and receiver. This decaying noise envelope is especially problematic at greater distances, where PcP arrives closer to P in time. Crossing phases such as PP and S are more easily observed at low frequencies (Figure 3.4). These phases are highly-attenuated at short periods, due to the extra legs in the upper mantle in the case of PP and to the greater intrinsic attenuation associated with shearing motions in the case of S. The coda is more attenuated at high frequencies, making PcP and ScP easier to observe Amplitude ratios The amplitude ratios as a function of distance are plotted in Figures 3.5 and 3.6. The amplitude ratios generally agree with previous observations [e.g., Müller et al., 1977; Schlittenhardt, 1986; Castle and van der Hilst, 2000]. Estimates of the noise are sensitive to the time windows chosen, so oscillations of the ratio are probably not indicative of actual variation in the amplitude ratios, but rather of the uncertainty in the measurement. In each plot, we compare the amplitude ratios with predictions for PcP or ScP reflection coefficients from the Preliminary Reference Earth Model (PREM) [Dziewonski and An- 26

45 70 PcP-aligned; bandpass Hz P PcP # seis in stack [444] 65 [458] [392] 60 [364] PP [382] Distance [degrees] [459] [316] [374] [343] [254] 40 [244] 35 [241] [204] Time [seconds] Figure 3.3: Stacks aligned on PcP in 3 distance bins, bandpass filtered between Hz. The number of seismograms in each stack is given at right. PcP is clearly visible despite the large envelope of background noise contributed by P -generated coda. At distances beyond about 55, PcP becomes less visible above the background. 27

46 60 ScP-aligned; bandpass Hz x 3 P PcP PP ScP ScP 60 # seis in stack [277] [363] [410] [326] Distance [degrees] S S [356] [350] [312] [306] [306] [289] [101] Time [seconds] Time [seconds] Figure 3.4: Stacks aligned on ScP in 3 distance bins, bandpass filtered between Hz. Panel on right shows the window from 50 seconds before ScP to 50 seconds after, magnified by a factor of three ScP to aid visibility. The number of seismograms in each stack is given at right. Both PP and S are visible as broad peaks along their travel time curves. 28

47 derson, 1981] and several representative ULVZ models with velocity reductions and density increases relative to PREM. We also compute the amplitude for a 1 km-wide linear transition in velocity and density from mantle to core. The P cp /P data clearly do not match ULVZs with 10% and 30% reductions in V P and V S, respectively, or a 1 km-wide core-mantle transition zone. With this data, however, we cannot discriminate between PREM and ULVZs with just 10% reductions in both V P and V S, and either no change in density or a 20% increase. The largest predicted difference between these ULVZs and PREM is at greater distances. The low observed amplitudes of the stacks are suggestive that the PcP/P ratio is declining with distance, but it is unclear from these measurements. The difficulty of fitting the noise window at larger distances is increased because PcP is closer in time to P, and depth phases pp and sp arrive between them. The pulse in amplitude around in the Hz bandpass (Figure 3.5) results from the coincident arrival of PP with PcP at that distance. PP is stronger at long periods, hence it does not affect the other frequency ranges as much. The interpretation of the ScP/P ratios is not as straightforward as that of PcP/P. The Hz bandpass agrees with the predictions of PREM and the PcP/P results. However the longer- and shorter-period bandpasses produce lower amplitudes. These curves seem to rule out PREM but allow a range of velocity and density changes at the CMB. We expect consistent results for the CMB from reflection amplitudes from PcP and ScP, and the PcP/P results appear robust. One possibility is that the ScP results reflect uncertainty in the Q model. 29

48 Amplitude ratio Stack amplitudes Hz Hz Hz PcP/P Model amplitudes PREM ULVZs ( V P, V S, ) (-0.1, -0.1, 0.0) (-0.1, -0.1, 0.2) (-0.1, -0.3, 0.0) (-0.1, -0.3, 0.2) 1.0 km CMTZ Distance [degrees] Figure 3.5: Solid lines: PcP/P vs. distance in three bandpasses. Dashed lines: Predicted PcP/P for PREM, ULVZs with velocity and density changes indicated, and for a 1.0 km-wide core-mantle transition zone. The average CMB for the regions we sample does not appear to have a highly-attenuating basal layer with large shear-wave velocity reductions or a core-mantle transition zone. Comparing the coverage of the CMB (Figures 3.1 and 3.2) with the observations of ULVZs (Figure 2.1), our densest coverage spans regions both with and without ULVZs (Mexico and Central America and south and east Asia). However, the region with strongest evidence for ULVZs (southwest Pacific) is not well-sampled by the core-reflections. 3.4 Mapping reflection properties Mapping reflection coefficients allows us to relate them to other observed patterns at the CMB. With evidence for lateral variability of D 00 properties such as the D 00 discontinuity, 30

49 Amplitude ratio Stack amplitudes Hz Hz Hz ScP/P Model amplitudes PREM ULVZs ( V P, V S, ) (-0.1, -0.1, 0.0) (-0.1, -0.1, 0.2) (-0.1, -0.3, 0.0) (-0.1, -0.3, 0.2) 1.0 km CMTZ Distance [degrees] Figure 3.6: Solid lines: ScP/P vs. distance in three bandpasses. Dashed lines: Predicted ScP/P for PREM, ULVZs with velocity and density changes indicated, and for a 1.0 km-wide core-mantle transition zone. ULVZ existence and velocity reduction, and anisotropy, it is reasonable to expect lateral variations in CMB reflection properties, as well. We will compare the maps with results from Chapter 4 and locations of ULVZs. The stacking process is the same as for the global stacks, with the following exceptions: Rather than bin by source-receiver distance, we apply a grid to the CMB surface (15 15 ) and compute the location of each P cp or ScP bounce point. Stacks for each grid element are produced from seismograms with bounce points within it. To account for variation of reflection coefficient with incidence angle, we use the predicted curve for PREM to adjust every seismogram to a source-receiver distance of 55. Finally, for the Hz and Hz bandpasses, we exclude seismograms in the distance ranges (PcP) and (ScP)toavoid contamination from crossing phases PP and S. 31

50 PcP/P ratios Hz 30 o -70 o 15 o x15 o bins N hit 8 60 o o o o o PREM PcP/P Figure 3.7: PcP/P from stacks in bins at the CMB. Bandpass Hz. Seismograms from distances are used and corrected for incidence angle to 55. Numbers in boxes indicate number of seismograms in stack; only bins with at least 8 seismograms stacked are plotted. Value for PREM at 55 is indicated on scale. Grid elements surrounded by black squares are compared with ULVZ models in Figure 3.9. We choose a bin size of to achieve a compromise between the desire to map on as fine a scale as possible and the need to have sufficient numbers of seismograms in each stack to have adequate signal-to-noise. Even with elements this size, many bins have only a few hits and the coverage is uneven (Figures 3.1 and 3.2). We measure the P cp=p and ScP=P ratios in the same manner as on the globally-averaged stacks and map them to the bounce point locations for those bins with at least eight hits (Figures 3.7 and 3.8). It is important to note that subdividing the data this way decreases the signal-to-noise 32

51 Hz 30 o -60 o excluding 37 o -39 o 15 o x15 o bins N hit 8 ScP/P ratios 60 o o o o o 9 10 PREM ScP/P Figure 3.8: ScP/P from stacks in bins at the CMB. Bandpass Hz. Seismograms from distances are used (excluding those between where S-generated noise is greatest) and corrected for incidence angle to 55. Numbers in boxes indicate number of seismograms in stack; only bins with at least 8 seismograms stacked are plotted. Value for PREM at 55 is indicated on scale. 33

52 of the stacks. Most bins have fewer than 100 hits; this contrasts with the global averages binned by distance, where each stack contained hundreds of seismograms. Fewer seismograms means that the stacks are not as smooth as the global averages and thus amplitude ratios can be very sensitive to the placement of windows. The effects can be seen in Figures 3.7 and 3.8: the most anomalous bins tend to have around 20 or fewer hits. Those with more than 100 are more stable and have smaller deviations from PREM. We consider several regions where coverage is greatest and where we search for ULVZgenerated precursors to P cp and ScP in Chapter 4. Under Mexico and the Caribbean Sea, PcP trends from PREM-like amplitudes to lower values from west to east. ScP has a similar pattern. We find no evidence for ULVZ precursors in that region, which is consistent with a PREM-like CMB. The east-west trend agrees with patterns observed by Havens and Revenaugh [2001]. In the northeast Pacific, where we also do not find ULVZ precursors, PcP has normal to somewhat high amplitudes, while ScP has somewhat low amplitudes. Castle and van der Hilst [2000] found strong ScP in that region. And under the Philippine Sea and Asia, PcP has high amplitudes trending to lower values towards the north and west. ScP also has an east-west trend, as part of a long gradient from low to high amplitudes starting under Arabian Peninsula and trending east. In Figure 3.9, we measure distance-dependence of PcP/P at three bounce point locations, marked by black squares in Figure 3.7. Comparing with Figure 2.1, the bounce point locations in the northern Pacific (denoted by the latitude and longitude of its northwestern 34

53 NW corner of bounce point lat: 60 lon: 210 (ULVZ detection) NW corner of bounce point lat: 30 lon: 120 (ULVZ non-detection) PcP/P 0.4 PcP/P Distance range [degrees] Distance range [degrees] PcP/P NW corner of bounce point lat: 30 lon: 255 (ULVZ detection) PREM ULVZ V P V S Distance range [degrees] Figure 3.9: PcP/P ( Hz bandpass) vs. distance at three bounce point locations. The bounce points plotted are indicated by black squares in Figure 3.7. The bounce point at left corresponds to a region of ULVZ non-detection (Figure 2.1). The upper and right bounce point bins correspond to ULVZ detections. corner: 60, 210 ) and under Mexico (30, 255 ) coincide with ULVZ detections, while the bounce point in the western Pacific (30, 120 )isinaregion with a non-detection. The amplitudes in the non-detection bin are similar to those of the global average and consistent with a PREM-like CMB. The amplitudes in one ULVZ-detected bin (60, 210 ) are generally lower, though the data is too scattered to discriminate between models. In the other ULVZ-detected bin, the amplitudes are not consistently lower than in the global average. This further subdivision of the data increases uncertainty of the measurements by decreas- 35

54 (a) (b) (c) PcP/P Hz PcP/P Hz PcP/P Hz PcP/P Hz PcP/P Hz PcP/P Hz Figure 3.10: Correlation of PcP/P in different bandpasses. The best agreement is between the two lowest-frequency bandpasses. The agreement between the Hz bandpass and the others is rather poor. Open squares in (a) and (c) represent a bin with Hz ratio of almost 8, not plotted on scale to facilitate visibility. ScP/P Hz 2 (a) 5 (b) 2 (c) ScP/P Hz ScP/P Hz ScP/P Hz ScP/P Hz ScP/P Hz Figure 3.11: Correlation of ScP/P in different bandpasses. The best agreement is between adjacent bandpasses. The Hz and Hz bandpasses are the least-correlated. ing the number of seismograms in each stack, but the results are consistent. Different behavior of reflection properties in the three bandpasses may indicate variations in the sharpness of the CMB. In Figures 3.10 and 3.11 we plot the correlations between maps from each frequency range. The P cp maps with Hz and Hz bandpasses show good agreement with each other, but not with the Hz PcP map. The ScP maps generally agree, though the correlation between adjacent bandpasses is better than between Hz and Hz. Much of the scatter likely derives from poor data 36

55 quality, not variations in CMB sharpness. If we restrict the data to those bins with at least 50 hits, the degree of correlation improves. 3.5 Discussion The global stacks of P cp and ScP provide an average picture of the CMB and constrain global low-velocity layers to be weak. With PcP/P, werule out worldwide average of 30% S-wave velocity reductions and a wide core-mantle transition zone. The data cannot distinguish between PREM and a model with 10% reductions in V P and V S, and possibly a 20% increase in density. If we take the PcP/P results to represent the properties of the CMB, we could in theory use the misfitofthe ScP/P amplitudes to recover a short-period Q model. In practice, this exercise is not straightforward: the P amplitude in the denominator will also be affected from adjusting Q to satisfy Equation 3.2 with the new Q. Through trial and error, however, some constraints on Q might be obtained. There are several sources of error in computing the stacks and measuring the amplitudes. The use of a simple two-layer Q model does not account for layering in the upper mantle and possibly a low Q region near the CMB. We only apply the attenuation correction at a single frequency; computing the spectrum would improve the accuracy of this factor. Removing the instrument response might help reconcile the results from different bandpasses for ScP/P. Finally, the determination of noise preceding the signal in the stacks is very sensitive to the search window. We tried many techniques to improve stability, but it is difficult 37

56 to create a general rule that accounts for varying noise levels due to crossing phases and the P -generated coda. Our attempts to map lateral variability of CMB reflection properties face these difficulties as well as poorer quality stacks from subdividing the data. In the best-sampled regions, we detect some patterns that are consistent with previous observations and with our results from regional searches for ULVZs. Several possibilities for future work on this problem exist. Data from temporary seismic instrument deployments could supplement the coverage of this data set. Other phases, such as the underside reflection P KKP, could also improve coverage. Deconvolving empirical source time functions would reduce effects of complicated source pulse shapes. An ultimate goal of mapping reflection amplitudes is to determine velocity and density at the CMB. However, the relationship between reflection coefficients and changes in velocity and density is not straightforward, and the individual amplitudes cannot be uniquely interpreted in terms of velocity and density. One way around this would be to jointly compare PcP and ScP amplitudes: for particular combinations of velocity and density, we can calculate the expected ratio of PcP/ScP. Ascatter plot of PcP versus ScP amplitudes from well-sampled bins might then show several clusters, representing particular velocity/density combinations. We could then map the velocity and density combinations to the bins locations. Unfortunately, we require many more seismograms per stack than are currently available. 38

57 Chapter 4 ULVZ precursor search 4.1 Introduction In this chapter we conduct three high-resolution searches for ULVZ-generated precursor arrivals to P cp and ScP. Weuse regional network data to test predictions of the effects of simple layering on the core-reflections. Waveform stacks of P, PcP, and ScP, from the lowest noise events enable us to search for precursor arrivals produced by reflections from ULVZ upper boundaries and place limits on the properties of possible ULVZs. We also search envelope stacks for scattered energy originating from ULVZs. These methods address the questions about ULVZs concerning sharpness of their upper boundaries, their variability on short length-scales, and the velocity and density changes within them. This work also complements the global investigation in Chapter 3 by investigating in greater detail some of the global network s densely-sampled regions. 39

58 4.1.1 ULVZ studies using PcP and ScP Several recent studies have sought arrivals from topside reflections from ULVZs. Two studies of ULVZs with P cp sampled the CMB southeast of Hawaii, on the Tonga-Fiji to California path: Mori and Helmberger [1995] identified a precursor arrival to PcP from two earthquakes, and modeled it with a layer of thickness 10 km and V P reduction 5-10%. Revenaugh and Meyer [1997] combined array data from tens of earthquakes and found a precursor from a layer about 14 km thick, with 3:1 ratio of V S to V P reduction. However, Mori and Helmberger [1995] failed to observe a precursor from a CMB bounce point southwest of Central America. Revenaugh and Meyer [1997] observed a small precursor near the same region, but its properties were more poorly determined than their other observations. They also found a precursor under the Aleutian Islands chain similar to that under the mid-pacific. In these studies, the source-receiver distance was quite large, meaning P and PcP arrive closely-spaced in time, making it difficult to distinguish ULVZ-produced arrivals. At shorter epicentral distances, Havens and Revenaugh [2001] found precursors to PcP under Mexico and the Gulf of Mexico. Their modeling supported a km-thick ULVZ with 10% V P reduction, 30% V S reduction, and 1-2% density increase at the western edge of their study area. The ULVZ tapers towards the east to less than 5 km. The modeling tradeoff between the velocity and density changes requires a reduced ln V S = ln V P ratio for larger density increases. ULVZ investigations with ScP have thus far met with limited results. Searches for the 40

59 pre- and postcursor arrivals described in Chapter 2 have produced mostly non-observations even in regions where ULVZs are thought to exist. The Gulf of Alaska produces clean, large amplitude ScP reflections, with no complexity or precursors [Vidale and Benz, 1992; Castle and van der Hilst, 2000], despite SP di KS indications of a ULVZ there. Reasoner and Revenaugh [2000] did not observe ULVZ-related arrivals preceding or following ScP reflections in the southwest Pacific where multiple evidence for a ULVZ exists. They suggested that relatively small density increases or large vertical transition zones between mantle and ULVZ can reduce the pre- and postcursor amplitudes. Two positive observations provide evidence for strong lateral variations on short length-scales: Garnero and Vidale [1999] found a precursor to a reflection in the southwest Pacific and modeled it with a 5 km-thick ULVZ with 10% and 30% V P and V S reductions, respectively. They saw no precursors to ScP sampling a neighboring zone. Rost and Revenaugh [2001] observed complicated ScP waveforms from reflection points between Tonga-Fiji and Australia. Their bounce points were interspersed among many producing simple arrivals. Some complex arrivals could be modeled with a ULVZ, while others seemed to require a thin layer in the outer core with nonzero rigidity (thickness 150 m and V S 0:6 0:8 km/s). The close spacing of simple and complex reflections suggests very short length-scale variations. In our precursor searches of PcP and ScP,wewill stack large numbers of seismograms for each earthquake, enabling us to examine individual event waveforms, unlike studies of Revenaugh and Meyer [1997], Reasoner and Revenaugh [2000], and Havens and Revenaugh [2001]. We will also concentrate on closer source-receiver pairs than Mori and Helm- 41

60 60 o 30 o Jarray NCSN SCSN LASA 0 o Earthquakes PcP / ScP Fresnel zones Networks 120 o 180 o -120 o -60 o Figure 4.1: Earthquakes, network and CMB bounce point locations. NCSN and SCSN are shown in gray; LASA in red; J-array in blue. The Fresnel zones are computed for a frequency of 0.8 Hz. berger [1995] and Revenaugh and Meyer [1997], so the separation is great enough to allow easy identification of any precursor phases. 4.2 Data Figure 4.1 shows the locations of the sources and arrays used in this study. The P cp and ScP bounce points are also indicated. Outlines of the regions sampled are also shown in comparison to ULVZ locations on Figure NCSN and SCSN We investigate two regions of the CMB using PcP and ScP recorded at the Northern and Southern California Seismographic Networks (NCSN and SCSN, respectively). This portion of the study was published as Persh et al. [2001]. 42

61 -125 o -120 o -115 o -125 o -120 o -115 o 40 o NCSN 40 o 40 o 35 o 35 o 35 o 30 o -125 o -120 o SCSN 30 o 30 o -115 o -125 o -120 o -115 o Figure 4.2: Stations used from the Northern and Southern California Seismographic Networks. We obtained short-period, vertical-component seismograms of 17 earthquakes for which data was archived from the NCSN and SCSN (Figure 4.2). The SCSN is an network of hundreds of short-period stations operated by Caltech and the United States Geological Survey (USGS). The NCSN consists of hundreds of short-period instruments operated by the USGS. The P cp and ScP phases sample the CMB underneath the northeast Pacific and the Mexico/Central America/Caribbean region (Table 4.1 and Figure 4.1). The search criteria used to select the earthquakes from the Harvard Centroid-Moment Tensor catalog were: 5:9 MW 6:5; depth>50 km; and Atshorter epicentral distances the incidence angle at the CMB becomes more vertical, and the amplitudes of ScP and PcP are reduced. At larger epicentral distances, there are high noise levels from the P coda. Therefore, the maximum range was set closer than that of wide-angle studies [e.g., Weber, 1993; 43

62 Table 4.1: Earthquakes used in ULVZ precursor search NCSN and SCSN Date Lat Lon Depth MW yymmdd N E km , , , , Events with two entries were recorded by both Southern and Northern California Seismographic Networks (first value is distance to SCSN). Event was recorded only by NCSN; all others were recorded only by SCSN. Mori and Helmberger, 1995; Revenaugh and Meyer, 1997]. We decimated the seismograms to 10 samples/second and lowpass filtered below 0.8 Hz (chosen by testing different values to find the range where we could best observe P, P cp and ScP). Each trace was inspected visually, and noisy or glitch-filled traces were removed. We aligned a common feature on the P -waves and stacked them. To stack PcP and ScP, weinitially aligned based on their predicted travel time relative to the P picks using iasp91 [Kennett and Engdahl, 1991]. For some events, the noise was low enough to pick and align PcP and/or ScP on a subset of the individual seismograms. This alignment reduces waveform distortion produced by travel time variations of the core-reflected phases, 44

63 so when possible these stacks were used in place of the moveout-based stacks. For the SCSN data, we average 120 traces per stack; for the NCSN data, we average 290 traces per stack. From the 17 earthquakes, we produced 21 stacks of P cp and ScP (four events were recorded by both arrays). In one case (931120), we were unable to identify PcP even after stacking; high noise levels made picking P itself on the original traces difficult, so this event is excluded in subsequent discussion. In addition, noise precludes identifying precursors to PcP for events , , (both networks), and (SCSN only), so these stacks are excluded. We throw out stacks of two events on which we cannot identify ScP: and (SCSN only) LASA The Large Aperture Seismic Array (LASA) operated between 1965 and 1978 in Montana. At various times, between 13 and 21 subarrays were maintained, each with short-period, vertical component seismometers [Green et al., 1965; Forbes et al., 1965; Hedlin et al., 2000] (Figure 4.3). We obtained seismograms recorded at LASA from 32 events between 1970 and 1974 within 80 of the array. At each subarray, we aligned the P -arrivals and stacked the velocity seismograms to create subarray stacks (Figure 4.4). The quality of the PcP observations at LASA is highly variable, as has been previously noted [Chowdhury and Frasier, 1973; Frasier and Chowdhury, 1974]. On many subarray 45

64 LASA configuration 48 o N North Dakota 46 o N South Dakota Montana Wyoming 44 o N 110 o W 108 o W 106 o W 104 o W 102 o W after Hedlin et al., 2000 Figure 4.3: Configuration of LASA. Red dots represent subarrays; inset shows seismograph station arrangement within subarray. From Hedlin et al. [2000]. Table 4.2: Earthquakes used in ULVZ precursor search LASA Date Time Lat Lon Depth m b yymmdd N E km) : : : : stacks within 80, P cp cannot be seen. One problem presented by LASA s configuration is that the seismograph stations within each subarray are so closely-spaced that some of the noise stacks coherently. Thus we do not gain the advantages typical of stacking seismograms. However, if we combine all the seismograms from the entire array together the incoherent noise cancels more effectively, allowing better imaging of the small-amplitude phases. We did this for the four best PcP observations (Table 4.2), repeating the processing steps 46

65 _1459; lat: 50.9 lon: depth: 9 km; 0-1 Hz P PcP F2 70 E2 E3 Distance [degrees] D2 F3 C2 B2 C3 A0 B1 D1 B3 D3 B4 C1 C4 F1 D4 E1 E F Time [seconds] Figure 4.4: Subarray stacks for an event recorded at LASA. Each seismogram represents a stack of the seismograms recorded at the stations of a subarray. They have been aligned on the P wave. PcP is visible as the phase moving in towards P at seconds. 47

66 from the NCSN and SCSN study, with lowpass filtering between 0-1 Hz. The stacks average 300 seismograms. The regions of the CMB sampled are shown in red in Figure 4.1. They coincide with the northeast Pacific area sampled by the NCSN and SCSN, with one event sampling farther north Japan array The Japan array (J-array) consists of over 400 seismograph stations distributed throughout Japan (Figure 4.5). The instruments are three-component and their dynamic ranges are mostly short-period (400 stations), with some broadband (50). The Earthquake Research Institute at the University of Tokyo maintains a J-array web site on which earthquake data since November 1996 is archived and is available for downloading, with time series long enough to include ScP. We obtained data for 16 earthquakes between 20 and 80 from the center of J-array, with moments between N-m. As with the LASA data, we found J- array seismograms are often too noisy to be useful. Even after stacking, only six events had visible PcP or ScP and quiet enough records to analyze for precursors (Table 4.3). For each event, we aligned the P -waves and stacked them, bandpass filtering between Hz. PcP and ScP were stacked by aligning the seismograms based on the predicted moveout from the P picks using iasp91. The two PcP stacks contain 236 (01/28/1999) and 315 (08/07/2000) seismograms. Five of six ScP stacks contain at least 195 seismograms (04/23/1997 has 72). The regions sampled are indicated in blue in Figure

67 130 o 135 o 140 o 145 o 45 o 45 o 40 o 40 o 35 o 35 o Japan array stations 30 o 30 o 25 o 25 o 130 o 135 o 140 o 145 o Figure 4.5: Locations of Japan array seismograph stations. The array consists of over 400 seismograph stations operated by various universities and the Japanese Meteorological Agency. Table 4.3: Earthquakes used in ULVZ precursor search Japan array Date Time Lat Lon Depth M0 MW Phase mm dd yy N E km N-m :44: ScP :34: ScP :10: PcP, ScP :16: ScP :09: ScP :33: PcP Indicates which phase was studied with event 49

68 4.3 Observations We compute both coherent and envelope stacks of P cp and ScP. The coherent stacks are computed by linearly summing normalized seismograms and are used to search for precursor arrivals resulting from reflections off the top of a ULVZ. The envelope stacks are used to search for precursory energy from scattered waves Coherent stacks Coherent stacks with the best signal-to-noise from the California networks are shown in Figure 4.6. The traces are normalized to the amplitude of the core-reflection and overlaid on the P -wave stack for each event, with predicted amplitudes and arrival times of PcP and ScP precursors (PdP and SdP, respectively) shown for four ULVZ models. The PdP and SdP amplitudes are calculated by computing reflection coefficients at a first-order discontinuity for an incident P -ors-wave converted to an upgoing P -wave. The travel time difference in the plot is the time required for the main core-reflection to traverse its extra legs within the ULVZ. There is no indication of coherent arrivals above the noise at the times or amplitudes predicted by the models. Background noise and lack of precursor detection allow us only to find upper bounds of allowable structures. The ratios of the average level of background noise to the theoretical precursor amplitude for PdP (for a 15 km-thick ULVZ with V P =V P = 0:1 and V S =V S = 0:3) range from 0.2 to 1.9, with four events exceeding 1.0. Likewise, the ratios of noise to predicted-sdp amplitude for all but one event range between 0.1 and 50

69 a) P SCSN PcP = SCSN = SCSN = NCSN = b) SCSN = P ScP SCSN = SCSN = NCSN = Time [s] Time [s] Figure 4.6: (a) NCSN and SCSN stacks of PcP for four events overlaid on P -wave stacks. Arrows indicate predicted amplitudes and arrival times of precursors to PcP, obtained by computing reflection coefficients for an P -wave incident on a simple discontinuity and converted to an upgoing P -wave. The travel time difference is the time required for the core-reflection to traverse its extra legs within the ULVZ. Both amplitude and time depend on incidence angle, and therefore on epicentral distance range. Model parameters (thickness, V P =V P, V S =V S, =): 1) (10 km, -0.1, -0.3, 0.0); 2) (40 km, -0.1, -0.3, +0.2); 3) (10 km, -0.1, -0.1, 0.0); and 4) (20 km, -0.1, -0.2, 0.0). (b) As in (a), for ScP. 51

70 = P PcP = Time [s] Time [s] = = Time [s] Time [s] Figure 4.7: LASA stacks of the four best quality PcP arrivals (black) overlaid on P stacks for the same events (blue). Arrows indicate time and amplitude of precursor PdP arrivals, obtained by computing reflection coefficients at a simple discontinuity. The travel time difference from PcP is the time required for PcP to traverse its extra legs within the ULVZ. Both amplitude and time depend on incidence angle, and therefore on epicentral distance range. Model parameters (thickness, V P =V P, V S =V S, =): 1) (10 km, -0.1, -0.3, 0.0); 2) (40 km, -0.1, -0.3, +0.2); 3) (10 km, -0.1, -0.1, 0.0); and 4) (20 km, -0.1, -0.2, 0.0). 1.7 (six events above 1.0); one earthquake is recorded at 46 degrees, where SdP s theoretical amplitude is near zero, which results in an extremely high noise-to-(predicted-sdp) ratio. The quietest events, in which the predicted amplitude exceeds the background noise by factors of two or more, do not have precursor arrivals. We make similar observations on PcP and ScP stacks from LASA and J-array (Figures 4.7 and 4.8). The three best-quality LASA stacks clearly do not contain ULVZ-produced precursors where the predicted amplitude exceeds the background noise; the fourth is too noisy to rule out any arrivals (Figure 4.7). On the J-array stacks, we can consistently rule out some ULVZ-produced arrivals with 52

71 both P cp and ScP stacks; others cannot be rejected because they fall within the noise. The thinnest ULVZ models in particular are difficult to assess because the travel time difference from PcP or ScP is small and the main core reflection arrivals are not perfectly aligned at time 0 (a result of stacking based on travel time instead of picking individual seismograms). We can compare the P waveforms to those of the core-reflections to investigate the possibility that scattering or reverberations within the ULVZ distorted PcP or ScP. For the lower noise events, PcP and P generally match quite well for all networks (Figures 4.6, 4.7, and 4.8). The agreement with ScP is not as consistent: greater attenuation often renders ScP longer period than P, and it is sometimes difficult to identify common peaks in the arrivals. However, for events and at the SCSN, the match is very good. In two events ( and ), P exhibits an extended wavetrain (5 s) that is significantly reduced in amplitude on the PcP and ScP stacks. The J-array ScP stacks also generally coincide with the P waveforms. The good agreement between P and PcP or ScP waveforms indicates that we detect no reverberations arising from fine structure Envelope stacks We combine envelopes of three of the cleanest SCSN events in a time window around ScP and search for a pickup of energy before the main reflection (Figure 4.9). The upper curve ( Envelope ) is an average of the envelope stacks of the three events. In the Corrected envelope curve, a power law fit tothe decaying P coda of the upper curve has been subtracted. No significant increase in energy precedes ScP, indicating that no extra scat- 53

72 Jarray = PcP P Jarray = Jarray = ScP P Jarray = Jarray = Jarray = Jarray = Time [s] Time [s] Figure 4.8: J-array stacks of P cp and ScP overlaid on P -wave stacks. Arrows indicate predicted amplitudes and arrival times of precursors to PcP, obtained by computing reflection coefficients for an P wave incident on a simple discontinuity and converted to an upgoing P wave. The travel time difference is the time required for the core-reflection to traverse its extra legs within the ULVZ. Both amplitude and time depend on incidence angle, and therefore on epicentral distance range. Model parameters (thickness, V P =V P, V S =V S, =): 1) (10 km, -0.1, -0.3, 0.0); 2) (40 km, -0.1, -0.3, +0.2); 3) (10 km, -0.1, -0.1, 0.0); and 4) (20 km, -0.1, -0.2, 0.0). 54

73 Amplitude Envelope Coherent 0 Corrected envelope Time [s] Figure 4.9: Combined coherent and envelope stacks of ScP from events , , and The curve labeled coherent is an average of envelope functions of the three coherent stacks. The envelope curve is an average of envelope stacks, and corrected envelope has had a power law fittothe decaying coda subtracted. The amplitude of the ScP pulse at around 300 s is set to 1.0. We do not see a pickup of energy preceding ScP. tered energy is arriving from a ULVZ. The curve labeled Coherent is an average of envelopes of the coherent stacks for the three events; we do this because waveforms from different earthquakes will not sum constructively. The quiet window preceding ScP provides further evidence for the lack of a precursor arrival from a constant thickness layer. One advantage of large networks is that we can use the moveout of the arrivals across the arrays to measure their horizontal slowness. Envelope stacks in slowness-time space enable us to easily inspect the windows preceding PcP and ScP for scattered energy. Furthermore, by adding the slowness dimension, we can also confirm whether any suspected precursor arrivals in the coherent stacks arrive at the same incidence angle as the core-reflections. Slowness stacks from the SCSN, LASA, and J-array are shown in Figures 4.10, 4.11, and All three exhibit quiet windows preceding the core-reflections at the same slowness, 55

74 providing further evidence for lack of scattered energy from the base of the mantle. 4.4 Modeling In the absence of observed ULVZ reflections, we attempt to place constraints on the properties of ULVZs in the regions of the CMB sampled here. Since the space of possible models is too large to test exhaustively, we choose three representative models for velocity and density changes. For each model, we calculate predicted amplitudes for P dp and SdP at a range of distances by computing reflection coefficients at a simple discontinuity, representing the top of the ULVZ. We also test a fourth model with a gradient ULVZ upper boundary rather than a discontinuity. We assume that effects of attenuation and geometrical spreading are identical for the precursor phases and their corresponding core-reflected phases. High attenuation within the ULVZ would only serve to increase the relative amplitudes of precursors to the core reflections. The difference in their amplitudes is thus attributable to the velocity and density contrasts at the top of the ULVZ (as well as slight variations in properties of the lower mantle). Figure 4.13 shows the four predicted curves of PdP=PcP and SdP=ScP. Reasoner and Revenaugh [2000] provides further discussion of amplitude curves for ULVZ-produced arrivals. We compare the predicted curves with measured upper bounds for the amplitude ratios of precursory energy to PcP or ScP in our stacks (Figure 4.13). To measure the ratios, we identify a time window in which we expect precursor arrivals. The arrival time depends on 56

75 SCSN lat: 54 lon: -170 depth: 300 km : 40 ; Hz Slowness [s/deg] P PcP ScP Time [s] Slowness [s/deg] ScP Time [s] 0 Figure 4.10: Envelope stack in slowness-time space of event , filtered Hz, recorded at SCSN. The windows before PcP and ScP are quiet, indicating no extra scattered energy precedes the arrivals. The lower panel shows a magnified view of the window surrounding ScP. 57

76 _1459; lat: 50.9 lon: depth: 9 km : 69.3; 0-1 Hz P Slowness [s/deg] Time [seconds] PcP Figure 4.11: Envelope stack in slowness-time space of event , filtered 0-1 Hz, recorded at LASA. The window before PcP is quiet, indicating no extra scattered energy precedes its arrival. 10 J-array _0810 M6.5 depth:51.1 km ~ Hz Slowness [s/deg] P PcP ScP Time [s] 0 Figure 4.12: Envelope stack in slowness-time space of event , filtered Hz, recorded at J-array. The windows before PcP and ScP are quiet, indicating no increase in scattered energy precedes the arrivals. The decline in the envelope preceding ScP is particularly clear. 58

77 PdP/PcP ln(v P ), ln(v S ), ln( ) A A: -0.1, -0.3, 0.0 B: -0.1, -0.3, 0.2 C: -0.1, -0.1, 0.0 D: -0.1, -0.3, 0.0, 10 km-wide transition C B D N/SCSN LASA J-array Distance [degrees] 0.3 same parameters as above N/SCSN J-array 0.2 B A SdP/ScP 0.1 C B D 0 C D Distance [degrees] Figure 4.13: (a) Ratios of stack amplitudes at expected times for precursors to PcP. Data points are maximum measured amplitudes of stacks in expected precursor arrival windows. Blue: NCSN and SCSN events. Red: LASA events. Green: J-array events. Curves show predicted amplitudes for four ULVZ models with velocity and density variations indicated. Models: A: Garnero and Helmberger [1998] and Wen and Helmberger [1998a]; B: Revenaugh and Meyer [1997]; C: Garnero and Vidale [1999]. D: Garnero and Helmberger [1998] with a 10 km wide transition from lower mantle to ULVZ. (b) As in (a), for ScP. 59

78 the height above the CMB of the ULVZ upper boundary, the velocity reductions within it, the epicentral distance, and on which phase we are considering. Therefore we use a variable search window whose start time is a function of epicentral distance and whose duration encompasses possible ULVZ thicknesses between five and 40 km, allowing for velocity reductions of about 0 to 20% for V P and 10 to 30% for V S. We compute envelopes of the coherent stacks and subtract the average noise level in a window preceding the precursor search window for that event and phase. We measure the maximum amplitude within the precursor search window and divide by the maximum PcP or ScP amplitude. It is clear that no single ULVZ model adequately describes the behavior of the data. Most of the PdP=PcP limits fall below the predicted amplitudes. The PdP=PcP ratios at greater are less restrictive because of the P -coda noise. The SdP=ScP ratios are generally higher, but also indicate that all models overpredict some observed amplitudes. The model with a gradual velocity reduction least violates the observed amplitude constraints. If the velocity reduction occurs over a vertical distance of 5-10 km rather than at a sharp boundary, the amplitude of the precursor is reduced by about half at high frequencies. Thus our data are compatible with low-velocity basal layers having gradational upper boundaries. 60

79 4.5 Discussion We do not observe short-period precursors from ULVZs under the northeast Pacific, the Mexico / Central America / Caribbean region, or several points under the western Pacific region. Stacks of P cp and ScP do not contain either coherent arrivals or incoherent scattered energy as precursors, and there is good agreement between P, PcP, and ScP waveforms. We cannot entirely rule out the presence of ULVZs in these regions, but we can restrict the properties they might have: If ULVZs are present, they are very thin, have less extreme velocity reductions than found elsewhere, or do not have sharp upper boundaries. If the layers are less than a few km thick, they may be too thin for the precursor to be distinguished from the main core-reflection. If ULVZ velocity reductions are less significant than previously suggested, the contrast with the lower mantle may not produce large precursor reflections. Or, ULVZ upper boundaries may be diffuse. This is more likely if ULVZs are thermally derived or result from melt than if they result from phase transitions or layering. At 0.8 Hz, the Fresnel zone for each PcP or ScP reflection point spans km in diameter at the CMB. This study primarily samples two regions of the CMB with dimension km. The consistent absence of ULVZ-generated precursors in the large regions jointly sampled by the California networks and LASA agrees with the extent of previously reported large-scale regions without ULVZs [Williams et al., 1998]. Using PcP, Revenaugh and Meyer [1997] detected a 8 3 km thick ULVZ south of the study area under Mexico. This can be reconciled with our and Castle and van der Hilst [2000] s non-detections if the ULVZ thins to less than 5 km towards the north, since we may 61

80 have difficulty detecting thicknesses less than that in our search. Havens and Revenaugh [2001] s results support thinning of the ULVZ under Mexico to less than 5 km towards the east, so variation to that extent is reasonable. A similar argument can be made for the northwest Pacific region, where Revenaugh and Meyer [1997] found a 11 6 km thick ULVZ slightly west of our study area (Figure 4.1). SP di KS studies also support a ULVZ there [Garnero and Helmberger, 1996]. However, this and other ScP studies have not detected one [Castle and van der Hilst, 2000; Vidale and Benz, 1992]. Thus these null results provide evidence for variation of ULVZs on relatively short length-scales. 62

81 Chapter 5 Diminished core-grazing P -waves 5.1 Introduction In this chapter, observations of core-grazing P -waves provide evidence for fine-scale structure at the CMB in the mid-pacific. The CMB region in the central Pacific isthought to contain a major upwelling [e.g., the Equatorial Pacific Plume Group of Su et al., 1994], and recent seismic and geodynamic models have proposed complicated small-scale structure and flow patterns at its base. The large-scale features in this region can be determined from global tomography: seismic velocities in D 00 in the southwestern Pacific are slower than average for shear waves ( ln VS = 1:5 to 3:0%)[Su et al., 1994; Masters et al., 1996; Mégnin and Romanowicz, 2000] and for compressional waves ( ln V P = 0:5%)[Van der Hilst et al., 1997]; travel times of diffracted waves yield similar results [Valenzuela and Wysession, 1998; Wysession, 1996]. The discrepancy in the size of V S and V P anomalies is often cited as evidence for chemical heterogeneity in D 00 [Grand et al., 1997]. Tomography using normal-modes sug- 63

82 gests a high-density region under the central Pacific[Ishii and Tromp, 1999]. Seismic evidence also exists for features with smaller length-scales in the central Pacific. D 00 discontinuities with increases in V P ( %) and V S (1.7%) have been observed 190 to 230 km above the CMB using precursors to the core-reflected phases PcP and ScS [Reasoner and Revenaugh, 1999; Russell et al., 2001]. An ultra-low velocity layer with V P reductions of 5-20% and thickness km is inferred from precursors to PcP with reflection points southeast of Hawaii [Mori and Helmberger, 1995; Revenaugh and Meyer, 1997]. Shear wave splitting of ScS indicates anisotropic velocity structure at the base of the mantle southeast of Hawaii, with a complicated pattern possibly related to convective flow at the root of the Hawaiian plume [Russell et al., 1999]. These observations are consistent with models of whole mantle convection that propose high-density materials collect underneath upwellings [e.g., Tackley, 2000]. Convection might then also occur within the dense basal layers, developing complicated thermal structure within D 00 [Montague and Kellogg, 2000]. Here we present further evidence for complex structure in this localized region of the CMB. We utilize core-grazing P -waves that sample adjacent paths just above the CMB along a southeast-northwest trend underneath the Hawaiian Island chain. Earthquakes with raypaths sampling the region just northwest of Hawaii have severely diminished waveforms, while those on either side appear normal. The anomalous waveforms are depleted at high frequencies. Amplitudes of 80 additional earthquakes sampling the same region reproduce the pattern. Stacks of globally-distributed core-grazing P -waves 64

83 indicate that for the distances and source parameters of our anomalous earthquakes, impulsive first arrivals are typical. We therefore propose that short-wavelength structure at the CMB is responsible for the observed diminished waveforms. 5.2 Data and Observations We obtained digitized LASA data for 23 earthquakes from the Tonga, New Hebrides, and South Solomon subduction zones (Table 5.1). For each earthquake, we compute a linear coherent stack of seismograms for each subarray, aligning the seismograms on the predicted arrival of P or P di (depending on source depth and distance) and filtering between 0.5 and 1.0 Hz; we then align the subarray stacks and sum them to create a single stack for each earthquake. Figure 5.1 shows raypaths for P and P di.atdistances between 96 and 101, the bottoming depth of P -waves for a 50 km deep source ranges from about 60 km above the CMB to diffraction along the CMB (Figure 5.1). In five of the 23 stacks we observe extremely weak first arrivals. They are emergent rather than impulsive and appear attenuated in higher frequencies. Energy continues arriving for more than 10 seconds following the first arrival. Eleven of the stacks have more typical P or P di, with strong first arrivals and short, well-defined time functions. The initial arrivals have clear endings within 10 seconds following the first arrival. The other seven stacks are too noisy to clearly identify any arrivals. 65

84 Core-grazing P and Pdiff raypaths source depth: 50 km 0 90 o ICB 95 o CMB 100 o Figure 5.1: Raypaths for P -waves at 90,95, and 100 for a source depth of 50 km. For distances greater than about 96 the ray passes within 60 km of the CMB. Generated using the TauP raypath utility [Crowell et al., 1999]. 66

85 Table 5.1: Earthquakes studied for diminished core-grazing P -waves Type z Date Time Lat Lon Depth m b mm/dd/yy N E km) n 08/19/70 02: n 09/23/70 12: n 09/23/70 23: n 11/18/70 01: b 12/22/70 19: n 03/30/71 02: a 10/27/71 17: a 09/04/72 18: n 09/06/72 05: b 09/07/72 20: n 09/08/72 17: n 09/09/72 02: b 09/13/72 06: b 09/13/72 12: n 09/13/72 14: n 02/24/73 07: b 10/09/73 09: a 12/29/73 00: a 12/30/73 16: b 12/30/73 17: a 01/10/74 08: b 03/03/74 13: n 03/03/74 14: z a : anomalous; n : normal; b : noisy Events with m b of 0.0 had no listed magnitude. 67

86 LASA Earthquakes CMB paths 180 o 20 s 240 o _1204 M km = _2311 M km = _0157 M km = _1811 M km = o 30 o _0211 M km = _0851 M km _0738 M km = _1433 M km = _1422 M km = o = o _1639 M km = _0019 M km = _1758 M km = o -30 o 180 o 240 o Figure 5.2: Earthquakes and raypaths in the lowermost 100 km of the mantle for P and P di arrivals at LASA. Waveforms are stacks of LASA seismograms. Black dots indicate predicted P or P di arrival time. Squares mark earthquake locations. Red paths and seismograms indicate stacks with diminished first arrivals. Solid black paths and seismograms indicate normal arrivals. Dashed black paths indicate noise-dominated arrivals. The raypaths of the four easternmost events do not pass within 100 km of the CMB and are not shown. The anomalously weak earthquakes sample a geographically localized region of the CMB slightly northwest of Hawaii (Figure 5.2). The cluster of red raypaths has northwest-southeast extent of 165 km at the CMB. The normal-looking events raypaths sample further northwest or southeast of this region. The five events with diminished waveforms are adjacent and no normal events are located amongst them. The four easternmost events have sharp P arrivals and appear normal, but are at closer range (87-92 ), so their rays turn above the base of the mantle. In the subsequent analysis, we focus on events beyond

87 10 0 Average displacement spectrum Anomalous Normal Frequency [Hz] Figure 5.3: Average spectra of the five anomalous events and the five normal events withm b 5:8. We computed frequency-domain stacks of each earthquake using the window between three seconds preceding the first arrival and ten seconds following, and averaged the spectra for the two groups. The anomalous events have less power at high frequencies. We can rule out the decrease in amplitude with epicentral distance as the factor differentiating the anomalous from the normal waveforms. The anomalous events range from 96.6 to 99.1, while the normal events are all beyond In order to examine the frequency content, we computed stacks for each event in the frequency-domain, using windows from three seconds before the first arrival time to ten seconds after. We separately averaged the spectra of the anomalous and normal events (Figure 5.3), using all five anomalous stacks and only the five normal stacks withm b 5.8, to compare events of similar magnitudes. The anomalous events are depleted at high frequencies relative to the normal events. One anomalous event, the Dec. 30, 1973, 16:39, earthquake, has no discernible arrival 69

88 until four seconds after the predicted P di time in the 0.5 to 1.0 Hz bandpass. Stacks computed in the 0.2 to 0.5 Hz bandpass, however, show a distinct arrival at the predicted time. The first arrival thus appears strongly attenuated at higher frequencies. 5.3 ISC amplitudes Although we have waveforms available for only a few events, we can supplement the data with P and P di amplitude measurements made at LASA and compiled by the International Seismological Centre (ISC). We obtained ISC amplitudes for 1821 seismograms recorded at LASA from earthquakes in the same source region [International Seismological Centre, 2001]. Of these, 350 did not have magnitudes listed; the amplitude as a function of magnitude for the remaining 1471 are shown in Figure 5.4. Three of our anomalous events are found in the catalog, as are six of the normal events and two noise-dominated events (Figure 5.4). The amplitudes at LASA for the diminished waveform events are low compared to other events with the same magnitude. Because the magnitudes listed in the ISC catalog were determined by averaging amplitudes at stations worldwide, we can infer that amplitudes for the anomalous earthquakes at other locations were more typical for magnitudes between 5.8 and 6.3. This implies that the source region itself is not the cause of the weak arrivals, since it would affect global observations equally. The low relative amplitudes at LASA therefore derive from either path effects or a nodal focal plane orientation. We do not have moment- 70

89 events shown here 20 ISC amplitude [A/T] : anomalous event +: normal event x: noise-dominated event # events with (magnitude, amplitude) Magnitude [m b ] 0 Figure 5.4: ISC amplitude at LASA as function of event magnitude. Color indicates number of earthquakes with a given (magnitude, amplitude) pair. Symbols indicate events for which we have waveforms that were found in the catalog: Open squares denote catalog amplitudes of three of our anomalous events; + denotes our normal events; x denotes our noise-dominated events. The ISC amplitudes of the anomalous events are quite low for their magnitudes. 71

90 -4 o -6 o Focal mechanisms from New Hebrides region -8 o -10 o -12 o -14 o -16 o -18 o -20 o -22 o LASA-recorded earthquakes Anomalous Normal. Noisy Recent focal mechanisms -24 o 150 o 153 o 156 o 159 o 162 o 165 o 168 o 171 o Figure 5.5: Recent focal mechanisms from the New Hebrides region do not show any systematic variation that would result in low-amplitude first arrivals at LASA. tensor solutions for these earthquakes. However, focal mechanisms from the Harvard Centroid Moment Tensor catalog for recent earthquakes show no systematic variation between the source regions of the normal and anomalous events (Figure 5.5). Mapping the ISC amplitudes to the bottoming points of their raypaths on the CMB enables a comparison with the spatial pattern observed with the stacked waveforms. The amplitudes must be corrected for magnitude, source depth, and source-receiver distance. From the catalog, we select the 184 events with source parameters similar to those of the anoma- 72

91 ISC catalog events Anomalous stacked events Normal stacked events 300 km -164 o N 24 o -164 o 20 o -160 o Corrected ISC amplitude [A/T] Figure 5.6: Corrected ISC amplitudes mapped to raypath bottoming points. ISC amplitudes for events with m b 5.0 to 6.5; depth 10 to 80 km; distance 96 to degrees were corrected for magnitude-, depth-, and distance-dependence. Bottoming points for the stacks are also shown: open squares for anomalous events and + for normal events. There is a cluster of low amplitude events within the region sampled by our anomalous stacks. lous and normal stacked events: magnitudes between 5.0 and 6.5; source depths between 10 and 80 km; and epicentral distances between 96 and The amplitudes correlate most strongly with magnitude. We sequentially perform least-squares fits of the amplitudes to magnitude, source depth, and epicentral distance, removing the slope of the distribution for each fit. Corrected amplitudes of the 80 events with midpoints closest to the anomalous region are mapped in Figure 5.6. We observe a cluster of low ISC amplitudes in the same region sampled by our anomalous stacked events. To the northwest and southeast of this region, where normal arrivals bottoming points are located, relatively large amplitudes predom- 73

92 inate. Overall, the region of the anomalous events bottoming points has a larger proportion of low amplitude observations. Some interesting structure can be observed within it, however. One cluster of anomalous waveforms is co-located with only moderately low ISC amplitudes, while the line of amplitudes trending northwest towards the outlying anomalous event consists almost exclusively of low amplitude data. 5.4 GSN stacks To assess how unusual the diminished waveforms are, we compute envelope stacks of Global Seismographic Network (GSN) core-grazing P -waves. We select seismograms recorded by the GSN at distances between 96 and 101 from earthquakes with similar source parameters as our anomalous arrivals. The seismograms sample the CMB in several different regions, including the central Pacific, Asia, and Canada, which allows us to establish the properties of typical core-grazing P -waves,. The stacks demonstrate that, on average, core-grazing P and P di have impulsive, welldefined first arrivals, even at distances greater than 96 (Figure 5.7). The envelopes of the stacks of our normal events have similar features. In contrast the envelopes of the stacks of our anomalous events have emergent first arrivals that are not sharply peaked. Thus the anomalous events arrivals are unusually weak compared to typical seismograms at these distances. 74

93 [11] 101 Distance [degrees] [9] [29] [14] Distance [degrees] [20] Time [s] Time [s] Figure 5.7: (left) Envelope stacks of GSN data in 1 distance bins. The number of seismograms in each stack is given in brackets. Selection criteria: MW 6.0 to 6.4; depth km. We imposed a signal-to-noise >5 selection criterion, using a 40 second-long signal window to allow for emergent arrivals like those of the anomalous stacks and to avoid a bias in favor of large signal in the initial few seconds. We bandpass filtered the seismograms between 0.5 and 1.0 Hz, computed the envelopes and stacked. (right) Envelopes of the LASA stacks. Anomalous waveforms are shown in red; normal waveforms in black. The anomalous LASA events have weak first arrivals, while the sharp-peaked first arrivals of the normal events match those of the GSN stacks. 75

94 5.5 Discussion We have presented observations of diminished first arrivals sampling a localized region of the CMB in the mid-pacific. The anomalous waveforms have reduced power in high frequencies. Stacks of GSN seismograms from a global distribution of sources and receivers demonstrate that earthquakes with similar source parameters are typically impulsive with well-defined first arrivals, even at distances beyond 96. We do not believe the pattern results from source orientation or source-region effects. Three earthquakes with anomalous stacks and magnitudes greater than 5.8 also appear in the ISC catalog. This implies that observations of these earthquakes at other stations in the world measured large amplitudes. A survey of recent focal mechanisms does not reveal systematic variation between the source regions of anomalous and normal stacks. If the variation derives from along-path phenomena, it is natural to consider the CMB region. These waveforms sample a portion of the CMB previously recognized to have complex features at a range of scales. The fine-scale variations we observe may be related to dynamical processes. Modeling of dense basal layers shows that convection within them can occur if the excess density is high enough and the layer thickness is about 200 km [Montague and Kellogg, 2000]. This can lead to lateral variation in D 00 temperatures on relatively short wavelengths (400 km) [Montague et al., 1998]. We sample a large upwelling that may encompass a high density basal layer, so our observation is consistent with this dynamical model. The increased heterogeneity could scatter 76

95 the P -waves as they pass through. Attenuation resulting from reduced Q also can occur at the base of an upwelling and further diminish the P -waves. Other dense arrays throughout the world offer the opportunity to sample different regions of the CMB for evidence of short-wavelength variations. If the anti-correlation of velocity and density, and the relationship between high density and D 00 convection exist, we would expect to see variation under Africa, but not under Asia. 77

96 Chapter 6 Conclusion Core-mantle boundary In this part of the dissertation, we have explored some of the questions about ULVZs and the CMB region in general by studying fine-scale structure. Towards that goal, we measured CMB reflection properties, searched for precursors from the upper boundaries of ULVZs, and mapped amplitude variations of core-grazing P -waves over short length-scales. Below, we consider the implications of these results for structure at the CMB. 6.1 Summary of results Reflection properties of the CMB The globally-averaged CMB reflection properties are consistent with PREM and allow basal layering with only up to 10% V P and V S reductions and a 20% density increase. The PcP data do not match predictions for reductions of 10% (V P ) and 30% (V S ). ScP agrees with PcP in the Hz bandpass, but admits greater velocity reductions at longer and shorter periods. Some of this discrepancy may be attributed to uncertainty in the attenuation 78

97 model. Mapped to their bounce points, reflection amplitudes reveal lateral variations in the CMB reflection properties. The limited number of regions with dense coverage is a major impediment, but in the best-sampled regions we detect some patterns that are consistent with previous detections and non-detections of ULVZs and the results from our precursor search Search for ULVZ precursors In stacks of P cp and ScP sampling the CMB under the northeast Pacific, the Mexico / Central America / Caribbean region, and several points under the western Pacific region, we do not observe short-period precursors from ULVZs. Neither coherent arrivals nor incoherent scattered energy are visible preceding the core-reflections, and there is good agreement between P, PcP, and ScP waveforms. These null results enable us to place constraints on the properties of ULVZs: If ULVZs are present in the regions we sample, they must be thin, have less extreme velocity reductions than found elsewhere, or have gradational upper boundaries. This evidence supports thermally-derived or partial melting origins of ULVZs rather than phase transitions or layering. Combining our results with previous observations and non-observations of ULVZ-produced precursors from neighboring and coincident regions, we suggest that ULVZ properties vary on relatively short length-scales. 79

98 6.1.3 Diminished core-grazing P -waves Further evidence for CMB variation over small distances is provided by observations of diminished first arrivals sampling a localized region of the CMB in the mid-pacific. The anomalous waveforms have reduced power in high frequencies. Mapped ISC amplitudes from additional earthquakes support the variation over short length-scales. Global stacks of GSN seismograms demonstrate that first arrivals at core-grazing distances, in contrast, are typically impulsive. These waveforms sample a portion of the CMB near Hawaii that has been previously recognized to have complex features at a range of scales. We propose that the fine-scale variations we observe may be related to dynamical processes. Modeling of dense basal layers shows that convection within them can lead to lateral variation in D 00 temperatures on relatively short wavelengths (400 km) [Montague et al., 1998; Montague and Kellogg, 2000]. The upwelling under the mid-pacific may encompass a high density basal layer, and increased heterogeneity could scatter the P -waves as they pass through. Attenuation resulting from reduced Q also can occur at the base of an upwelling and would also diminish the P - waves. 80

99 6.2 Implications for structure at the CMB Intriguing discoveries have raised new questions about the CMB, and evidence suggests that fine-scale structure exists, but is not yet well-constrained. This work has enabled us to establish properties of ULVZs in response to the questions we raised in the introduction. In particular, it appears likely that ULVZs do not have sharp upper boundaries, which might be expected if they derive from chemical layering. In that case, they should produce arrivals preceding P cp and ScP that would be visible in our stacks. We have also determined, in accord with previous results, that ULVZ properties can vary laterally over relatively short distances. The varying pattern of diminished core-grazing P - waves occurs on the edge of ULVZ. Our observations do not support large reductions in VS, which casts doubt on the likelihood that partial melt is widespread. Of course, the possibility remains that localized regions have more extreme velocity reductions. We can generalize the conclusions about ULVZs to the major questions about the CMB region. The causes of layering at the base of the mantle may be compositional in origin, but the transition from the overlying mantle is gradual, which suggests heating plays a significant role. Based on the global stacks, the CMB itself must be less than 1 km wide, which constrains core-mantle chemical reactions to those that retain a sharp boundary. 81

100 6.3 Future work Our continued investigation should yield more information about the nature of this important region in the Earth. Some practical improvements for the broadband stacking include incorporating improved mantle attenuation models, and deconvolving the instrument response and empirical time functions from the seismograms. Another seismic phase that could prove useful is P KKP, which reflects from the underside of the CMB and would improve spatial coverage. The mapping results require additional data to be more robust since many bins have so few hits. Accumulation of data over time and additional seismic stations will aid this effort. For the ULVZ precursor searches, we are limited in the data available from LASA, but we can improve the signal-to-noise for Japan array data by using larger earthquakes. The study of the diminished core-grazing P -waves could be further supported by modern earthquakes sampling the same region. This would allow us to test the ambiguity over whether the variation in the waveforms is source- or path-related. In addition, other dense arrays throughout the world offer the opportunity to sample different regions of the CMB for evidence of short-wavelength variations, allowing further insight in the dynamics of the CMB. 82

101 Part II Source properties of deep-focus earthquakes 83

102 Chapter 7 Introduction Deep earthquakes From the first recognition of deep-focus earthquakes in the 1920s [Wadati, 1928], geophysicists have sought to explain the mechanism by which unstable slip on faults occurs between 100 and 700 km depth. Deep earthquakes locations at collisional plate boundaries and their dipping planes of seismicity (Wadati-Benioff zones) clearly associate them with subducting lithosphere (Figure 7.1). But at those depths, constitutive laws for the lithosphere seem to preclude brittle failure of the type we observe in the seismogenic portion of the crust [e.g., Kirby, 1987]. Based on current understanding of olivine (the major constituent of the upper mantle), stresses should be relieved via flow of mantle rock at temperatures and pressures in the transition zone. High pressures suppress dilatancy, a feature of mode I tensile cracks in brittle fracture, and increased temperatures reduce yield strength of rocks [Scholz, 1990]. And yet, many properties of deep earthquakes (magnitude-frequency relationship, double-couple source, stress drop) are generally similar to those of shallower events, with the notable exception of fewer aftershocks [Frohlich, 1989; Green and Houston, 1995]. Giardini [1988] found b-values (the slope of the magnitude-frequency curve) 84

103 Earthquakes deeper than 100 km from the Harvard CMT catalog with M 0 >= 5.0 x N-m (M W >= ~ 5.74) 60 o 60 o 30 o 30 o 0 o 0 o -30 o -30 o -60 o -60 o Depth (km) Figure 7.1: Locations of earthquakes in the Harvard CMT catalog ( ) with depth 100 km and moment 5: N-m (MW 5.74). The Tonga subduction zone dominates deep seismicity, but the bimodal distribution of Figure 7.2 remains even if the Tonga events are subtracted [Frohlich, 1989]. Deep earthquakes occur at collisional plate boundaries within subducting lithosphere, as shown by Wadati-Benioff zones of dipping seismicity. for earthquakes deeper than 350 km to average 0.87 worldwide. Significant regional differences exist, however: Tonga has relatively few large events (b =1:2), while South America has relatively few small events (b =0:4). Deep earthquakes primarily have double-couple focal mechanisms [Green and Houston, 1995]. Although an isotropic component to the moment tensor has been long sought as evidence for volume changes during phase transformations (a possible mechanism), recent work limits isotropic components to less than 10% of total moment [Kawakatsu, 1991]. Two 85

104 large, well-recorded deep earthquakes (Bolivia, June 9, 1994, M W 8.2 and Tonga, March 9, 1994, M W 7:6) had virtually no isotropic component [Kikuchi and Kanamori, 1994; Hara et al., 1995; Tibi et al., 1999]. The occasional large compensated linear vector dipole (CLVD) component of the moment tensor is usually explained by complex rupture, occurring on multiple faults with different focal mechanisms [e.g., Frohlich, 1989; Kuge and Kawakatsu, 1993; Houston, 1993]. The 1994 Bolivia and Tonga events, however, had insignificant CLVD [Green and Houston, 1995]. The behavior of stress drop as a function of depth is unclear [Frohlich, 1989], but values are often found to be similar to those at the surface [e.g., Houston and Williams, 1991]. The 1994 Bolivia earthquake had an exceptionally high stress drop, perhaps as high as 100 MPa [Kanamori et al., 1998; Wiens, 2001]. Deep earthquakes are notable for producing very few aftershocks [Frohlich, 1987], but there are some cases (e.g., 1994 Tonga) in which aftershock sequences of deep earthquakes are as numerous as those for shallow events [Wiens and McGuire, 2000]. 7.1 Proposed mechanisms Many mechanisms have been proposed to explain the origins of deep-focus earthquakes. For intermediate depths ( km), the presence of fluids within the descending oceanic plate might produce seismicity by dehydration embrittlement [Green and Houston, 1995], but the supply of free fluids is presumed to be exhausted at greater depths [Kirby et al., 1991; Green and Houston, 1995]. It has also been proposed [Silver et al., 1995; Jiao et al., 2000] 86

105 that intermediate-depth earthquakes occur on pre-existing faults that have been preserved within the slab as it subducts. Jiao et al. [2000] found that focal mechanisms to depths of about 450 km are similar to those at the outer rise, after rotating to account for slab dip. Tibi et al. [2002] inverted body-waves for six intermediate-depth earthquakes and found rupture zones extending greater distances in the direction of plate strike than perpendicular to dip. They note the consistency of this extent with orientations of trench-parallel faults observed in near-trench and outer rise regions. One inference is that intermediate-depth earthquakes represent re-rupture of pre-existing faults. The fault zones may have compositional differences that render them intrinsically weaker than the rest of the plate, or slab heating may release fluids from hydrous minerals concentrated in the faults. The recognition that the population of deep earthquakes reaches a minimum at about 350 km and then peaks between 400 and 600 km (Figure 7.2) led to many suggestions that the polymorphic phase transitions in olivine (occurring at 410 km and 660 km in normal mantle conditions) are implicated in the mechanism of deep earthquakes [e.g., Sung and Burns, 1976; Vaisnys and Pilbeam, 1976; Kirby, 1987]. Green and Burnley [1989] demonstrated that deviatoric stresses applied to an analog of mantle olivine could produce shear instability through transformational faulting. They proposed that deep earthquakes occur when metastable olivine (persisting into the spinel stability field as a wedge within the cold interior of the plate) transforms into spinel, with shear instability assisted by the exothermic nature of the reaction and the superplasticity of the fine-grained spinel [for reviews see Green and Houston, 1995; Kirby et al., 1996]. 87

106 Depth distribution of earthquakes in Harvard CMT catalog earthquakes with M x N-m (M W ~5.74) Number of earthquakes Depth [km] Figure 7.2: Depth distribution of earthquakes in Harvard CMT catalog. Note that the bin of the shallowest events goes off scale. The distribution is bimodal, with a minimum around 350 km and a peak around 600 km. (More detail regarding these observations and the modeling of the phase change is supplied in Appendix D). Some unresolved problems with this model remain, however. The spatial extent of the June 9, 1994, Bolivia event appeared to rupture a zone wider than the expected width of the metastable wedge [Silver et al., 1995]. The distribution of aftershocks to the March 9, 1994, Tonga event also extends beyond the previously seismic portion of the plate [Wiens et al., 1994]. Transformational faulting predicts few aftershocks and no repeating ruptures because once an earthquake occurs, little or no untransformed material remains for further faulting. Thus, recent observations of an extensive aftershock sequence with outlying events 88

107 (to Tonga, 1994) [Wiens and McGuire, 2000] and repeating deep earthquakes in Tonga [Wiens and Snider, 2001] may also pose difficulties for the model. Thermo-kinetic slab modeling shows that for most subducted slabs (except Tonga) a metastable olivine wedge, if present, is not expected to persist below about 550 km depth and thus would not be available to support deep transformational faulting [Devaux et al., 1997, see Appendix D for more details]. Other suggested mechanisms include plastic instabilities [e.g., Hobbs and Ord, 1988] and shear-induced melting [e.g., Griggs and Baker, 1969; Kanamori et al., 1998; Karato et al., 2001], both of which invoke a localized reduction in strength from either grain-size reduction or heating. There have also been attempts to explain the seismicity minimum as the depth where stress goes to zero as it changes from downdip tension (shallow) to downdip compression (deep) [e.g., Vassiliou et al., 1984; Vassiliou and Hager, 1988]. Tension derives from negative buoyancy of the cold plate, while compression arises when the plate s descent is impeded at the base of the upper mantle. However, while observations of stress orientations of deep earthquakes are consistently downdip compression deeper than 400 km, slabs are not uniformly in downdip tension at shallower depths [Apperson and Frohlich, 1987]. 7.2 Source time functions The mechanism by which deep earthquakes occur remains unresolved. One strategy for further investigation is to analyze the temporal history of moment release in the earthquakes 89

108 themselves. Earthquake source time functions (STFs) represent moment release as a function of time, spatially integrated over all areas of the fault that contribute energy arriving at a given time. Although no spatial resolution of rupture is conveyed, parameters measured from STFs can yield important clues to the mechanism of moment release during deep-focus earthquakes. Models for faulting mechanism do not directly predict how different processes will manifest themselves in the source time functions. By measuring how properties such as rupture duration and complexity depend on depth and subduction zone, this study will offer constraints for those models to satisfy. We will present evidence for a change in mechanism at 550 km, which could suggest a future direction for mineral physics experiments. There have been several recent studies of deep-focus earthquake source time functions, and some disagreement over how their properties vary with depth. Houston et al. [1998] examined 42 earthquakes from 1992 to 1995, with depth100 km and MW 6.5 and found shorter durations with increasing depth. They also found more complex rupture histories in the depth range 350 to 550 km. Bos et al. [1998] stacked GSN records of 48 earthquakes from 1991 to 1996, with depth100 km and magnitudes larger than 5.5. They found similar depth dependence of duration but drew no conclusion about rupture complexity. Campus and Das [2000] obtained time functions of 32 earthquakes deeper than 70 km along the Fiji and Japan subduction zones. They found no depth dependence of duration or STF shape. In this study, we compute STFs of 111 earthquakes deeper than 100 km, determined from stacks of broadband seismograms recorded by the Global Seismographic Network. Thus we 90

109 achieve an improvement of more than a factor of two in the size of our catalog. In particular, in the km depth range, we have 18 events, compared with eight for Houston et al. [1998], nine for Bos et al. [1998], and nine for Campus and Das [2000]. Further, many of our events are more recent, with more seismograms recorded, taking advantage of the GSN s expansion. In our stacks to compute source time functions, we use between 10 and 53 broadband seismograms per event. Houston et al. [1998] used 8-15 and Bos et al. [1998] used about And, compared with Houston et al. [1998], our global distribution of seismographic stations allows us to include events farther than 90 from North America and to avoid potential problems with using stations from a narrow range of azimuths. The goal of this part of the dissertation is to systematically examine deep earthquake STF properties as a function of depth, moment, and subduction zone. We will measure duration, shape, stress drop, energy release, initiation and termination, and aftershock production. By following a global approach, we can study many earthquakes from a large number of subduction zones at the same time. This allows us to ascertain the most general characteristics of deep earthquakes, along with specific geographical variations. Our observations are evaluated in the context of the transformational faulting hypothesis and a simple model of rupture propagation for their implications regarding the mechanism of deep earthquakes. In Chapter 8, we describe the GSN database we use and the procedure for constructing and scaling STFs. Chapter 9 examines the STFs and their durations and shapes as a function of depth, and compares them to predictions from a standard model of earthquake scaling. In Chapter 10, we evaluate how deep earthquakes differ by subduction zone. Finally, in 91

110 Chapter 11, we examine the beginnings, endings, and aftershocks of deep earthquakes as functions of depth, moment, and subduction zone. 92

111 Chapter 8 Data and Processing 8.1 Earthquakes We stack waveforms recorded by Global Seismographic Network (GSN) stations and archived by the IRIS Data Management Center in the FARM database. The database contains 3048 earthquakes between January 1, 1988, and December 31, 2000, with more than 500,000 seismograms. The seismograms have been decimated to a sampling rate of five samples per second. Stacking GSN records offers several advantages for earthquake source studies: (i) global distribution of stations; (ii) broadband recordings; and (iii) many stations recording each event. Using a global network eliminates some problems that can arise with regional arrays, such as limited coverage of source regions. It also provides better azimuthal coverage to mitigate the effects of disadvantageous orientation with respect to nodal planes and directivity of rupture. Broadband records enable us to extract more information about the sources than short-period seismograms, especially for the longer-duration events which have large moment at long periods. In addition, broadband records mitigate the effects of 93

112 lost information due to attenuation of high-frequencies at teleseismic distances. The everincreasing number of seismographic stations allows us to achieve significant noise reduction through stacking. This enables more accurate estimates of rupture initiation and termination, and therefore better estimates of the source durations. We identify 149 earthquakes in the database with hypocenters at depths 100 km depth and MW 6.4 (according to the Harvard Centroid-Moment Tensor catalog). For each earthquake, we examine vertical-component seismograms at teleseismic distances (epicentral range from 30 to 90 ), removing noisy or glitch-ridden traces. As a result of the expansion of the GSN during the 1990s, the number of seismograms in the database associated with each event rises from just a handful for the earliest events to tens of traces for more recent events. We require each stack to contain a minimum of 10 seismograms to ensure sufficient noise reduction to pick the start and end times of moment release accurately. Relaxing this standard adds only a few additional events, which have greater uncertainty in their durations (Figure E.1). Discarding the earthquakes with fewer than 10 seismograms leaves 111 events (Figure 8.1 and Table 8.1). All but one of the 38 discarded earthquakes occurred between 1988 and 1992, when the GSN had fewer stations (13 earthquakes in that time period had 10 or more traces and were retained). The 111 earthquakes depths range from 100 to 648 km and their magnitudes are between MW 6.4 and 8.2. Noted in Table 8.1 are the events in common with four other recent studies of deep earthquakes (Houston et al. [1998], Bos et al. [1998], Campus and Das [2000], Houston [2001]). This study represents the largest yet conducted of deep-focus earthquake source time functions. 94

113 -60ß -60 o -30 o -30 o 0 o 0 o 30 o 30 o 60 o 60 o Station km km >=550 km Figure 8.1: Earthquakes and stations used. 95

114 Table 8.1: Deep earthquakes studied Date Time Latitude Longitude Subduction N MW M0 Depth 0 Nzc Nas Common to :12: Aleutian :50: Kurile :14: Izu-Bonin B :50: Chile B :21: Tonga CD H :37: Izu-Bonin :01: Aleutian :44: Tonga H98 CD H :08: New-Hebrides :09: Tonga H :50: Java/Indonesia B :24: New-Hebrides :49: Izu-Bonin H98 CD :06: Kurile H98 CD :39: Japan H98 CD N: number of seismograms stacked for each event M0: moment in units 10 of N-m, obtained from the Harvard CMT catalog 19 and : unscaled and scaled durations, respectively Nzc: number 0 of zero-crossings Nas: number of aftershocks H98: Houston et al. [1998]; B: Bos et al. [1998]; CD: Campus and Das [2000]; H01: Houston [2001] continued on next page 96

115 Table 8.1 Deep earthquakes studied (continued from previous page) Date Time Latitude Longitude Subduction N MW M0 Depth 0 Nzc Nas Common to :08: Tonga H98 CD :19: Philippine :51: Chile H :00: Ryukyu :53: Tonga :42: Himalaya :16: Philippine :54: Izu-Bonin H98 CD H :53: Peru H98 H :17: New-Hebrides H :28: Tonga H98 CD H :51: Middle-America H98 B :40: Tonga H98 H :11: Chile H :36: Chile H98 B N: number of seismograms stacked for each event M0: moment in units of N-m, obtained from the Harvard CMT catalog 19 and : unscaled and scaled durations, respectively Nzc: number 0 of zero-crossings Nas: number of aftershocks H98: Houston et al. [1998]; B: Bos et al. [1998]; CD: Campus and Das [2000]; H01: Houston [2001] continued on next page 97

116 Table 8.1 Deep earthquakes studied (continued from previous page) Date Time Latitude Longitude Subduction N MW M0 Depth 0 Nzc Nas Common to :33: Chile H98 H :45: Java/Indonesia H :36: Japan H98 B H :02: Chile H :39: Java/Indonesia B :10: Kurile H98 H :20: Tonga H :18: Java/Indonesia :32: Tonga H :06: Peru H :59: Himalaya B :58: South-Solomon B :24: New-Hebrides H98 B :29: Tonga :43: Peru H01 N: number of seismograms stacked for each event M0: moment in units of N-m, obtained from the Harvard CMT catalog 19 and : unscaled and scaled durations, respectively Nzc: number 0 of zero-crossings Nas: number of aftershocks H98: Houston et al. [1998]; B: Bos et al. [1998]; CD: Campus and Das [2000]; H01: Houston [2001] continued on next page 98

117 Table 8.1 Deep earthquakes studied (continued from previous page) Date Time Latitude Longitude Subduction N MW M0 Depth 0 Nzc Nas Common to :06: Marianas B H :39: Tonga B H :38: Middle-America H :43: Java/Indonesia B :44: Philippine B H :04: Izu-Bonin B :48: New-Hebrides B :30: Tonga H :34: South-Solomon B H :12: Marianas B :04: New-Hebrides B :22: Java/Indonesia H :38: Tonga B CD H :53: Tonga :41: Tonga N: number of seismograms stacked for each event M0: moment in units of N-m, obtained from the Harvard CMT catalog 19 and : unscaled and scaled durations, respectively Nzc: number 0 of zero-crossings Nas: number of aftershocks H98: Houston et al. [1998]; B: Bos et al. [1998]; CD: Campus and Das [2000]; H01: Houston [2001] continued on next page 99

118 Table 8.1 Deep earthquakes studied (continued from previous page) Date Time Latitude Longitude Subduction N MW M0 Depth 0 Nzc Nas Common to :53: Japan H :15: Chile H :44: Marianas :46: Tonga H :13: Himalaya :22: Tonga H :13: Peru H :23: Tonga H :30: Philippine H :53: Tonga CD H :15: Peru H :56: Middle-America :59: New-Hebrides H :53: Chile H :56: Peru N: number of seismograms stacked for each event M0: moment in units of N-m, obtained from the Harvard CMT catalog 19 and : unscaled and scaled durations, respectively Nzc: number 0 of zero-crossings Nas: number of aftershocks H98: Houston et al. [1998]; B: Bos et al. [1998]; CD: Campus and Das [2000]; H01: Houston [2001] continued on next page 100

119 Table 8.1 Deep earthquakes studied (continued from previous page) Date Time Latitude Longitude Subduction N MW M0 Depth 0 Nzc Nas Common to :05: South-Solomon H :11: New-Hebrides H :05: Tonga H :18: Marianas :18: Himalaya :48: Tonga H :01: Peru H :22: Tonga :45: Tonga :56: New-Hebrides :40: Izu-Bonin :34: Java/Indonesia :38: Tonga :35: South-Solomon :24: South-Solomon N: number of seismograms stacked for each event M0: moment in units of N-m, obtained from the Harvard CMT catalog 19 and : unscaled and scaled durations, respectively Nzc: number 0 of zero-crossings Nas: number of aftershocks H98: Houston et al. [1998]; B: Bos et al. [1998]; CD: Campus and Das [2000]; H01: Houston [2001] continued on next page 101

120 Table 8.1 Deep earthquakes studied (continued from previous page) Date Time Latitude Longitude Subduction N MW M0 Depth 0 Nzc Nas Common to :08: South-Solomon H :10: Japan H :38: Tonga H :33: South-Solomon H :16: Java/Indonesia :01: Chile :45: Himalaya :01: Chile :29: Tonga :47: Tonga H :09: Java/Indonesia :00: Marianas H :27: Chile :36: Tonga H :43: Chile H01 N: number of seismograms stacked for each event M0: moment in units of N-m, obtained from the Harvard CMT catalog 19 and : unscaled and scaled durations, respectively Nzc: number 0 of zero-crossings Nas: number of aftershocks H98: Houston et al. [1998]; B: Bos et al. [1998]; CD: Campus and Das [2000]; H01: Houston [2001] continued on next page 102

121 Table 8.1 Deep earthquakes studied (continued from previous page) Date Time Latitude Longitude Subduction N MW M0 Depth 0 Nzc Nas Common to :15: Tonga :55: Chile :27: Izu-Bonin H :33: Java/Indonesia H :30: Tonga H :19: Tonga N: number of seismograms stacked for each event M0: moment in units of N-m, obtained from the Harvard CMT catalog 19 and : unscaled and scaled durations, respectively Nzc: number 0 of zero-crossings Nas: number of aftershocks H98: Houston et al. [1998]; B: Bos et al. [1998]; CD: Campus and Das [2000]; H01: Houston [2001] 103

122 8.2 Computation of source time functions We determine the STF of each earthquake by stacking P -waves recorded at teleseismic distances by the GSN and scaling the amplitude of the time function (in displacement units) so that its area equals the event moment. This method accurately reproduces the moment release history of large, deep earthquakes (e.g., Figure 5 of Houston et al. [1998]). Because the earthquakes are deeper than 100 km, the depth phases pp and sp are delayed by an interval longer than the duration of rupture. Therefore the P -wave stack represents a temporal history of moment release. To align the waveforms for stacking, we pick a common feature early in the P -wave arrival on each velocity seismogram. All traces for each event are adjusted to have the same polarity. The instrument response is removed by spectral deconvolution: we detrend, taper, and perform a water-level spectral division (Figure 8.2a). We normalize and linearly sum the aligned seismograms to create a stack (Figure 8.2b). Normalizing discards amplitude information, but correcting individual seismograms for path and source effects is unnecessary because we later insert the event moment by scaling the stack. The stack is performed in velocity units to cancel incoherent noise. The number of seismograms stacked per earthquake ranges from 10 to 53, with a mean value of 23 and a median of 21. (Figures E.2 and E.3 show how the the number of seismograms varies with depth and moment, respectively.) To pick the start and end times, we simultaneously examine the velocity, displacement and acceleration forms of the stack, seeking evident breaks in the waveform. Stacks of all 104

123 a) b) c) Figure 8.2: Computation of a source time function. (a) Deconvolved seismograms, aligned for stacking. (b) Stack of 36 seismograms with initiation and termination picks marked by dashed vertical lines. Noise reduction greatly improves ability to pick termination. (c) Integrated stack, scaled so that shaded region has area equal to event moment. 105

124 Velocity stacks (increasing depth) (16) (21) (24) (24) (39) (30) (18) (15) (26) (31) (10) (31) (12) (10) (20) (12) (16) (12) (25) (30) (28) (16) (10) (25) (38) (20) (29) (11) (20) (14) (29) (17) (16) (29) (11) (44) (22) (14) (26) (32) (10) (20) (34) (29) (53) (21) (17) (10) (19) (10) (26) (14) (32) (12) (34) Time [s] (20) Time [s] Figure 8.3: Velocity stacks in order of increasing depth. The start times are aligned at time 0; vertical bars denote the end times. Event depth, date, magnitude, and number of seismograms stacked are given. Continued in Figure

125 Velocity stacks (increasing depth) (20) (26) (41) (25) (16) (25) (37) (26) (15) (36) (25) (15) (18) (11) (29) (15) (17) (11) (24) (18) (32) (35) (25) (21) (13) (24) (14) (26) (47) (21) (14) (37) (33) (38) (12) (16) (10) (21) (41) (15) (39) (13) (16) (22) (12) (28) (28) (10) (15) (26) (31) (15) (31) (36) Time [s] (35) Time [s] Figure 8.4: Continued from Figure 8.3. Velocity stacks in order of increasing depth. The start times are aligned at time 0; vertical bars denote the end times. Event depth, date, magnitude, and number of seismograms stacked are given. 107

126 Moment-rate [N-m/s] x Bolivia M W km Ihmle & Jordan (1995) 8 x Tonga M W km McGuire et al. (1997) x x 1019 Moment-rate [N-m/s] 10 5 This study This study Time [s] Time [s] Figure 8.5: Comparison of our source time functions for June 9, 1994, Bolivia, and the March 9, 1994, Tonga, earthquakes (with Ihmlé and Jordan [1995] and McGuire et al. [1997], respectively). 111 earthquakes are shown in Figures 8.3 and 8.4, with the start times aligned at time 0 and picked termination times indicated by a vertical bar. The far-field displacement is proportional to the moment release rate at the source [Aki and Richards, 1980]. After the initiation and termination picks are made, we therefore integrate each stack to units of displacement and scale the stack amplitude so that the integrated area from start to end equals the total moment released during the earthquake (Figure 8.2c). In this form, the time function has units of moment-rate and is termed an STF. Figure 8.5 shows that this technique yields very similar STFs to those computed from inversion of waveforms. It is important that we pick the onset of large and small earthquakes similarly. The signalto-noise may be much lower for small events, and assigning start times when the waveform 108

127 d 2 M 0 /dt 2 [(N-m/s)/s] e e e Time [s] Figure 8.6: Start picks shown on derivatives of the source time functions, listed by increasing moment (smallest in upper left, largest in lower right). Vertical bar at time 0 indicates start pick. Preevent noise is retained. There is no systematic difference in identification of start times as a function of moment. 109

128 emerges from background could result in systematically picking smaller events later in rupture. Figure 8.6 shows the (differentiated) moment-rate functions, with the pre-event noise level retained. Although the signal-to-noise is sometimes quite small for the MW6.4 events, we do not see any systematic difference in the identification of start times. Earthquake durations are obtained from the initiation and termination picks and listed in Table 8.1. Because rupture duration is an important quantity for much of the following analysis, we examine several factors related to its measurement and the computation of scaled durations in Appendix E: The measured duration is not a function of the number of seismograms stacked (Figure E.4). We also find that directivity of the source is not likely to significantly affect our measured durations (Figure E.5). The picking procedure invokes some subjective judgement, so we check our consistency by applying an automated picking algorithm. The duration picks made by this method yield similar results to those picked by hand (Figure E.6). The analysis that follows is based on the human picks because we decided that the improved accuracy accorded by human judgement outweighed the objectivity of a predefined algorithm. Figure E.7 compares the durations measured here for events common to four other studies (Table 8.1) and shows that they generally agree even when different processing techniques and/or waveforms were used. 110

129 8.3 Scaling relationships Starting from the definition of moment, one can derive a standard relation between earthquake duration and moment [e.g., Kanamori and Anderson, 1975; Vidale and Houston, 1993]: / M 1=3 0 (8.1) VS 1=3 where is duration, M 0 is moment, VS is the source region shear-wave velocity and is the stress drop. This expression assumes that rupture velocity is a constant fraction of VS, and that a self-similar relation exists between fault length, average slip and seismic moment. We will use Equation 8.1 to re-scale the STFs to have a common size. First, we investigate whether the measured durations obey this expression. For constant VS and stress drop, Equation 8.1 predicts log( ) is proportional to log(m 0 ) with slope 1/3. Observational evidence supports this relationship within 0:1 [Furumoto and Nakanishi, 1983; Tanioka and Ruff, 1997; Singh et al., 2000]. Some recent studies of deep earthquakes have found slopes of: 0.25 [Bos et al., 1998], 0.32 [Houston et al., 1998], and 0.38 [Fukao and Kikuchi, 1987]. The durations from Table 8.1 are plotted in Figure 8.7; the least-squares fittoall the data has slope 0:26 0:03. The misfit from slope 1/3 may derive at least partially from a non-uniform distribution of moments with depth (Figure 8.8). In addition, the earthquakes in Figure 8.7 occur over a wide depth range in which VS is not constant, but increases as a function of depth, which can be seen in the generally shorter durations for the deeper events. We account for the increase in VS by multiplying by VS (h) (where h is source depth), using a radial velocity 111

130 10 2 Duration [s] 10 1 slope = 1/ km least squares fit km slope = km Moment [N-m] Figure 8.7: Unscaled durations of time functions vs. earthquake moment. Based on simple scaling relations, we expect the duration to follow / M n 0, with n =1=3. The dashed line describes this relationship, with =6:0 satthe reference moment, N-m. The solid line plots the least-squares fit tothe data from all depths, with slope 0:26 0:

131 Moment [N-m] Depth [km] Figure 8.8: Moment vs. depth. No systematic trend exists, but the distribution is not uniform. 113

132 km km 550 km (Duration x V S ) [km] 10 2 slope = 1/3 least squares fit slope = Moment [N-m] Figure 8.9: Duration V S (h) vs. moment, where h is source depth. Dashed line plots / M n 0, with n = 1=3 and = 6:0 satthe reference moment, N-m. The solid line plots the least-squares fittothe data, with slope 0:27 0:03. Accounting for the depth dependence of V S brings the slope closer to 1/3. model for the mantle (iasp91 [Kennett and Engdahl, 1991]), to obtain an effective source dimension (not the true source dimension, since the rupture velocity is somewhat less than VS(h)). Figure 8.9 shows this velocity-corrected duration, or effective source dimension, as a function of moment. The slope of the least-squares fit isnow 0:270:03, sothe correction accounts for some but not all of the disagreement. There are additional factors that may account for the discrepancy, including the possible variation of stress drop and the combination of subduction zones with different thermal properties that may affect source properties such as duration. We shall examine these factors in Chapters 9 and 10. Given these uncertainties in fitting for the scaling exponent, we decide to adopt the theoretical value (1/3) in the scaling procedure described below. (Figure 114

133 E.9 shows that the results using the empirical fit for the scaling exponent are very similar to those shown in Chapter 9.) 8.4 Moment- and duration-scaling Since an earthquake s moment determines its duration as a first-order effect, and the moments of the 111 earthquakes vary by nearly three orders of magnitude, we would like to remove the effect of seismic moment from the STFs by scaling them to a common reference size. This allows us to compare the scaled STFs, visually and quantitatively, as a function of depth or subduction zone. Scaling also enables us to stack together STFs of earthquakes within various subgroups to compare their average shapes. We follow the procedure described in Houston et al. [1998] for scaling the individual time functions. We employ two methods of scaling: moment-scaling and duration-scaling. M ref 0 In the former, the time axis of the STF is scaled by M 0 and the amplitude axis by M ref 2=3 0, where M 0 is the earthquake moment and M ref is the reference moment, chosen 0 M 0 here to be illustrates the process. 1=3 N-m. After this procedure all STFs have an area equal to M ref 0. Figure 8.10 The scaled duration 0 is thus given by 0 = M ref 1=3 0 (8.2) M 0 where is the unscaled duration. Table 8.1 provides scaled durations. Figure 8.11a shows scaled durations versus moment. As we would expect from Figure 8.7, there is a slight misfit 115

134 a) 4 x 1019 M W 7.6 area=m 0 =2.7x x 1019 M W 6.4 area=m 0 =5.1x10 18 Moment-rate [N-m/s] b) 4 x 1018 area=m 0 ref = x 1018 area=m 0 ref =10 19 Moment-rate [N-m/s] Time [s] Time [s] Figure 8.10: (a) STFs for two earthquakes with MW7.6 and MW6.4. The factor of 50 difference in moment overwhelms our ability to compare the STFs. (b) STFs after moment-scaling. The curves now have equal areas and can be directly compared. from the predicted slope of 0. And, as before, we can improve the agreement by multiplying the (scaled) duration by VS to account for varying source-region velocity (Figure 8.11b). Duration-scaling is useful for averaging groups of STFs (such as those within a given depth range and/or subduction zone). In duration-scaling, STFs are squeezed or stretched in time so that they have a common reference duration ( ref =6s), and then the amplitude is adjusted so that the area under the scaled STF equals the reference moment. (Houston et al. [1998] provides further discussion of duration-scaling.) Because all duration-scaled STFs have equal durations, a stack of them gives a better impression of the average shape than one of moment-scaled STFs, which produces an extended tail of moment release due to the varying durations. 116

135 Scaled duration [s] km km 550 km least squares fit slope = Moment [N-m] (Scaled duration x V S ) [km] km km 550 km least squares fit slope = Moment [N-m] Figure 8.11: (a) Scaled duration vs. moment. Slope is 0:07 0:02. (b) Velocity-corrected scaled duration ( 0 VS (h). Slope is 0:06 0:02. Weexpect 0 slope after moment-scaling. 117

136 8.5 Frequency-domain stacking Seismically-radiated energy can be computed by integrating the square of first derivative of the moment-rate function, which is more easily done in the frequency-domain. Therefore, to compute energy, we compute spectra from the original seismograms and re-stack after correcting for source and path effects. We do not simply take the spectrum of the STFs determined in Section 8.2 because the time-domain stacking reduces the high-frequency content somewhat and because we will later want to compute the energy-to-moment ratio, for which we want energy to be an independent quantity. Furthermore, this provides a check that our source- and path-corrections yield the same moment as long-period inversions. To compute an earthquake s spectral stack, we deconvolve the instrument response from the velocity seismograms as before. We then Fourier-transform the deconvolved seismograms using a cosine-squared taper, and integrate by dividing by 2f, where f is the frequency, to obtain an instrument-corrected displacement spectrum ^u(f). The moment rate spectrum ^_ M 0 (f) for each seismogram can be recovered by applying source- and path-corrections to ^u(f) [Lay and Wallace, 1995]: M ^_ 0 (f) = 4V 3R P E g()r C eft ^u(f) (8.3) where and V P are the density and P -wave velocity, respectively, at the source depth (from iasp91 [Kennett and Engdahl, 1991; Kennett et al., 1995]), R E is the radius of the Earth, t is the attenuation operator (computed from the Q model of Warren and Shearer [2000]). 118

137 g() is the geometrical spreading factor, R represents the radiation pattern, and C accounts for the free surface effect [Aki and Richards, 1980]. A water level of 0.5 is implemented for the radiation pattern factor. We stack the complex-valued moment-rate spectra, preserving both amplitude and phase, and then differentiate and square the result to compute the energy radiated [Haskell, 1964; Vassiliou and Kanamori, 1982; Houston, 1990]: 1 E rad =2 + 15V 5 P 1 10V 5 S Z1 0 j2f ^_ M 0 (f)j 2 df (8.4) Radiated energy and the apparent stress will be examined in Chapter

138 Chapter 9 Depth dependence In this chapter, we examine the depth dependence of deep earthquake properties. Temperature, pressure, material density, shear-wave velocity, the amount of available metastable olivine, and stress orientations and magnitudes all change in the plate as a function of depth. It is therefore reasonable that properties of moment release in earthquakes will also change. We will measure the depth dependence of basic properties from our STFs such as rupture duration, shape, energy release, and stress drop. To facilitate comparison as a function of depth, we group the STFs into three ranges: 100 to 350 km (65 events), 350 to 550 km (18), and deeper than 550 km (28). The division at 350 km occurs at approximately the depth of the global minimum in seismicity, as well as the depth below which proposed explanations for some deep earthquakes (dehydration of the slab and reactivation of faults) are no longer viable [e.g., Kirby et al., 1991; Jiao et al., 2000]. The division at 550 km falls naturally out of the observed properties, as we will see below. 120

139 9.1 Source time functions The 111 moment-scaled source time functions are shown in Figures 9.1 and 9.2, presented in order of increasing depth. All of the STFs in the two figures have the same area (moment), with scaled durations computed as described in the previous chapter. We observe an abrupt change in character (duration, shape, variability within the population) below about 550 km. Events deeper than 550 km display less variability than those in the shallower depth ranges. We observe greater consistency of duration and shape in this group. The deepest events possess short scaled durations, with a typical value around 6 seconds. Only one event below 550 km has a scaled duration exceeding 10 seconds. The shapes of this group s time functions are generally simple, with a single episode of significant moment release and positive skewness [Pollard, 1977], in which the STF is asymmetric with the peak closer in time to the beginning. These STFs are more sharply peaked, with higher maximum moment-rates, since they release the same scaled moment in a shorter time. We do not observe an abrupt change between the shallowest group (100 to 350 km) and the middle group (350 to 550 km), as we do between the middle and deep groups. Unlike the deepest earthquakes, the earthquakes in shallower depth ranges exhibit a wide range of behaviors. Scaled durations range from values similar to those of the deepest events to three times longer. There is no consistent pattern to the time functions shapes. Some are simple like the deepest group, but many are complex, with several episodes of significant moment release. A slightly higher fraction of shallow and middle group events STFs have negative skewness, in which the rise to peak moment-rate is gradual and the decline to termination 121

140 Moment-rate [N-m/s] Moment-scaled time functions (increasing depth) e Time [s] Time [s] Figure 9.1: Moment-scaled source time functions in order of increasing depth. Event date, magnitude and depth are given. All STFs have been scaled to a common moment. The vertical bar indicates scaled duration of rupture. The deepest events have shorter durations than other depth ranges, and are more uniform. The shallowest and intermediate depths have greater variability of durations, with longer values. Continued in Figure

141 Moment-scaled time functions (increasing depth) Time [s] Time [s] Figure 9.2: Continued from Figure 9.1. Moment-scaled source time functions in order of increasing depth. Event date, magnitude and depth are given. All STFs have been scaled to a common moment. The vertical bar indicates scaled duration of rupture. The deepest events have shorter durations than other depth ranges, and are more uniform. The shallowest and intermediate depths have greater variability of durations, with longer values. 123

142 is comparatively rapid. In the following sections, we will quantify these observations and measure other properties as a function of depth. 9.2 Duration The scaled durations of the 111 STFs are plotted as a function of depth in Figure 9.3. The deepest group appears distinct from the shallower groups, with the shortest average scaled duration and the least scatter. The shallower ranges mean values lie within the standard error of each other. To assess whether the depth ranges are actually distinct, we perform a bootstrap resampling analysis. We make 10,000 resamplings of each population: each resampling consists of a set of N randomly-selected events from the depth range population being tested, where N is the number of events in that depth range. (Selected events are returned to the sample, so they can be chosen more than once in a resampling). We compute the mean scaled duration for each resampling, and plot the distribution of the means (Figure 9.4). This analysis demonstrates that the deepest group is distinct from the other two, but the 100 to 350 km events cannot be distinguished from the 350 to 550 km events. In Appendix E, we show that the automated duration picks mentioned in Section 8.2 yield a similar depth dependence (Figure E.8) as does using the best-fit scaling exponent from Figure 8.7 rather than the theoretical value of 1/3 (Figure E.9). 124

143 < > = 9.1±0.3 s = 8.7 s median Scaled durations vs. depth < > = 9.2±0.8 s = 9.4 s median < > = 6.3±0.3 s = 6.2 s median Scaled duration [s] V [km/s] s V S Depth [km] Figure 9.3: Scaled duration vs. depth (left axis). The average and median durations for each depth range are given. The events deeper than 550 km have short durations and not much scatter. The km and km depth events have longer average durations and much greater individual variation. No obvious break distinguishes the two shallower groups. The red line depicts 1=V S vs. depth (right axis), with constant of proportionality chosen to match the best fit to the data at 100 km. The overall decrease in duration from 100 km to 650 km is greater than predicted by the inversevelocity curve. The similar durations of the km and km populations and the abrupt change at 550 km imply a more complicated relationship of scaled duration with depth than / 1=V S. 125

144 resamplings km km 550 km # Mean scaled duration Figure 9.4: Distribution of mean scaled durations for each depth range from 10,000 bootstrap resamplings. The 550 km events are clearly a separate population from the km and km events. The shallower groups, however, overlap and are not statistically different. 126

145 A decrease in duration with depth has been noted previously for deep earthquakes [Furumoto and Nakanishi, 1983; Fukao and Kikuchi, 1987] and shallow earthquakes (<100 km) [Bilek and Lay, 1999; Houston, 2001]. Equation 8.1 predicts a decrease in scaled duration at greater depths due to the increase in shear-wave velocity, assuming constant stress drop. The solid line in Figure 9.3 plots 1=V S, with the constant of proportionality chosen so the value at 100 km matches the least-squares fittothe data. The total duration decrease in the data exceeds that predicted from the increase in rupture speed. From 100 to 600 km, the inverse of shear wave velocity (1=V S ) decreases 17.9%. We perform a least-squares fit to the durations; the difference between the fitted function at 100 km and 600 km is 26.4%. If we compare median scaled durations, the decrease from the km group to the 550 km group is 28.7%. Moreover, the durations do not decrease steadily with depth following 1=V S (Figure 9.3). Rather, the entire decrease occurs at the break at 550 km. An alternate model for the depth dependence could be obtained by fitting separately the depths 100 to 550 km and below 550 km (Figure 9.5). The shallow fit has almost 0 slope, while the deeper events have a slight increasing trend. The amount of duration decrease over the entire depth range has been controversial [Vidale and Houston, 1993; Bos et al., 1998; Houston et al., 1998; Singh et al., 2000]. Vidale and Houston [1993] found a relatively large decrease in duration from 100 to 600 km depth (45.5%) using short-period stacks, but some of their longest scaled durations in the 100 to 250 km depth range may have resulted from additional seismic phases arriving before the end of the source waveform [Bos et al., 1998]. However, the amplitudes of the core- 127

146 20 Scaled durations vs. depth Scaled duration [s] fit to all data separate fits for km and 550 km Depth [km] Figure 9.5: Two least-squares fittings to the scaled durations. The dashed line is a least-squares fit to all the data. The dot-dash line consists of separate fits to the 100 to 550 km data and 550 km data. 128

147 reflections posited by Bos et al. [1998] are generally small, and the short-period stacks of Vidale and Houston [1993] probably have greater sensitivity to weak endings. Our results are closer to those found by Bos et al. [1998] (22.2%) and Houston et al. [1998] (23.5%). All three exceed the amount of decrease in 1=V S. Other recent studies have found depth dependence similar to our observations. Figure 9.6 compares the depth dependence of scaled duration for this study and four previous studies of deep earthquakes: Houston et al. [1998], Bos et al. [1998] (total event durations), Campus and Das [2000] (high-frequency durations) and Houston [2001]. The variations of scaled duration with depth in Figure 9.6 are generally similar: the deepest events are shortest and the 350 to 550 km depth events durations do not show the expected decrease with depth, although there is considerable scatter. (Figure E.7 in Appendix E shows how durations for events common to these four previous studies compare to our values. There is good agreement, even for different processing techniques.) The main observations from analysis of scaled duration are: (i) discontinuity in the distribution at 550 km; (ii) overall change in duration exceeds change in 1=V S, but no trend from 100 to 550 km. This suggests a different population of earthquakes below 550 km, possibly due to a change in mechanism, which may be manifest in the rupture velocity. The km and km may be part of the same population, although traditionally explanations of the shallower group do not apply in the middle depth range. 129

148 20 (a) This study (b) Houston et al Scaled duration [s] 20 (c) Bos et al (e) Houston (d) Campus and Das Depth [km] Depth [km] Figure 9.6: Scaled duration vs. depth for (a) this study and four others: (b) Houston et al. [1998]; (c) Bos et al. [1998]; (d) Campus and Das [2000]; and (e) Houston [2001]. Although the methods for measuring the durations are different, the pattern of shorter durations for deepest events and longerthan-predicted durations of km events is found in all five panels. Filled circles indicate mean values in ranges , and 550 km. Vertical bars on the filled circles indicate standard errors; in most cases they are smaller than the filled circle. 130

149 9.3 Shape Complexity of STF shape results from temporal and spatial variability in rupture progression and might therefore reflect the physical state at the rupture plane. Greater heterogeneity of material properties or stress field on the fault plane may produce more complicated time functions. In the 350 to 550 km range, Houston et al. [1998] found complicated STFs with somewhat more late moment release, but others have found no variation of STF shape with depth [e.g., Campus and Das, 2000]. We observe a change in character in the STFs at around 550 km: deeper STFs have relatively simple shapes, while shallower STFs exhibit a wide variety of shapes, from simple to multi-peaked (Figures 9.1 and 9.2). For the deepest STFs, the timing of moment release is rather condensed, and there is less variability within the group. Shallower than 550 km, the timing of major moment release varies widely, from relatively early during rupture to much later, with no systematic tendency for early or late moment release. In more complicated shallower STFs, moment release can be spread out over several episodes. Any depth dependence of the complexity of STF shapes does not result from variations in the number of seismograms stacked. The mean number of seismograms per event remains roughly constant as a function of depth (Figure E.3). We will examine shape by averaging groups of time functions, by treating STFs as statistical distributions to compute their means and widths, and by counting subevents. We first investigate how average shape varies with depth, by stacking scaled STFs within each depth range (Figure 9.7). The deepest events stand apart from the others: they initi- 131

150 Moment-rate [10 18 N-m/s] Moment-rate [10 18 N-m/s] Stacks of moment-scaled time functions Time [s] Stacks of duration-scaled time functions km (65) km (18) 550 km (28) km (65) km (18) 550 km (28) Time [s] Figure 9.7: Average STFs in three depth ranges. Number in parentheses indicates number of time functions in each stack. (a) Stacks of moment-scaled STFs. (b) Stacks of duration-scaled STFs. In (a), an extended tail of moment release results from combining STFs of varying duration. Combining duration-scaled stacks, as in (b), eliminates this problem. The stacks in (b) are re-duration-scaled to have the average scaled duration of each group to emphasize the differences. The 550 km average shape rises faster and has shorter duration. It has a higher peak moment-rate since it releases the same scaled moment in a shorter time. The km and km stacks are quite similar. The bumpier appearance of the km stack results from having less than one-third as many STFs contributing. 132

151 ate faster, reaching higher peak moment-rates earlier. The shallower two depth ranges are very similar to each other, with broader average shapes (The km average STF is smoother than the km average STF partly because more than three times as many events are stacked.) Another way to examine the STFs shapes is to treat them as statistical distributions. We can then make measures of shape such as the mean and the second moment about the mean, as well as skewness. Figure 9.8 shows the first moment (mean) of the STFs as a function of depth. This weighted average of the timing of moment release provides an alternate means of measuring duration and displays a similar pattern to that of the scaled durations. The second moment about the mean (Figure 9.8) measures the width of the STFs. We find moment release in the earthquakes below 550 km is more concentrated in time. Twenty-four of 28 events deeper than 550 km have positive skewness; a similar percentage of 350 to 550 km events (15 of 18) do, too. But only 50 of 65 events 100 to 350 km have positive skewness. A negative skewness could indicate heterogeneity that prevents rupture from getting up to speed quickly. Finally, we measure complexity of the STFs. We note that STFs of larger earthquakes should have greater detail visible, even after moment-scaling. For example, the two largest earthquakes (June 9, 1994, depth 637 km and June 17, 1996, depth 587 km) have higherfrequency features not generally visible in the other scaled STFs. The source detail visible in scaled STFs of smaller earthquakes will be reduced relative to that of larger events because smaller earthquakes have higher corner frequencies and attenuation acts to reduce 133

152 First moment of moment-scaled time functions First moment [s] Mean values in each depth range: km: 4.3 ± km: 4.3 ± km: 2.8± Depth [km] Second moment [s] Second moment of moment-scaled time functions Mean values in each depth range: km: 1.6 ± km: 1.7 ± km: 1.1± Depth [km] Figure 9.8: First and second moments of the moment-scaled STFs vs. depth. By treating the STFs as probability density functions, we can compute standard measures of shape. The first moment (or mean) provides a weighted average of the timing of moment release. The deepest events have smaller first moments, consistent with their shorter durations and more peaked shapes. The second moment about the mean measures the width of the STFs and shows that moment release is much more concentrated in time for deep events. 134

153 high-frequency content in waveforms [Aki, 1967; Houston et al., 1998]. To equalize the scaled STFs so that we may quantify the variation of shape with depth, we apply a low-pass filter with a cosine taper between 0.3 and 0.6 Hz in scaled frequency. This reduces the detail in large events and ensures that the complexity of scaled STFs of different-sized events can be compared directly. Zero-crossings of the first derivative (points where the value crosses from negative to positive or vice-versa) mark peaks and troughs in the original STF and therefore indicate subevents. About half (54) of our STFs have one zero-crossing and are therefore singlepeaked. This agrees with previous counts of deep earthquake subevents [Fukao and Kikuchi, 1987; Houston and Williams, 1991; Bos et al., 1998; Houston et al., 1998]. However, in the km depth range, only 33.3% are single-peaked, while in the 550 km depth range, 64.3% are single-peaked. Houston et al. [1998] found a similar variation, although Bos et al. [1998] found no difference between the depth ranges. Figure 9.9 shows the average number (by depth range) of zero-crossings of the momentscaled STFs. On average, the deepest events are simpler, while the shallower groups have more complex rupture histories. This pattern is similar to the results of Houston et al. [1998]. The major observations of deep earthquake STF shape are: (i) shorter and more peaked average shape for 550 km events; (ii) earlier mean time of moment release and narrower width for550 km events; (iii) fewer subevents for550 events and more subevents in 350 to 550 km events. These results suggest more homogeneous fault planes deeper than 550 km, resulting in smooth rupture propagation and simple time histories of moment release 135

154 4 Zero-crossings of 1st derivative of time functions Moment-scaled 3 Average # of zero-crossings >=550 Depth ranges [km] Figure 9.9: Average number of zero-crossings of first derivatives of moment-scaled time functions by depth range. This is a measure of the number of subevents in the time function. The km events average the most subevents, while the 550 km events average the fewest. The STFs were low-pass filtered to account for differential effects of attenuation on large and small earthquakes. Error bars represent standard errors of the means. 136

155 with shorter durations. Shallower depth ranges may have more heterogeneity that impedes rupture. 9.4 Stress drop The stress drop during earthquakes provides information about the forces driving rupture and the general state of stress in the surrounding region. For deep earthquakes, the stress drop is of particular interest because it provides a minimum measure of the shear stresses in subducting plates that result from volumetric changes during phase transformations, thermal expansion from heating, and buoyancy forces. For shallow earthquakes, stress drop is traditionally taken to be constant, ranging between 1 and 10 MPa [Kanamori and Anderson, 1975]. The behavior of stress drop as a function of depth remains uncertain [Frohlich, 1989]. Houston and Williams [1991] obtained stress drops for 68 earthquakes deeper than 120 km from spectra of broadband seismograms and found no trend with depth. Wyss and Molnar [1972] estimated stress drops from body wave spectra and found slightly elevated values between about 100 and 400 km, but values similar to those near the surface for deeper events. Fukao and Kikuchi [1987] inverted waveforms to obtain STFs for 18 earthquakes and found stress drops varying as a function of maximum moment rate down to 400 km but constant stress drops deeper. Mikumo [1971] found stress drops increasing steadily with depth. The stress drop in deep earthquakes is difficult to measure because we usually lack in- 137

156 formation about the size of the fault plane. (Aftershocks can be used to delineate the rupture area in shallow earthquakes, but the small number of aftershocks hampers this technique for deep events [Frohlich, 1989; Wiens and McGuire, 2000].) However, by assuming rupture velocity is a constant fraction of V S,wecan use the STF durations and scaling laws to estimate the fault area and thereby static stress drop. The static stress drop provides a measure of the overall reduction in stress as a result of the earthquake [Ruff, 1999] Circular crack model To interpret the STF durations in terms of static stress drop, we employ the model of an expanding circular crack to describe rupture. We begin with the definition of moment (M 0 ): M 0 = A d (9.1) where is the shear modulus, A is fault area, and d is the average slip. For a circular fault with radius r, A = r 2, and the stress drop is [Eshelby, 1957; Keilis- Borok, 1957]: 7 d = 16 r (9.2) Substituting 9.2 and the definition of A into 9.1, we obtain: M 0 = 16 Ar (9.3) 7 = 16 7 r3 (9.4) Rupture duration is given by = L=VR, where L is the fault dimension and VR is the rupture velocity. The relationship between L and r depends whether we consider rupture to 138

157 have propagated unilaterally (L = 2r) or bilaterally (L = r). Here we assume unilateral rupture and substitution into 9.4 yields: M 0 = VR (9.5) 2 Rearranging, we obtain an expression for stress drop: = M 0 (9.6) 16 V R We can express V R = fv S, where V S is the source-depth shear-wave velocity, and f represents the fraction of V S at which rupture propagates, usually taken to be 0.8 [Kanamori, 1994], although it may be lower for deep earthquakes [Fukao and Kikuchi, 1987; Willemann and Frohlich, 1987]. The static stress drop as a function of depth is shown in Figure The 550 km earthquakes have a higher average stress drop, mostly representing an absence of low stress drop events. The 350 to 550 km range has a disproportionate number of low stress drop events. Chung and Kanamori [1980] found a similar pattern, with a minimum between 450 and 560 km. The pattern is the inverse of Figure 9.3, since stress drop is inversely proportional to scaled duration (Equation 9.6). In fact, Figure 9.10 represents a correction to the scaled durations by V S,soone can interpret this result as the degree of departure from the 1=V S prediction in Figure 9.3. The Bolivia, June 9, 1994, earthquake s rupture velocity is recognized to have been unusually slow (1.5 km/s) [e.g., Wiens, 2001]. If we use this value in Equation 9.6 we obtain a (larger) corrected static stress drop of 37 MPa, which is consistent with others results, al- 139

158 km km 550 km Mean: 1.5± ± ±0.2 (3.4±1.3) Median: (1.9) Stress drop (static) [MPa] Depth [km] Figure 9.10: Static stress drop (computed from Equation 9.6, using f = V R =V S =0:8) vs. depth. The red symbol represents a recalculation for the Bolivia, June 9, 1994, event, using a slower rupture velocity (V R =1:5 km/s) [Wiens, 2001]. There is a slight increase for the stress drops deeper than 550 km, which can be viewed as a reduction in the number of low stress drop events relative to the shallower depth ranges. Median and mean values are given for each depth range (red numbers use the recalculated value for Bolivia). 140

159 beit on the low end of the range [Wiens, 2001]. Our stress drops for some other well-studied events are also low. For Tonga, March 9, 1994, we find 4.5 MPa, compared to MPa [Tibi et al., 1999]. For Flores Sea, June 17, 1996, we find 3.2 MPa, compared to 10 MPa [Antolik et al., 1999] and MPa [Tibi et al., 1999]. Why do our results differ? In some cases, such as Bolivia, the actual rupture velocity may be slower than 0:8 VS. This means a smaller area slips in a given duration, which would raise the stress drop over our estimate (Equation 9.6). The aspect ratio of the fault and the nature of rupture propagation could be very different from unilateral rupture across a circular fault, which would change the constants in Equation 9.6. Another factor is the way we pick durations. The final stages of rupture likely have smaller average slip, and including these will tend to lower the value we find for stress drop. These types of uncertainties are not unusual in estimates of stress drop [Frohlich, 1989]. One additional comment is that the point measurement of duration is not ideal for an average property such as stress drop; using the corner frequency of the spectrum may yield better results. Shallow (less than 100 km) stress drops are usually 1-10 MPa, so our results are within that range. However, if we accept that our values are consistently low for the reasons discussed, the implication is that deep earthquake stress drops are generally higher than shallow ones. For the largest deep earthquakes, static stress drop seems to fall within MPa But, even the highest stress drops are much lower than calculated differential stresses from 141

160 phase transformations [e.g., Devaux et al., 2000]. 9.5 Energy The amount of energy released in earthquakes is a fundamental quantity for our understanding of rupture dynamics and the physical state of fault planes. In particular, for deep earthquakes the seismic efficiency (the ratio of energy radiated as seismic waves to total strain energy released) may be quite low (0.1) which could be implicated in failure mechanisms such as frictional melting [Frohlich, 1989; Kanamori et al., 1998; Wiens, 2001]. Unfortunately, radiated energy is a notoriously difficult parameter to measure even for shallow earthquakes [Kanamori, 1994; Winslow and Ruff, 1999], and particularly for deep earthquakes, for which an independent measurement of the stress drop cannot be obtained easily [Frohlich, 1989]. However, using the frequency-domain stacking method described in Section 8.5 we can accurately compute the radiated energy (E rad ). As a check, for the Bolivia, June 9, 1994, event, our value (1: J) is similar to previous results (1:5 5: J[Estabrook and Bock, 1995; Kanamori et al., 1998]). For Tonga, March 9, 1994, we find 8: J, compared to 3: J[Tibi et al., 1999]. For Flores Sea, June 17, 1996, we find 9: J, compared to 2: J[Tibi et al., 1999]. Figure 9.11 shows E rad versus M 0. The energy-to-moment ratio (E rad =M 0 ) represents the apparent strain release in the earthquake ( apparent because it only reflects energy that is seismically radiated. There can be significant potential strain energy that goes into over- 142

161 km km >=550 km Energy (J) Moment (N-m) Figure 9.11: Energy computed from the spectra stacks vs. moment. The log-average energy-tomoment ratio is 0:7 10 5, with the 100 to 350 km events having a slightly higher average than the 350 to 550 and 550 events. These values are lower than those of crustal earthquakes, but in agreement with previous estimates for deep earthquakes. This suggests a lower average stress or lower seismic efficiency for deep-focus earthquakes. Lines of constant energy-to-moment ratio are drawn for values of (0:1 1:0 10:0)

162 coming resistance to fracture and/or friction and is not observed in the seismic waves.) Our energy-to-moment ratios range from about 6: to 1:0 10 4, but nearly half fall within 0:5 2: The log average is 0:710 5, similar to the value found by Winslow and Ruff [1999] for a smaller set of large deep earthquakes, but lower than is typical for crustal earthquakes ( [Kanamori, 1977]). Departure from self-similarity would be reflected in a variation of E rad =M 0 with moment [Kanamori and Heaton, 2000]. We do not find any systematic variation with moment, but our events encompass a relatively narrow range compared to most studies of self-similarity [Kanamori and Heaton, 2000]. The depth dependence in Figure 9.11 is very small. The log average for 100 to 350 km events is 0:810 5 compared to 0:610 5 for both the 350 to 550 km and 550 km events. Kikuchi [1992] found a log average of 0: for five earthquakes deeper than 550 km Apparent stress The energy-to-moment ratio can be used to compute the apparent stress [Wyss and Brune, 1968; Kanamori and Anderson, 1975]. Apparent stress is similar to apparent strain in the sense that what we can observe seismically may be incomplete. We can only measure the product of average stress and efficiency, as shown below. The seismic efficiency is the ratio of the seismically-radiated energy to the total strain energy released [Kanamori and Heaton, 2000]: = W E F EG W = E rad W (9.7) where W is the total elastic strain energy released, EF is heat lost to friction, and EG is 144

163 fracture energy. W can be written [Knopoff, 1958; Orowan, 1960]: W = 1 2 ( )A d =A d (9.8) where 0 and 1 are the initial and final stresses, respectively, A is fault surface area, and d is average slip. is the average stress during the earthquake. Substituting the definition of moment M 0 = Ad into Equation 9.8, we obtain: W = M 0 (9.9) We use this expression for W in Equation 9.7 to obtain: = E rad M 0 (9.10) Rearranging, we define the apparent stress app : app = E rad M 0 (9.11) Only a fraction of the average absolute stress is apparent in seismic waves. The apparent stress embodies a tradeoff between average stress and seismic efficiency. As more work goes into overcoming friction and/or creating new surface, the average stress rises and drops. Without additional information, we can only measure app. Using the values of energy in Figure 9.11 and a depth-dependent (PREM [Dziewonski and Anderson, 1981]), we compute app as a function of depth using Equation 9.11 (Figure 9.12). The roughly constant apparent stress with depth is consistent with previous re- 145

164 km km 550 km Mean: 0.8± ± ±0.4 Median: Apparent stress [MPa] Depth [km] Figure 9.12: Apparent stress vs. depth. The apparent stress is roughly constant as a function of depth. The median values in all three depth ranges are similar. sults [Abe, 1982; Houston and Williams, 1991]. As we will find in the next section, constant apparent stress combined with increased stress drops for the deepest events implies a low maximum seismic efficiency for those events Seismic efficiency Seismic efficiency is a measure of how much of the strain energy released goes into elastic waves versus fracture energy and overcoming friction. We cannot measure the absolute levels of stress on the fault, so we cannot determine the change in strain energy [Kanamori, 1977]. However, it is possible to use the ratio of apparent stress to static stress drop to estimate a maximum for the efficiency with which energy is converted to elastic waves. The apparent stress is plotted versus static stress drop in Figure This ratio is a 146

165 10 Apparent stress [MPa] Static stress drop [MPa] Figure 9.13: Apparent stress vs. static stress drop. Twice the ratio provides a measure of the seismic efficiency. The red symbol represents the corrected static stress drop for the Bolivia, June 9, 1994, event. 147

166 10 2 Maximum seismic efficiency Depth [km] Figure 9.14: Maximum seismic efficiency vs. depth. The values higher than one provide further evidence that our stress drop results are low. The depth dependence is consistent with previous suggestions of lower efficiency for the deepest events. The value for Bolivia, June 9, 1994, using the modified stress drop is measure of the seismic efficiency. To derive an expression for maximum efficiency, we note that if the stress drop is complete, then = 0. More generally, 1 0 and 0. Making use of these limits and substituting for = 1 2 ( ),wecan rewrite Equation 9.10 as an inequality: 2E rad M 0 max (9.12) In Figure 9.14, we investigate how max varies with depth. Some max exceed 1, but the actual efficiency is likely much smaller than the limiting value. Furthermore, we previously discussed reasons that actual static stress drops are probably larger than our estimates. For the Bolivia, June 9, 1994, earthquake we find max = 0:048 using the corrected static stress drop. This agrees well with previous estimates ( max =0:036 [Kanamori et al., 148

167 1998]). The trend is toward lower max with increasing depth. This is consistent with previous suggestions that deep earthquakes have low seismic efficiencies. Kikuchi [1992] used independent estimates of radiated energy and strain drop to compute seismic efficiencies and found values between and 0.13 for large earthquakes deeper than 100 km. Wiens [2001] reported 0:01 max 0:37 for seven events deeper than 540 km with MW 7:6. For a general understanding of deep earthquakes, the question is whether the Bolivia event was unusual in this respect. The rupture velocity can be related directly to the efficiency such that low VR implies high energy loss at the crack tip and therefore low [Kanamori et al., 1998]. From Equation 9.6, low VR implies high. Thus the viewpoints are consistent, and independent measures of the rupture velocity (or the fault area and geometry combined with duration) for all the events would resolve whether low efficiency is a general property. Rupture velocity was slow for two large South American deep earthquakes (1970 Colombia and 1994 Bolivia) [Kanamori et al., 1998], but it is unclear whether this is the case in general for deep events [Wiens, 2001]. From this reasoning, we are faced with the problem with which we began when considering stress drop: lack of knowledge about the size of the fault plane. For individual well-studied events, this information can be determined, but to study large numbers of earthquakes, some assumptions are required. So, while we cannot determine absolute levels of stress drop or seismic efficiency, we have found the relative variation of these properties with depth. Lower efficiency at depth 149

168 suggests a more dissipative process, though it is not clear how to reconcile this result with the faster durations and simpler STFs. 9.6 Summary We divide our events into depth ranges 100 to 350 km, 350 to 550 km and 550 km. The phenomenological evidence presented consistently shows earthquakes deeper than 550 km to have different source properties from shallower events. Below 550 km, scaled durations decrease, STF shapes are more compact and simpler, static stress drops increase, and seismic efficiency is lower. (Alternatively, rupture velocity as a fraction of V S increases below 550 km.) The shallower depth ranges scaled durations are statistically indistinguishable from each other, though the 350 to 550 km group has more subevents on average. The populations are similar although many of the proposed mechanisms for 100 to 350 km earthquakes do not apply at greater depths. The total decrease in scaled duration from 100 km to 600 km exceeds that predicted from the increase in V S. However, the entire drop occurs at 550 km, as duration remains roughly constant between 100 km and 550 km, despite the steady increase of V S throughout the upper mantle and transition zone. Consequently, either static stress drops are smaller between 350 and 550 km (Figure 9.10) or f = V R =V S drops between 100 and 550 km. Whether this implies a change in mechanism around 350 km is unclear. Perhaps the 150

169 same mechanism applies on more heterogeneous fault planes, or perhaps transformational faulting begins around this depth. These observations offer stronger support for a change in mechanism or in fault properties at 550 km. Modeling of subducting slabs shows that metastable olivine is not likely to persist deeper than 550 km in most subduction zones [Devaux et al., 1997]. It is possible that transformational faulting occurs in a different solid-state phase transition, such as enstatite-to-ilmenite [Hogrefe et al., 1994]. In the next chapter we will attempt to address some of these unresolved questions by adding a geographical dimension to the categorization of our time functions. 151

170 Chapter 10 Subduction zone variation Many aspects of deep seismicity vary by subduction zone. The maximum depth of seismicity depends on the thermal parameter [Kirby et al., 1996]. Deep earthquakes in cold slabs have more numerous aftershocks, while warm slabs have lower b-values [Wiens and Gilbert, 1996]. Duration-magnitude scaling may vary by subduction zone [e.g., Campus and Das, 2000]. It is therefore reasonable to expect variations in the character of moment release in deep earthquakes from different subduction zones. We classify the earthquakes by subduction zone, dividing them into 15 geographical regions: Kurile, Japan, Izu-Bonin, Marianas, Ryukyu, Himalaya, Philippine, Java/Indonesia, South Solomon, New Hebrides, Tonga, Chile, Peru, Middle America, and Aleutian (Figure 10.1). This categorization has two goals: (i) to seek differences between subduction zones that may be attributed to geophysical properties of the plates; and (ii) to establish whether the global properties are common to many subduction zones or if they represent disproportionate sampling of some zones. Subdivision of the STFs by subduction zone as well as depth range creates some groups 152

171 60 o Aleutian Station km km >=550 km Japan Kurile 30 o Himalaya Ryukyu Izu-Bonin Philippine Marianas Middle America 0 o South Solomon Peru New Hebrides Java Tonga Chile -30 o -60 o Figure 10.1: Earthquakes studied, grouped by subduction zone. with a small number of events. Thus we must be cautious in interpreting our results. Three zones (Tonga, Japan, and Marianas) contain earthquakes in all three depth ranges, but only Tonga has more than one event in each depth range. The 18 earthquakes between km occur in five zones: Izu-Bonin (7), Tonga (6), Japan (2), South Solomon (2), and Marianas (1). Although Izu-Bonin has the most earthquakes in the km depth range, it has no events in any other range. The depth-distribution of seismicity in Izu-Bonin is shifted towards shallower depths, with the minimum between 200 and 300 km, the second peak between 400 and 500 km, and virtually no earthquakes below 550 km [Helffrich and Brodholt, 1991]. 153

172 Scaled duration [s] Kurile Japan Izu-Bonin Marianas Java/Indonesia Tonga Peru Chile Middle America Aleutian South Solomon New Hebrides Ryukyu Philippine Himalaya Depth [km] Figure 10.2: Scaled duration vs. depth with symbols for subduction zone. Many zones have fairly uniform behavior within a particular depth range: Chile, Peru, Middle America, and Tonga each have relatively little scatter between 100 and 350 km. Tonga, Chile, and Java/Indonesia each have little scatter below 550 km. This suggests that individual plate properties influence characteristics of rupture Duration We first consider scaled duration as a function of geography and depth. Figure 10.2 reproduces Figure 9.3 using a different symbol for each subduction zone. The km events occurred in all but one subduction zone (Izu-Bonin). There is considerable scatter in this population, but we can identify by inspection some zones whose durations are fairly uniform. For example, Chile, Peru, and Middle America each have fairly tightly clustered groupings (as do Kurile and Aleutian, albeit with only two events each). Chile and Peru 154

173 both average 9.1 seconds, while Middle America averages 11.4 seconds. Tonga s durations are consistently short (8.2 seconds), with the exception of one long event. A few zones durations have greater variability, including New Hebrides, Marianas, South Solomon, and the Philippines, but we can begin to establish regular behavior of earthquakes in different plates. Standard deviations for each zone are consistent with these observations. Similarly, the 550 km earthquakes occurred in six different zones, and each of the most populous ones (Tonga, Chile, Java/Indonesia) has little scatter. We can infer from the lack of scatter that there is a typical duration for each subduction zone in each depth range. This suggests that plate properties influence some aspects of rupture. We plot average scaled durations of the events in each subduction zone in each of the three depth ranges in Figure The relative durations of different zones do not change with depth: The zones with shorter durations between km also have shorter 550 km durations (e.g., Japan, Kurile, Tonga). Likewise, zones with longer durations between km also have longer deep durations (e.g., Peru, Java/Indonesia). And we note that the zones with the longest shallow durations have no deeper than 550 km earthquakes (Ryukyu, Middle America, South Solomon, Himalaya, Philippine). This consistency supports the hypothesis that plate properties influence rupture. Slab temperature could affect the local shear wave velocity and therefore the velocity at which the crack propagates, although this will only lead to differences of a few percent. Figure 10.3 also enables us to check whether the depth dependence of the global popu- 155

174 Average scaled duration [s] Kurile Japan Izu-Bonin Marianas Java/Indonesia Tonga Peru Chile Middle America Aleutian South Solomon New Hebrides Ryukyu Philippine Himalaya km km >=550 km Depth range Figure 10.3: Average scaled durations in each depth range for each subduction zone. Dashed lines connect values for individual subduction zones. The subduction zones with relatively short durations from km also have short durations deeper than 550 km, and zones with long average durations between km have long durations 550 km. These patterns suggest that rupture duration is controlled in part by plate properties. The depth dependence in individual zones is similar to the global population as a whole: The durations below 550 km are consistently shorter for every subduction zone in which they occur. The average km duration is longer than the km average for all subduction zones with events in both ranges except Tonga (Izu-Bonin has no km events). 156

175 lation is reproduced in individual zones. Three of the four zones with both km and km earthquakes (Japan, Marianas, South Solomon) have an increase in average duration between km and km (Figure 10.3). Only Tonga s average duration decreases. Every zone has a shorter average duration for its events deeper than 550 km than for its shallower events. The similar depth-dependent behavior in many different zones indicates that our aggregate results reflect a global property of earthquake duration as a function of depth, rather than the disproportionate influence of more active zones. The fact that the three longest duration events in the 350 to 550 km range occurred in three different subduction zones (Izu-Bonin, Japan, and South Solomon), provides further evidence for this conclusion Shape To study the average shapes of the time functions, we stacked the STFs from each subduction zone-depth range group (Figure 10.4). Between 100 and 350 km, South Solomon and Java/Indonesia also exhibit significant moment release late in rupture (Figure 10.4). (Kurile does, as well, but only two events occurred there.) Similarly, between 350 and 550 km, South Solomon and Izu-Bonin feature late moment release. (The one event in the Marianas in this range also has a complicated shape.) This is not seen in Tonga, where the km events have a similar average shape to Tongan STFs from other depths. Moment release occurring relatively late in an 157

176 km km 550 km Tonga (12) (6) (13) N. Hebrides (9) (0) (0) S. Solomon (5) (2) (0) Java (5) (0) (5) Philippine (4) (0) (0) Ryukyu (1) (0) (0) Marianas (3) (1) (1) Izu-Bonin (0) (7) (0) Japan (1) (2) (1) Kurile (2) (0) (1) Aleutian (2) (0) (0) M. America (3) (0) (0) Peru (6) (0) (1) Chile (7) (0) (6) 4 Himalaya (5) Time [s] 4 0 (0) Time [s] 4 0 (0) Time [s] Figure 10.4: Stacks of duration-scaled STFs grouped by subduction zone and depth range and rescaled to the average duration for each group. Number of STFs in each stack is given in parentheses. Vertical scale has units of N-m/s km: South Solomon, Java and Middle America have longer durations, with significant late moment release; km: South Solomon and Izu-Bonin have late moment release. Tonga s shape is not much different from its stacks in the other depth ranges; 550 km: There is less variation; Java has more late moment release than the others. 158

177 Average # zero crossings of moment-scaled time functions Tonga Philippine Japan Peru New_Hebrides 1.9 Ryukyu 1.0 Kurile Chile South_Solomon Marianas Aleutian 1.0 Himalaya Java_Indonesia Izu_Bonin 3.1 Middle_America Figure 10.5: Average zero-crossings by subduction zone and depth range. The three zones with events in all three depth ranges each exhibit the same depth dependence seen in Figure 9.9. Zones with complex average STFs in Figure 10.4 have more subevents (e.g., South Solomon, Java/Indonesia). event could indicate greater heterogeneity which prevents large amounts of slip early after initiation. Another measure of shape we used in Chapter 9 was the average number of subevents (as measured by counts of zero-crossings of the first derivative). The strong variation with depth in Figure 9.9 is evident in individual subduction zones (Figure 10.5). All three zones with events in all three depth ranges have more subevents in the km range and fewer in the 550 km range. South Solomon and Izu-Bonin are the other two zones with

178 550 km events, and both have a large number of subevents in that range. In the km range, South Solomon and Java/Indonesia have a large number of subevents, consistent with the qualitative inspection of their average STFs Thermal parameter The varying average scaled durations among different plates, and their consistent relationship over all depths, suggest that some property of the lithosphere, such as temperature, influences earthquake rupture. One way to quantify thermal properties is with the thermal parameter. The thermal parameter is a measure of slab temperature at a given depth [Kirby et al., 1991]. It is defined by = AV n sin(), where A is the age of the lithosphere being subducted, V n is the convergence rate, and is slab dip [Kirby et al., 1991]. A larger thermal parameter corresponds to a cooler slab. The thermal parameter correlates with the maximum depth of seismicity in subduction zones, but not linearly. Rather, for < 5000 km, the maximum earthquake depth is about 300 km, and for > 5000 km, maximum earthquake depth is about 680 km [Kirby et al., 1991, 1996]. We use values for the thermal parameter from Kirby et al. [1991] (with a correction to Tonga to account for back-arc spreading [Wiens and Gilbert, 1996]). We do not have values for for Himalaya, South Solomon, or Philippines. While individual scaled durations do not show a simple relationship to thermal parameter, we find an inverse relationship between the median scaled duration for some depths and the thermal parameter (Figure 10.6). 160

179 20 Middle_America Ryukyu Aleutian Peru, Chile New_Hebrides Izu_Bonin Kurile Japan Java_Indonesia Marianas Tonga Scaled duration [s] Thermal parameter Scaled duration [s] Median values in each depth range Thermal parameter Figure 10.6: Scaled duration vs. thermal parameter. Although the individual scaled durations do not have an simple relationship with the thermal parameter (upper panel), the median values within each depth range have a small decrease with thermal parameter (lower panel). The km durations decrease up to 5000 and then are constant. The km durations decrease slightly for The 550 km durations appear constant. 161

180 For km events, the scaled duration decreases with increasing thermal parameter up to 5000, and is roughly constant for larger. The km durations decrease slightly for The 550 km durations appear constant versus. The observation that the subduction zones with the longest durations km do not have 550 km events (Figure 10.3) is consistent with this inverse relationship and the relationship between maximum depth of seismicity and thermal parameter, though it may reflect selection effects, as well. Wiens [2001] used the inverse relationship between and duration to support a proposal that the mechanism of deep earthquakes is temperature-activated (e.g., thermal shear instabilities) Summary By subdividing our STFs by subduction zone, we find that: (i) the depth-dependent duration behavior seen in the aggregate is widespread, not restricted to a limited number of regions; and (ii) differences between zones in duration and character of moment release could be related to lithospheric temperature. Based on the consistent depth-dependent behavior across multiple subduction zones, we can conclude that some aspect of deep earthquake failure mechanism is global. The differences between subduction zones suggest that individual plate properties such as temperature or heterogeneity also affect how rupture propagates. Unresolved is whether those properties are implicated in the failure mechanism of deep earthquakes or whether they merely imprint 162

181 distinct signatures onto a common process. 163

182 Chapter 11 Initiation, Termination, and Aftershocks The processes that initiate and terminate slip in earthquakes remain mysterious despite many years of investigation. Even for shallow earthquakes, the sequence of events that leads to unstable slip and causes it to cease is not well-understood. For deep earthquakes, it may be possible to detect changes in mechanism by studying how moment release initiates. It is also conceivable that different failure mechanisms are manifest in the observed termination properties of moment release. For example, slip from a mechanism controlled by available untransformed material and thermal state could end much differently from one controlled by stress levels and rock strength. Our data set of deep earthquake STFs is useful for a systematic investigation of the initiation of large, deep earthquakes. The STFs also provide an opportunity to study the termination of rupture directly in the waveform, facilitated because the depth phases arrive after the completion of the earthquake. Aftershocks provide insight into the immediate post-earthquake environment of the fault plane. For example, aftershock sequences are often used to study the redistribution of stress 164

183 after an earthquake [e.g., Stein, 1999]. Deep focus earthquakes are notable for their paucity of aftershocks [Frohlich, 1989]. We will examine aftershock production in relation to other parameters we have studied, as well as more generally as a function of depth and subduction zone Initiation In dynamical models for self-similar rupture with constant stress drop and rupture velocity, the far-field velocity grows linearly, at the same rate for all event sizes [Madariaga, 1976]. Other models propose that large and small events begin differently, and the nucleation phase of earthquakes scales with total event size. In cascade models, small earthquakes trigger subsequent events, building to the largest subevent [Beroza and Ellsworth, 1996]. If there is some structural hierarchy, the final subevent size can scale with that of the penultimate subevent. In pre-slip models, a region of aseismic slip expands until it reaches a critical size and seismic failure occurs [Beroza and Ellsworth, 1996]. Scaling occurs if the final stages of pre-slip control the size of the earthquake. Pre-slip is similar to models based on laboratory-derived rate- and state-friction constitutive laws, in which precursory slip reaches a critical length before instability [Dieterich, 1992; Ohnaka, 1992]. Recently the observational debate over models for earthquake nucleation has intensified, with some observations of a low-moment-rate nucleation phase whose moment and duration scale with total event size [Iio, 1992; Ellsworth and Beroza, 1995; Beroza and 165

184 Ellsworth, 1996]. Nucleation phases, as observed in earthquakes from magnitude 1.1 to 8.1, release about 0.5% of the total moment of the earthquake and their durations scale as total moment to the power 1/3. Dodge et al. [1996] observe foreshock sequences that seem to result from an aseismic pre-slip process, whose extent scales with the mainshock size. However, others have observed self-similarity over the magnitude range -2 to 8 [Abercrombie and Leary, 1993], as well as for deep focus earthquakes [Houston et al., 1998]. Studies of earthquakes initial subevents have found no difference between them and comparablysized regular earthquakes [Abercrombie and Mori, 1994; Kilb and Gomberg, 1999]. Mori [1996] s study of a high-stress-drop foreshock to the 1992 Joshua Tree earthquake suggests the difference between it and the mainshock is in what stopped rupture, not how it initiated. We will study nucleation of large, deep earthquakes by direct measurement of initial moment release rates from individual STFs as well as by comparison of average functions. For this analysis, we use unscaled source time functions (with areas equal to the earthquakes moments) rather than the moment-scaled STFs (which had effects of moment removed) to enable detection of any variation with event size. We measure unscaled momentrates of each time function at regular intervals after initiation (0.5, 1.0, 1.5 and 2.0 seconds). Figure 11.1 plots the moment-rates as a function of event depth and moment. The events that start more quickly tend to be large and/or deep. We perform joint linear fits of moment-rate to depth and log(m 0 ) and find positive correlation with both independent variables. Multiple-regression analysis of the joint fit exceeds the 99% confidence level. The total amount of variance reduction from the fit todepth is roughly constant at all four times, 166

185 Moment [10 19 N-m] x s s Moment [10 19 N-m] s s Depth [km] Depth [km] Figure 11.1: Moment-rate vs. earthquake moment and depth at 0.5, 1.0, 1.5, and 2.0 seconds after initiation. Symbol size is scaled to the moment rate; units are N-m/s. Note different scale in each panel. The events that have high early moment-rates tend to be either deep or large. Multipleregression analysis of joint linear fits to depth and log(m 0 ) indicate a slightly stronger dependence on depth up to 1.0 second, and a much stronger dependence on M 0 at 1.5 and 2.0 seconds. but between 1.0 and 1.5 seconds the variance reduction attributable to the fit tomoment increases dramatically. The slope of the fittolog(m 0 ) increases so that moment-rate after 1.5 seconds rises more quickly as a function of event size than at earlier times. The result is that the fittodepth is (slightly) more important at 0.5 and 1.0 seconds, while the fittomoment dominates at 1.5 and 2.0 seconds. While the fast beginnings of the deepest earthquakes can be explained by faster rupture velocities (consistent with the decreased durations), the dependence on moment is central to the debate over initiations discussed earlier. The stronger dependence on moment at 1.5 and 167

186 2.0 seconds could result either from a change in the smaller events towards lower momentrates or in the larger events towards higher moment-rates. If the latter, it could signal the onset of a rapid moment release period following a nucleation phase. One way to discriminate between these explanations is to compare average unscaled time functions from different moment ranges to determine whether large or small events moment-rate functions change after 1-2 seconds (Figure 11.2). We first group the events by depth range to minimize complications from depth-dependent rise times and durations. We then group the events within each depth range by moment and stack. The stacks in Figure 11.2 demonstrate that for the smaller events the time functions have begun to turn over by 2.0 seconds at all depths. No dramatic increase in the moment-rate occurs between 1.0 and 2.0 seconds in the large events. Therefore, the increased dependence of moment-rate on moment at 1.5 and 2.0 seconds in Figure 11.1 results from the tailing off of small events rather than the onset of rapid growth after a nucleation phase in large events. We can use the moment-binned stacks to study self-similarity in the first 1.5 seconds. In the 100 to 350 km stacks, the moment-rates are nearly equal for all earthquake sizes, except for the stack of the two largest earthquakes in the group, which has a much higher initial moment-rate than the others. In the 350 to 550 km depth range, the stack of the five largest events has a higher average initial moment-rate than stacks of smaller events. Deeper than 550 km, all the stacks have relatively high initial moment-rates. The two largest events (June 9, 1994, and June 17, 1996) are plotted individually and are not distinguished by high initial moment-rates. 168

187 Moment-rate [10 19 N-m/s] Moment-rate [10 19 N-m/s] Moment-rate [10 19 N-m/s] <1.0 (31) (10) (10) (8) (4) 30.0 (2) Time [s] <1.11 (8) (5) 2.5 (5) Time [s] <1.5 (12) (7) (5) (2) 73.0 (960617) (940609) Time [s] Figure 11.2: Stacks of unscaled STFs binned by moment, in three depth ranges ( ; ; 550, respectively). The boundaries of the moment bins are chosen to avoid too great a span of moment, which would result in the largest event dominating each stack. The ranges of each moment bin are given in units of N-m and the number of STFs stacked is given in parentheses. The stacks show generally self-similar behavior, with similar initial moment-rates until the smaller events reach their maxima. The largest events show a slight departure from self-similarity with higher initial moment-rates. In the deepest group, the moment-rate for events of all sizes is elevated. 169

188 Higher initial moment-rates in large events might be observed if we systematically make later onset picks for those events, but Figure 8.6 shows that this is not the case. Thus, we observe initiations consistent with self-similarity for smaller events but with higher early moment release rates for the very largest events in each depth range. This is inconsistent with the existence of a low moment-rate nucleation phase. However, if earthquakes begin self-similarly, then the combination of small variations in initial rupture velocity and heterogeneous fault planes could lead to a selection effect such that larger events tend to develop from those that were faster-starting Termination If earthquakes begin self-similarly over a large magnitude range, dynamic stresses may determine final event size [Abercrombie and Mori, 1994]. In this case, the end of earthquake rupture may differ based on magnitude, and it would be instructive to examine the terminations of deep earthquakes. Certainly, the STFs exhibit a wide variety of endings (Figures 9.1 and 9.2), so it is worthwhile to investigate for systematic behavior. In Figure 11.3, we plot the moment-rates as a function of event moment and depth at four times before the termination of rupture. While there does not appear to be much depth dependence, the moment-rate does seem to depend strongly on moment, with large events possessing higher moment-rates in the final 2.0 seconds of rupture than small events. Joint fits to moment and depth support this 170

189 Moment [10 19 N-m] x s s Moment [10 19 N-m] s s Depth [km] Depth [km] Figure 11.3: Moment-rate vs. earthquake moment and depth at 0.5, 1.0, 1.5, and 2.0 seconds before termination. Symbol size is scaled to the moment rate; units are N-m/s. Note different scale in each panel. The largest events tend to have high moment-rates near the termination of rupture. There is not very much depth dependence. 171

190 observation: at -1.0 seconds, the variance reduction from a linear fit to log(m 0 ) is nearly nine times greater than the variance reduction from a fittodepth. Moment-binned stacks support this observation. In Figure 11.4 the moment- and depthbinned STFs have been aligned on their termination times, rather than initiations, and summed. The large event STFs have higher average moment-rates in the final several seconds. We calculated several additional measures of nucleation and termination, such as time to peak and time required to release the final 25% of moment, but did not identify any relationships between these measures and event magnitude or depth. This result is similar to the observation of initiation properties, which suggested selfsimilarity, with the largest events developing from faster-starting rupture. However, one caution about the termination measurement is that signal-generated noise is higher for the larger events, which could result in a bias towards picking terminations earlier than for smaller events. This might account for some of the differences observed Aftershocks We measure aftershock production for two sets of mainshocks: the 111 deep earthquakes for which we compute source time functions and a larger set selected from the Harvard Centroid Moment Tensor catalog. The former data set allows comparison of aftershock production with measured source properties, while the latter provides stronger statistical support for depth- and geographical-dependence of aftershock production. 172

191 Moment-rate [10 19 N-m/s] Moment-rate [10 19 N-m/s] Moment-rate [10 19 N-m/s] <1.0 (31) (10) (10) (8) (4) 30.0 (2) Time [s] <1.11 (8) (5) 2.5 (5) Time [s] <1.5 (12) (7) (5) (2) 73.0 (960617) (940609) Time [s] Figure 11.4: Stacks of unscaled STFs aligned on the terminations, and binned by moment and depth range ( ; ; 550). The ranges of each moment stack (units of N-m) are given in each panel. The number of STFs stacked is given in parentheses. The largest events have higher moment-rates as the end of rupture approaches. 173

192 Aftershocks are counted using the Preliminary Determination of Epicenters (PDE) catalog compiled by the USGS National Earthquake Information Center. We locate each mainshock in the catalog and search the subsequent 20 days, counting events whose depths and epicenter are within 50 km and 0.5, respectively, of the mainshock hypocenter, and with body-wave magnitudes m b 4.5. We normalize the number of aftershocks for each earthquake using [Wiens and Gilbert, 1996]: log Nnorm =lognobs +8:3 MW (11.1) where Nnorm and Nobs are the number of normalized and observed aftershocks, respectively. This equation assumes that Nobs / M 2=3 0 (i.e., that the number of aftershocks scales with the area of the fault plane), which seems to hold for shallow earthquakes [Yamanaka and Shimazaki, 1990]. However, the scaling may be different for deep earthquakes. In Section , we examine this scaling relationship for deep earthquake aftershocks Mainshocks: Source time functions We first count aftershocks of the 111 events for which we computed STFs. This enables us to compare aftershock production with source properties previously measured, such as scaled duration and stress drop. One might expect the termination properties to influence aftershock production, especially if large events terminate abruptly, but we found no relationship. 174

193 1000 # aftershocks (normalized) Scaled duration [s] Figure 11.5: Normalized number of aftershocks vs. scaled duration. The events with 0 aftershocks are shown in the lower panel. No relationship is suggested between event duration and number of aftershocks. More than half (67) of the earthquakes have no recorded aftershocks in the time period and volume searched. Of those that do, 23 have one aftershock, while only two have more than 10 (Table 8.1). The variation with depth will be examined in the next section using the larger data set. Aftershock production does not appear to be a function of scaled duration (Figure 11.5). The relationships between aftershocks and scaled duration and between stress drop and scaled duration suggest a negative relationship between aftershocks and stress drop. We do find the number of aftershocks to be weakly negatively correlated with static stress drop (Figure 11.6). However, Figure 11.6 is somewhat ambiguous since there are many low stress drop events with 0 aftershocks. Furthermore, we also find (in the next section) that the deep- 175

194 # aftershocks (normalized) Stress drop (static) [MPa] Figure 11.6: Number of aftershocks vs. static stress drop in each depth range. The adjusted stress drop for Bolivia, June 9, 1994, is indicated by the arrow (see Figure 9.10). 176

195 est events, which have higher stress drops, have the most aftershocks, and the km events, which have lower stress drops, have almost no aftershocks. Thus the relationship in Figure 11.6 is left somewhat in question Mainshocks: Harvard CMT catalog Using mainshocks from the Harvard CMT catalog allows us to include earlier times and lower magnitudes than the source time function catalog. We identify mainshocks from January 1, 1977, to December 31, 2001, with depth 100 km and M 0 3: N-m (about MW 6.3). This yields 281 mainshocks (174 in 100 to 350 km; 47 in 350 to 550 km; 60 in 550 km). We use the same parameters as before to search the PDE catalog for aftershocks. The scaling with moment is shown in Figure The best fit slope (for events with at least one aftershock) is 0.23, much different from 2/3. The use of a constant search volume for all magnitudes probably produces a relative overcount in the number of aftershocks to small-magnitude events. Another possible explanation for the departure from the expected scaling is that if transformational faulting causes failure, aftershocks might occur only on the periphery of the fault area, in untransformed material. In this case, Nobs / M 1=3 0, closer to our observation. For the purpose of comparison with previous studies, however, we continue to normalize by M 2=3 0 (Equation 11.1). If we normalize using the empiricallydetermined exponent, the qualitative results are unchanged. Aftershock production as a function of depth is shown in Figure Overall, 31% of the Harvard mainshocks have at least one aftershock, but that value decreases dramatically 177

196 100 # aftershocks Moment [N-m] Figure 11.7: Number of aftershocks vs. moment of mainshock. The best-fit slope is 0.23, much different from the expected 2/3. 178

197 1000 # aftershocks (normalized) Depth [km] Figure 11.8: Normalized number of aftershocks vs. depth. There are almost no aftershocks in the 350 to 550 km depth range. Bolivia, June 9, 1994, is notable for having very few aftershocks (one meeting our criteria, in the bottom right of the upper panel) despite its magnitude. in the 350 to 550 km depth range. Only 8.5% of 350 to 550 km events have 1 aftershock, compared with 29% of 100 to 350 km events, and 53% of 550 km events. (We continue to use the same depth ranges although the distribution here suggests boundaries at about 300 km and 500 km.) Though the depth boundaries differ, this agrees with Frohlich [1987], who found a minimum of aftershock production between km and an increase deeper. Before we accept this as anomalous, however, we must consider two possibilities. First, we recognize that in general seismicity is reduced at those depths, so perhaps we should not be surprised to find a small number of aftershocks. This argument implies that we are counting background seismicity rather than aftershocks. We test this by comparing the aftershock 179

198 distribution to the overall seismicity. Figure 11.9 compares the depth distribution of our aftershocks with that of all PDE earthquakes deeper than 100 km with m b 4.5. Though the pattern is similar, there are notable differences in the 350 to 550 km range, where there are relatively fewer aftershocks than typical seismicity, and in the 550 km range, where there are relatively more aftershocks. Thus, the aftershock distribution differs from regular seismicity and we conclude that the absence of aftershocks between 350 and 550 km does not simply reflect the generally low seismicity there. A second possibility is that the true rate of aftershock production between 350 and 550 km is similar to that in one of the other two depth ranges, and the near absence of observed aftershocks occurs by random chance. We must therefore assess the likelihood that a random sample of 100 to 350 km or 550 km earthquakes could produce the same distribution seen for the 350 to 550 km events. We compare the populations by resampling from the larger ones a subset equal in size to the smaller one. For example, to compare the 100 to 350 km and 350 to 550 km groups, we randomly select 47 of the 174 earthquakes between km and compute this subset s mean number of aftershocks. (Selected earthquakes are not returned to the population.) We repeat this procedure 10,000 times to build a distribution of mean values of random subsets with 47 members, which we can compare to the mean value of the 350 to 550 km population (Figure 11.10). It is very unlikely that a random sample of 47 earthquakes in a population with mean 180

199 1 0.8 Aftershocks (# / ) PDE catalog (# / 8236) 0.6 # Depth [km] 1 % with aftershocks Depth [km] Figure 11.9: (upper panel) Histograms of number of aftershocks and overall seismicity from the PDE catalog. Aftershocks are normalized by moment using Equation 11.1 and binned by depth. PDE seismicity consists of all events deeper than 100 km with m b 4.5. Each is normalized to aid comparison (see legend). The distribution of aftershocks differs from that of the background seismicity, implying that the depth-variation in Figure 11.8 does not simply reflect the overall seismicity pattern. (lower panel) Percent of mainshocks with aftershocks. The production of aftershocks varies as a function of depth. This suggests that something is suppressing aftershocks in the middle depth range. 181

200 km km 550 km 800 # Mean # aftershocks (normalized) per earthquake Figure 11.10: Distribution of mean number of aftershocks per earthquake from 10,000 resamplings of the km and 550 km populations. Resampling consists of randomly selecting 47 of the 174 events in the km range (or 47 of the 60 events in the 550 km range) and computing the average number of aftershocks (normalized). This was repeated 10,000 times to obtain the distributions of mean values. The green vertical line, which indicates the mean value of the km range, is more than two standard deviations ( 4.6) outside the average of the km group, demonstrating that the populations are distinct. 182

201 (17.5) and standard error (4.6) of the 100 to 350 km group would have as few aftershocks as the 350 to 550 km group (mean 5.0). Therefore, we conclude that the 100 to 350 km and 350 to 550 km ranges constitute separate populations with different aftershock properties. A similar argument can be made for the 550 km group (mean 39.5, standard error 3.6). The lower panel of Figure 11.9 shows the percentage of mainshocks with at least one aftershock as a function of depth. If aftershocks are produced by the same mechanism at all depth, we would expect mainshocks on average to produce aftershocks at the same rates. This suggests that something is suppressing aftershocks in the middle depth range. Why are there so few aftershocks between 350 and 550 km? Frohlich [1987] proposed variations in the degree of heterogeneity. But our observations of STF complexity suggest greater heterogeneity in the depth range with fewer aftershocks, which is opposite Frohlich [1987] s model. Changes in the stress drop are a second possibility: We found a lower static stress drop for events between 350 and 550 km (Figure 9.10). But we also found a weak inverse relationship between stress drop and number of aftershocks (Figure 11.6). These observations can be reconciled by noting the large number of events with low stress drop and 0 aftershocks in Figure Transformational faulting between km explains the lack of aftershocks by invoking the consumption of most available metastable material during the mainshock [Green and Houston, 1995; Kirby et al., 1996]. More complete transformations (and fewer aftershocks) coincide with the tapering of the metastable olivine wedge in that depth range. The onset of a new metastable material or mechanism below 550 km could account for the resumption of larger aftershock sequences. Or, it may be that some 183

202 property generally inhibits seismicity in this depth range and causes stress to be released aseismically. This would limit the number of mainshocks as well as aftershocks. Finally, we consider the variation of aftershock production by subduction zone. Wiens and Gilbert [1996] found that significant aftershock sequences are limited to cold slabs, but Frohlich [1987] found no difference in aftershock production by geographic region. For shallow earthquakes, Singh and Suárez [1988] attributed variations in aftershock productivity to differences in strength of coupling and heterogeneity. We classify each of the 281 mainshocks into 17 subduction zones and plot the number of aftershocks as a function of each subduction zones thermal parameter [Kirby et al., 1991] (with a correction to Tonga to account for back-arc spreading Wiens and Gilbert [1996]). Figure shows the individual events and mean values for each thermal parameter. We find that for events below 550 km, the maximum number of aftershocks is highest for subduction zones with the largest thermal parameters. This concurs with Wiens and Gilbert [1996] s finding. For km events, we find no trend with thermal parameter. If earthquakes below 550 km are caused by transformational faulting (of a metastable mineral other than olivine), then colder slabs would be expected to have more available material for aftershocks. In the km range, transformational faulting does not operate, so thermal state may not be as important for aftershock production. 184

203 # aftershocks (normalized) South Sandwich Middle America Ryukyu Aleutian Peru, Chile New Hebrides Izu-Bonin Kurile Japan Java/Indonesia Marianas Thermal parameter Tonga # aftershocks (normalized) Mean values for each depth range Thermal parameter Figure 11.11: Number of aftershocks vs. thermal parameter. For events below 550 km, the maximum aftershock productivity is highest for subduction zones with the largest thermal parameters. For km events, there is no trend with thermal parameter. 185

204 11.4 Summary There were two primary motivations for studying how deep earthquakes begin and end. First, we wanted to assess the self-similarity of deep earthquakes in the context of the debate over nucleation phases in shallow earthquakes. Second, we hoped to gain further insight into the failure mechanism of deep earthquakes by using aftershocks to study how the system responds to stress changes. On the first issue, we do not find support for a low moment-rate nucleation phase whose duration scales with the total event size. Instead, we see evidence for self-similarity in smaller events, and higher initial and final moment-rates in larger events. One explanation for this is that deep earthquakes begin self-similarly, and small variations in initial rupture velocity and heterogeneity produce a selection effect such that larger events tend to develop from those that were faster-starting. It should be noted that the range of magnitudes considered here is relatively small (6:4 MW 8:2) compared to most studies of self-similarity. Another comment is that the very largest deep earthquakes may be somehow different from other deep events. Anomalously low rupture velocities for the 1970 Colombia (MW8:2) and 1994 Bolivia (MW8:2) deep earthquakes are consistent with this idea [Kanamori et al., 1998]. On the second issue, we observe a strong variation in the number of aftershocks as a function of depth and a relationship between cold slabs and deep aftershock production. The depth dependence may arise from changes with depth in the amount of untransformed material locally surrounding deep earthquakes or from some other mechanism which suppresses 186

205 seismic stress release between 350 and 550 km. The geographical differences could reflect greater heterogeneity or more available untransformed metastable material in colder slabs. 187

206 Chapter 12 Conclusion Deep earthquakes 12.1 Summary of results We have determined source time functions of 111 deep earthquakes by stacking broadband seismograms recorded by the GSN. Scaling the STFs enables direct comparison of earthquakes spanning a factor of 675 in moment. We divide the STFs into depth ranges ( km, km, and 550 km) and observe two patterns with depth: (i) The deepest events consistently have different source properties than events in the shallower groups. Deeper than 550 km, scaled durations are shorter, STF shapes are more compact and simpler, static stress drops increase and seismic efficiency is lower. (ii) The two shallower depth ranges durations are indistinguishable, although we do observe that the km events have more subevents on average. Overall, the scaled durations decrease with depth slightly more than expected for a V 1 S - dependence. The entire drop occurs at 550 km, however, rather than throughout the upper mantle and transition zone. Durations are essentially constant between 100 and 550 km. 188

207 Subdividing the STFs into 15 subduction zones, we find that the depth dependence of duration is consistent across many regions. The 550 km durations are consistently the shortest in each zone where they occur. There is also a plate-dependent component to the character of the time functions. We found an inverse relationship between scaled duration and the thermal parameter. Studies of the initiation and termination of moment release revealed largely self-similar behavior, although the largest events tend to begin more rapidly. Deeper events reach high moment release rates more rapidly than shallower events. Aftershock productivity declines precipitously between 350 and 550 km, but rises again deeper than 550 km. We also find a positive relationship between maximum aftershock productivity and the thermal parameter Implications for mechanism of deep earthquakes Although the km and km have similar characteristics, the steady increase of VS through the upper mantle requires that some aspect of earthquake rupture changes in order to maintain similar scaled duration. Furthermore, proposed explanations for intermediate earthquakes, such as reactivation of faults and dehydration embrittlement, do not operate below depths of about 300 to 400 km [Kirby et al., 1996; Jiao et al., 2000]. Thus it is reasonable to admit a change in mechanism around 350 km leading to more heterogeneous fault zones and either smaller stress drops or slower rupture propagation compared to the local shear wave velocity. Transformational faulting is a promising candidate, since the 189

208 wedge of metastable olivine is more likely to exist between km. Transformational faulting could also produce a more heterogeneous fault zone, explaining the increase in STF complexity [Frohlich, 1987]. However, it is difficult to satisfactorily explain deep earthquakes below 550 km within the context of transformational faulting of metastable olivine. The abrupt shifts we observe at 550 km suggest another change in mechanism or at least a significant alteration of fault zone properties. Based on recent thermo-kinetic modeling, transformational faulting due to metastable olivine probably does not operate below about 550 km, except perhaps in Tonga [Devaux et al., 1997]. One straightforward explanation is that this depth marks the onset of transformational faulting of enstatite to ilmenite. Since the kinetic inhibition of this transformation is greater than for olivine, the enstatite wedge could persist deeper [Hogrefe et al., 1994]. The consistent depth-dependent behavior across subduction zones indicates that some common aspects of the failure mechanism must exist. The differences between subduction zones suggest that individual plate properties such as temperature or heterogeneity are important factors, either in the failure mechanism itself or by imprinting signatures on rupture propagation. One explanation for the initiations and terminations results is that deep earthquakes begin self-similarly, and small variations in initial rupture velocity and heterogeneity produce a selection effect such that larger events tend to develop from those that were faster-starting. In the very largest events, there may be enough slip to induce melting [Kanamori et al., 190

209 1998]. The depth dependence of aftershock production could be a consequence of the proposed changes in mechanism, although it is unclear why transformational faulting of metastable enstatite would lead to more aftershocks than that of metastable olivine. The variation of aftershocks with thermal parameter for events below 550 km could indicate larger metastable wedges (of enstatite) in colder slabs Future work Although we have explored many source properties of deep earthquakes with this work, we have not exhausted the possibilities. Focal mechanisms represent a potential direction for future work. Since they offer insight into the orientation of stresses in the slab, it would be interesting to compare them to our results on duration, stress drop, energy release, and aftershocks, and as a function of depth and subduction zone. We can use our frequency-domain stacks to compare spectral shapes of deep earthquakes. Using the corner-frequency of the spectrum to obtain the stress drop may provide a better estimate than our point-measurement of duration in Chapter 9. We can improve our aftershock search algorithm to account for the variation of fault area with magnitude and extend our analysis to calculate the moment released in aftershocks, rather than simple counts of earthquakes. It would also be straightforward to search the catalog for foreshocks. 191

210 Performing these measurements on the catalog of deep earthquake source time functions will provide a unique link with the properties of moment release determined in this dissertation. The opportunity to systematically compare these parameters offers hope for further progress in the understanding of the mechanism of deep earthquake through seismological observation. 192

211 Appendix A Acronyms Acronym CMB FARM GSN IRIS ISC LASA NCSN PREM SCSN STF ULVZ Table A.1: List of acronyms Description Core-mantle boundary Fast Archive Recovery Method Global Seismographic Network Incorporated Research Institutions for Seismology International Seismological Centre Large Aperture Seismic Array Northern California Seismic Network Preliminary Reference Earth Model Southern California Seismic Network Source time function Ultra-low velocity zone 193

212 Appendix B Review of core-mantle boundary properties B.1 Overview The core-mantle boundary (CMB) represents the most significant discontinuity within the Earth: crossing from the lower mantle into the core, compressional-wave velocities drop over 40% (13.7 to 8.0 km s 1 ), shear-wave velocities decrease from 7.3 to 0 km s 1, density increases almost 80% (5550 to 9910 kg m 3 ), and viscosity drops at least 20 orders of magnitude [Loper and Lay, 1995]. Perovskite is likely the major component of the lower mantle, along with magnesiowüstite, periclase and stishovite and possible infiltration of iron [Stixrude, 1998], while the core consists of iron alloyed with lighter elements. The transition occurs over a short distance, < 1 km [Kanamori, 1967; Vidale and Benz, 1992]. The density contrast prohibits bulk material exchange between the mantle and core. Hence, the outflow of heat from the core occurs via conduction, and a thermal boundary layer forms at the base of the mantle. The lowermost 300 km of the mantle is often called D 00, which originally referred to a layer in the lowermost mantle which had reduced gradients in radial 194

213 velocity models [Bullen, 1950]. Now D 00 is used more broadly to describe the CMB region where a variety of complex, laterally-varying seismic features are observed. The reduced velocity gradient in D 00 is characteristic of its thermal boundary layer role: increased temperatures reduce seismic wave velocities. Lateral heterogeneity of seismic wave velocities and scattering structures may derive from fine-scale structure whose location and strength varies laterally. B.2 Seismological results The majority of our knowledge about the CMB and D 00 comes from seismology. Investigators measure travel times, scattered and reflected energy, diffracted waves, and anisotropic splitting. For each of these categories, results indicate the presence of fine-scale structure. B.2.1 Velocity structure Tomography Tomographic studies employ long-period absolute and differential travel times, free oscillations and waveform modeling to develop three-dimensional global models. As a consequence of this data set, lateral resolution is limited to long-wavelength structures ( km) and anomalies in the lower mantle are dominated by spherical harmonics two and three. The rms amplitude for velocity heterogeneity increases in D 00 [Liu and Dziewonski, 1998; Su et al., 1994], typically up to (V S =V S ) 2:5% for S velocity models [Loper and 195

214 Lay, 1995]. Although P - and S-wave models generally agree in the upper mantle, their correlation breaks down to some extent in the lowermost mantle [Grand et al., 1997], which is generally believed to indicate compositional heterogeneity in addition to thermal perturbations [Van der Hilst et al., 1998]. This is also supported by theoretical and experimental consideration of thermodynamic relations and the elastic moduli [e.g., Stacey, 1992; Chopelas, 1992]. Recent tomographic models also have established that downwelling lithosphere can penetrate the 660-km discontinuity and, in some cases, apparently reach the CMB [Grand et al., 1997]. This has implications for the thermal and chemical composition of the CMB region, as well as for the possible presence of anisotropy. Richards and Engebretson [1992] have shown that the large-scale thermal patterns in the deep mantle deduced by seismology correlate with the time-integrated history of subduction during the past 180 million years. Diffracted waves Diffracted waves are commonly-used for studying D 00 velocity structure because they traverse long paths close to the CMB, sample a unique range of frequencies and length scales, and improve global coverage [Wysession et al., 1992]. As with tomography, the spatial scales are quite large (thousands of km) [Wysession, 1996]. Major findings from diffracted wave studies include a high degree of rms variation in velocity near the CMB [Sylvander et al., 1997; Valenzuela and Wysession, 1998], evidence for a discontinuity 200 km above the CMB, and large velocity reductions in a laterally-varying, thin layer just above 196

215 the CMB [Sylvander et al., 1997]. As with tomography, lack of correlation between V P and V S supports the presence of compositional heterogeneity [Wysession et al., 1992]. Scattered energy Complex velocity structure and CMB topography can be deduced by studying seismic waves that scatter off fine-scale heterogeneities. Scattering near the CMB that produces precursors to PKP and PKKP has been used to infer CMB topography with an rms amplitude of 300 m and/or 1% volumetric inhomogeneities [Bataille et al., 1990; Hedlin et al., 1997; Shearer et al., 1998]. In contrast to tomography results, precursors to PKPdf suggest heterogeneities are distributed throughout the lower mantle with no particular concentration in D 00 [Shearer et al., 1998]. B.2.2 D 00 discontinuity Like scattered energy, reflections reveal structure with smaller scale lengths ( km) [Liu and Dziewonski, 1998] and many studies have investigated the D 00 discontinuity [see Wysession et al., 1998, for a review]. The first evidence for a velocity discontinuity in D 00 came from detection of an S-wave triplication, attributed to a thin boundary with a velocity increase of % about 275 km above the CMB [Lay and Helmberger, 1983]. The D 00 discontinuity has been observed using triplications and precursors, with both P -[Vidale and Benz, 1993; Reasoner and Revenaugh, 1999] and S-waves [Revenaugh and Jordan, 1991; Kendall and Shearer, 1994]. There have also been non-detections from ap- 197

216 parently sharp and clean CMB regions [Vidale and Benz, 1992]. The discontinuity is laterally variable in its presence, height above the CMB, and magnitude of velocity increase. On average, the discontinuity has a velocity jump of % at a height of km (standard deviation: 50 km) [Wysession et al., 1998]. The sharpness is difficult to ascertain: it may be close to first-order, but the data also allow a gradual transition tens of km wide. The velocity changes and heights inferred from P - and S-wave observations generally coincide, but detection of the discontinuity in a location with one type of wave does not always imply detection with the other. Lateral coherence of the discontinuity varies from a few hundred km to 1500 km, and there is no apparent correlation between observation/nonobservation of the discontinuity and the large-scale velocity structures determined by other methods. Possible explanations for the D 00 discontinuity include [Wysession et al., 1998]: (i) a change in chemistry, whether primordial, from continued mantle differentiation, or coremantle reactions; (ii) a transition in flow regime, deformation mechanisms, mineral alignment or structural fabric; (iii) an isochemical phase change; and (iv) a thermal discontinuity, possibly related to subducted lithosphere. Each has difficulties: (i) would have to explain the intermittence of the features; (ii) might not produce a sharp feature; (iii) must explain the intermittence, and demonstrate that phase transitions occur in mantle components at CMB conditions; and (iv) must explain how to emplace cold material and maintain the temperature contrast presumed necessary to account for the velocity changes. It is likely that some combination of thermal and compositional heterogeneities cause the discontinuity. 198

217 B.2.3 Anisotropy Detection of anisotropy in the CMB region can shed light on dynamic processes there. Most measurements of D 00 anisotropy derive from polarization analysis of S, ScS, and S di. Some circum-pacific areas produce shear-wave splitting times as large as 4-9 s, with SH preceding SV, produced by 1-3% transverse isotropy [Kendall and Silver, 1996]. In the central Pacific, however, variable results sometimes SV precedes SH and sometimes the opposite occurs have been attributed to varying flow patterns [Russell et al., 1999]. Two possible mechanisms for D 00 anisotropy are lattice-preferred orientation (LPO) and shape-preferred orientation (SPO) [Kendall and Silver, 1998]. In LPO, flow or strain induces a preferred arrangement of the crystals. Downwellings and upwellings entraining material could influence the flow regime to produce anisotropy. In SPO, inclusions with a velocity different from the surrounding matrix are embedded with a particular orientation. SPO might arise from mixing and layering of subducted lithosphere [Kendall and Silver, 1998] or from diking associated with partial melt near the CMB [Stixrude, 1998] B.2.4 Ultra-low velocity zones The recent discovery of thin basal layers with extremely large velocity reductions (ultralow velocity zones, or ULVZs) merits special mention. ULVZs are laterally variable layers 5-50 km thick with V P reductions of 10% [Garnero et al., 1998]. Most seismic evidence for ULVZs comes from the phases SP di KS and PKP. The long-period SP di KS is a variant of SKS which contains a CMB-diffracted P leg on either 199

218 the source or receiver side. Comparing this phase s travel time with SKS reveals anomalously slow arrivals, attributable to the diffracted leg s sampling of a slow basal layer because the mantle paths of the two phases are otherwise similar [e.g., Garnero et al., 1993; Garnero and Helmberger, 1998]. Waveform modeling of SP di KS further supports the travel time anomalies [Wen and Helmberger, 1998a; Helmberger et al., 2000]. Precursors to PKPdf, which passes through the inner core, result from scattering of PKPaband PKPbc, which bottom in the upper and lower parts of the outer core, respectively, at the CMB. PKP scattering from earthquakes in Tonga require 10-15% rms velocity variations confined to a km thick layer near the CMB in the southwest Pacific[Vidale and Hedlin, 1998; Wen and Helmberger, 1998b]. Combined with evidence for marked shear velocity reductions in that region, this supports the presence of partial melt. Similar results have been obtained from beneath the Comoros hotspot, albeit within a thicker layer (360 km) [Wen, 2000]. Further association of ULVZs with mantle upwellings comes from the results of Helmberger et al. [2000], who modeled complicated SP di KS sampling beneath Africa and Iceland. In modeling ULVZs, a tradeoff exists between the layer thickness and velocity reductions [Garnero and Helmberger, 1998]: smaller layer thicknesses accommodate more extreme velocity reductions, and vice-versa. Some limits exist, though: waveform modeling indicates that layers up to 300 km with 2.5 to 5.0% V P reductions do not reproduce the observed SP di KS seismograms; a minimum velocity reduction required is about 10%, with thicknesses between 20 km and 40 km, depending on the V S and density reductions [Garnero and Helmberger, 1998]. Modeling of ULVZs also suggests that the density within the 200

219 layer may be increased by 10% or more [Garnero and Helmberger, 1998]. Possible explanations for ULVZs include partial melting [Williams and Garnero, 1996; Holland and Ahrens, 1997], phase transitions [Garnero et al., 1998], layering associated with subducted crust or primordial differentiation [e.g., Tackley, 1998], reactions with core material [Knittle and Jeanloz, 1989, 1991; Manga and Jeanloz, 1996], partitioning of iron from mantle melt [Knittle, 1998], and a thin layer of finite rigidity at the top of the outer core [Buffett et al., 2000; Garnero and Jeanloz, 2000]. Garnero et al. [1998] favor partial melt because it can account for the large velocity reductions, the correlation between ULVZs and upwellings, and the confinement of ULVZs to the very base of the mantle. Partitioning of iron into the melt phase of perovskite (Mg Fe)SiO 3 at high pressure and temperature could produce chemical layering and low basal velocities [Knittle, 1998], as could chemical reactions between liquid iron and perovskite and magnesiowüstite (Mg Fe)O [Knittle and Jeanloz, 1989, 1991]. If partial melt is present, then the consequent reduction in VS is 30% [Williams and Garnero, 1996]. Recent experimental results indicate it may be possible to exceed the solidus in the thermal boundary layer [Holland and Ahrens, 1997], though direct evidence for strong VS reductions indicative of partial melt remains elusive. B.3 Geodynamical properties The superadiabatic temperature increase in D 00 is constrained by [Williams, 1998]: (i) the temperature at the inner core boundary and the adiabat in the outer core and (ii) the su- 201

220 peradiabatic temperature change in the upper mantle transition zone and the adiabat in the lower mantle. Major uncertainties arise from the melting behavior of iron and whatever alloying components exist in the core, so that a broad range of parameters allows T across the thermal boundary layer to be K [Williams, 1998]. D 00 is proposed to serve as the source region for mantle plumes: Instabilities develop into plumes, which carry hot material upwards [e.g., Stacey and Loper, 1983; Christensen, 1984; Thompson and Tackley, 1998]. Recent geodynamical work [Sidorin and Gurnis, 1998; Tackley, 1998, 2000] has modeled a chemically-distinct, high-density basal layer whose slow velocities agree with recent tomographic joint inversions for mantle wavespeed and density [Ishii and Tromp, 1999], while possibly satisfying geochemical requirements for primitive mantle reservoirs. This layer is found to be depressed under cold downwellings and elevated under upwellings. Small-scale convection might develop within it [Montague and Kellogg, 2000]. For sufficient density contrasts (a few percent), the layer avoids becoming entirely entrained within the upwelling, and so could be related to ULVZs. Core-mantle coupling is often cited as a potential source for the decade-timescale variation in the length of day. Angular momentum transfer might occur by torques related to electromagnetic, topographic or gravitational forces [Holme, 1998; Buffett, 1998]. The nature of deep mantle anomalies may shed light on which mechanism is most likely. 202

221 Appendix C Core-mantle boundary supplemental information In this appendix, we present supporting material for some data selection and processing issues in Chapter 3. Here we expand on the text s discussion of selection criteria for the Global Seismographic Network envelope stacks. C.1 Selection criteria After applying the source selection criteria described in Chapter 3, we measure the signalto-noise on each remaining seismogram for both P and P cp (or ScP). The signal amplitude is measured on velocity seismograms in a second-long window surrounding the P, PcP, orscp arrival. Noise is measured in the window from 30 to 10 seconds before the P -arrival. We then assign the minimum signal-to-noise level for each phase to be the ratio which selects 1/3 of the seismograms (Figures C.1 and C.2). This is done separately for each bandpass since the observed amplitudes of the core-reflections and P depend on the frequency content. 203

222 Hz PcP-to-preP P-to-preP Number of seismograms retained Hz Hz Minimum signal-to-noise Figure C.1: Number of seismograms retained vs. minimum signal-to-noise. Dashed line: P amplitudes. Solid line: P cp amplitudes. Upper panel is Hz bandpass; middle panel is Hz; lower panel is Hz. The horizontal dotted line in each panel marks level at which 1/3 of seismograms are retained, and the vertical dotted lines note the signal-to-noise ratio at which this is obtained for each phase. Note that the values of signal-to-noise are not meaningful as actual phase amplitudes because we have not yet applied any path- or source-corrections. This exercise is aimed at simply identifying seismograms with measurable phases. 204

223 Hz ScP-to-preP P-to-preP Number of seismograms retained Hz Hz Minimum signal-to-noise Figure C.2: Number of seismograms retained vs. minimum signal-to-noise. Dashed line: P amplitudes. Solid line: ScP amplitudes. Upper panel is Hz bandpass; middle panel is Hz; lower panel is Hz. The horizontal dotted line in each panel marks level at which 1/3 of seismograms are retained, and the vertical dotted lines note the signal-to-noise ratio at which this is obtained for each phase. Note that the values of signal-to-noise are not meaningful as actual phase amplitudes because we have not yet applied any path- or source-corrections. This exercise is aimed at simply identifying seismograms with measurable phases. 205

224 This process ensures that the P and P cp (or ScP) signal-to-noise selection are equallyweighted. Applying them jointly yields a final number of seismograms somewhat less than 1/3 of those meeting the source-property criteria. In practice, the database yields 21,334 seismograms satisfying the source-property criteria and with measurable P and PcP amplitudes. For the bandpass Hz, we choose a minimum signal-to-noise of for P and for PcP, each of which, independently applied, returns 7111 seismograms (the signal-to-noise values bear no relation to actual amplitudes since no corrections have been applied; we are simply trying to identify seismograms with measurable PcP). We stack the 5589 seismograms that match both the P and PcP signal-to-noise requirements. Likewise for Hz, we recover 5728 seismograms, and for Hz, 5549 seismograms. The ScP data set begins with 15,367 seismograms satisfying the source-property criteria. The signal-to-noise criteria then yield 3785 ( Hz), 3956 ( Hz), and 3769 ( Hz) seismograms to stack. 206

225 Appendix D Transformational faulting D.1 Thermo-kinetic modeling In normal mantle material, seismic velocity discontinuities at 410 km, 520 km, and 670 km are associated with phase transitions of the upper mantle s dominant material (olivine, [Mg Fe] 2 SiO 4 ) from the -phase to - and -spinel phases, and from spinel to lower mantle materials perovskite ([Mg Fe]SiO 3 ) and magnesiowüstite (MgO). -spinel is about 6% denser than olivine, and -spinel is another 2% denser than -spinel; perovskite is about 8% denser than -spinel [Green and Houston, 1995]; the velocity increases at 410 km and 670 km are [7.3% (V P ); 9.7% (V S )] and [4.6% (V P ); 6.5% (V S )], respectively [Shearer and Flanagan, 1999]. The presence of a cold descending plate complicates the situation. Because of the positive Clapeyron slope of the olivine-spinel equilibrium P T diagram (Figure D.1), in lowtemperature regions within the slab or just outside it, the high-density phase will appear at lower pressures (shallower depths) than in normal mantle [Sung and Burns, 1976]. 207

226 Temperature ( o C) Temperature ( o C) Depth (km) Pressure (GPa) Depth (km) Pressure (GPa) 700 Pv + Mw Pv + Mw 25 Figure D.1: From Kirby et al. [1996]. (a) Phase diagram for mantle olivine, showing equilibrium stability fields of olivine (), and and spinel. In two phase fields, the ratio Mg/(Mg+Fe) varies [Akaogi et al., 1989]. (b) Simplified phase diagram without two-phase fields. Within the coolest parts of the slab, however, the reaction rates for these transitions are reduced and a wedge of metastable olivine can persist into the stability field of spinel (Figure D.2) [Sung and Burns, 1976]. Recent thermo-kinetic modeling has attempted to establish the extent of the wedge by computing nucleation and growth rates of spinel, accounting for latent heat release and thermo-kinetic coupling [e.g., Devaux et al., 1997; Däßler and Yuen, 1996]. The transformation involves two processes: nucleation of the new phase and growth of the new phase at the expense of the host phase [Kirby et al., 1996]. The nucleation (I) and growth (Y ) rates are given by [Devaux et al., 1997]: I = I 0 T exp G t RT G k b T (D.1) 208

227 Depth, km Modified spinel & spinel Olivine stable + Olivine metastable Transformational faulting 100 km Pv + Mw Figure D.2: From Kirby et al. [1996]. Cartoon of mineralogy in a subducting slab, with shading representing metastable olivine wedge. Y = Y 0 T 1 exp G d exp G t RT RT (D.2) where G and G t are the activation energies for nucleation and growth, respectively, and G d is the free energy difference of the phases (driving potential). T is temperature, k b is Boltzmann s constant, and R is the universal gas constant. These expressions can be used to solve for the degree of transformation as a function of time and location, as in Devaux et al. [1997] s equations 12 and 21, for example. Nucleation occurs on olivine grain boundaries for differential stress less than about 1 GPa [Kirby et al., 1996]. Competing factors affect the nucleation and growth rates, depending on the degree of overstep of equilibrium. Increased driving potential (G d ) with higher pressure serves to increase the rates, but decreased thermal energy with temperature understep and increased G t from activation volume effects serve to reduce the rates [Däßler 209