Energy and Rupture Dynamics are Different for Earthquakes on Mature Faults vs. Immature Faults

Transcription

1 1 2 Energy and Rupture Dynamics are Different for Earthquakes on Mature Faults vs. Immature Faults 3 Rebecca M. Harrington Karlsruhe Institute of Technology Geophysical Institute rebecca.harrington@kit.edu Emily E. Brodsky University of California, Santa Cruz Dept. Earth Sciences brodsky@pmc.ucsc.edu 4 February 12,

2 Abstract We compare radiated energy per unit moment, seismologically observable fracture energy per unit moment, and static stress drop between earthquakes on immature fault surfaces in Parkfield, California, and Mount St. Helens Volcano, and on a mature fault surface, namely the San Andreas fault near Parkfield, California. A comparison between the two populations indicates that earthquakes on immature fault surfaces exhibit more self-similar behavior. Energy to moment ratios and static stress drop values remain roughly constant for immature faults, and decrease with magnitude for mature fault surfaces. The decrease in the parameters for the mature population results from an unchanging fault area for earthquakes smaller that M 3.3 on the San Andreas fault. The ratio of seismologically observable fracture energy to the total energy associated with the dynamic stress drop suggests that the seismologically observable fracture energy scales with the dynamic energy. We estimate the seismologically observable fracture energy accounts for approximately 70% of the energy associated with dynamic stress drop. A comparison of energy-moment scaling with other studies suggests that the values observed here are a general feature, and within the expected range. The difference in source parameter scaling between immature and mature populations suggests that ordinary scaling relationships relating moment and area and an assumed constant stress drop are not valid for every earthquake population individually. However, constant seismologically observable fracture energy-dynamic energy ratios between populations suggest that energy partitioning is the same, regardless of fault surface geometry. 2

3 28 1 Introduction Seismically observable earthquake source parameters such as duration (τ), seismic moment ( ) and the radiated seismic energy (E R ) provide the only direct clues as to how faults rupture [Wesnousky, 2006; Kanamori and Rivera, 2004; Choy and Kirby, 2004; Wyss and Brune, 1968]. Theoretical relationships are often used to derive other source parameters such as static stress drop ( σ), average slip on the fault surface ( D), and the seismically observable fracture energy (E G ), as well as to determine theoretically expected scaling relationships between parameters. As an example, one commonly calculated source parameter relationship, namely static stress drop vs. seismic moment, suggests that σ is roughly constant with respect to, i.e. that earthquake rupture is scale invariant [Kanamori and Brodsky, 2004; Kanamori and Anderson, 1975; Abercrombie, 1995; Ide et al., 2003; Imanishi and Ellsworth, 2006; Abercrombie and Rice, 2005; Prieto et al., 2004; Shearer et al., 2006]. The commonly accepted values of roughly constant static stress drop range over tion that earthquake source properties are in fact scale invariant, particularly when parameters such as the ratio of radiated energy to seismic moment ( E R ) seem to vary with moment [Abercrombie, 1995; Prejean and Ellsworth, 2001; Venkataraman and Kanamori, 2004; Mayeda et al., 2007; Venkataraman et al., 2006b]. Certainly some of the scatter in measured values of source parameters results from difficulty in accurately measuring parameters such as E R, and consequently E R 2 to 3 orders of magnitude for small earthquakes, calling into question the assump- [Venkatara- man et al., 2006a]. However, some work suggests that heterogeneous properties in the faulting environment might influence parameters such as static stress drop, and E R, suggesting that geophysical factors might also account for some of the range 3

4 in observations [Venkataraman and Kanamori, 2004; Choy and Kirby, 2004]. One such physical factor which may contribute to the range in source observations is fault maturity. Recent studies using laser techniques to image fault surfaces indicate that they become smoother with more cumulative displacement, suggesting that immature fault surfaces, with less cumulative displacement, are rougher than more mature faults, with more cumulative displacement [Sagy et al., 2007; Sagy and Brodsky, 2009]. Given the physical differences in surface geometry between mature and immature faults, it follows that earthquakes might rupture differently, depending on the faulting environment in which they occur. The results of Sagy et al. [2007]; Sagy and Brodsky [2009] suggest that immature fault surfaces may be assumed self-affine in the direction of slip, i.e. surface roughness is scale invariant. However, mature fault surfaces become more smooth, and develop quasi-elliptical geometric asperities on the order of 10 s of meters for faults with cumulative slip on the order of 100 s of meters [Sagy and Brodsky, 2009]. Cumulative slip values of the San Andreas fault near Parkfield are on the order of hundreds of kilometers [Sims, 1993; U.S. Geological Survey, California Geological Survey, 2006], and we can therefore speculate that such elliptical bumps are also present on the fault surface. Harrington and Brodsky [2009] show that a group of small earthquakes on the San Andreas fault have an approximately constant duration over two orders of catalog magnitude. They argue that an assumption of constant rupture velocity requires that the fault area remain constant over the magnitude range observed, and interpret their observations as the repeated rupture of an asperity with radius of roughly 75 m (assuming a circular geometry). An asperity of such dimensions is consistent with the smoothed elliptical bumps observed by Sagy 4

5 et al. [2007] in mature faulting environments, suggesting that differences in fault surface geometry are observed seismically as well. The question then follows of whether there are observable differences in dynamic source properties, such as seismically radiated energy, between earthquakes on faults with different amounts of cumulative slip. Ohnaka [2003] suggests that there are observable differences in dynamic source 82 properties between rough and smooth faults. He develops a constitutive relation dependent on fault friction and seismologically observable fracture energy that governs fault rupture. The relation relates seismologically observable fracture energy to fault surface roughness, suggesting that the energy partitioning in an earthquake (and therefore the amount of radiated energy) depends on surface roughness as well. In this study, we examine whether dynamic properties between rough and smooth faults differs on a larger scale, by using a new compilation data set of earthquake recordings. Harrington and Brodsky [2009] showed that a group of earthquakes on the San Andreas fault have a duration-seismic moment scaling suggestive of an approximately constant fault area. Here we present new evidence using an expanded data set to suggest that fault maturity affects the seismically radiated energy (E R ), as well as the seismologically observable fracture energy (E G ). By comparing the energy-moment ratios ( E R, E G ) of earthquakes on the San Andreas fault to those on secondary faults in the Parkfield area, and on new fault surfaces in the Mount St. Helens edifice, we will show that the earthquakes on immature faults obey the energy scaling expected for constant stress drop, while those on mature faults do not. We will also show that although energy scaling varies between immature and mature earthquake populations, the ratio of seismologically observable fracture energy to the total energy associated 5

6 with the dynamic stress drop remains constant across both earthquake populations. In addition, we will present our results in the context of other studies which examine fault roughness and damage and offer an interpretation of energy partitioning in the context of our observed energy scaling. We begin the paper with a description of the data set and the methods and theory used to determine source time functions and energy terms. Next, we present in the observations section the observed differences between ratios of radiated seismic energy to moment, and seismologically observable fracture energy to moment ( E R, E G ). We compare our observations with other studies which measure similar source properties in other locations, in order to show that they are a general feature. In the discussion section we will also show that the ratio of the seismologically observable fracture energy to the total energy assiciated with the dynamic stress drop during rupture does not vary for either earthquake population. The constant energy ratios suggest that E G is directly related to off-fault damage, when viewed in the context of a straightforward damage model. We discuss the interpretation of our observations in the context of fault surface evolution, and summarize our findings in the conclusions section Methods and Observations Our data set consists of earthquakes in the Parkfield area, and earthquakes located in the volcanic edifice of Mount St. Helens volcano. All earthquakes in our data set are below a catalog magnitude of 3.7. We note that most of the earthquakes at Mount St. Helens are not cataloged, as the numerous events resulting from the ongoing eruption 6

7 in 2005 prevented many earthquakes from being analyzed. Because the earthquakes in our data set are small, accounting for high-frequency attenuation (particularly in the volcanic edifice) is crucial to investigating source parameter scaling. We use an empirical Green s function approach to eliminate attenuation effects caused by the path the seismic waves travel from the source to the receiver, as well as the site effects at the station, and instrument response. In both Parkfield and at Mount St. Helens, we use co-located event pairs to spectrally deconvolve the path, site, and instrument response from earthquake recordings, and then use the remaining source time function spectra to model source spectral parameters. We discuss the details further in the methods subsection Methods Our data set includes two populations of similar sized earthquakes: one population contains (1) earthquakes on a mature fault (namely, the San Andreas fault near Parkfield), and (2) earthquakes on immature faults with negligible cumulative displacement relative to the San Andreas fault. The events on immature faults occur on secondary faults at least 5 km away from the main San Andreas fault system in Parkfield, and on fresh fault surfaces created during the 2004 dome building eruption at Mount St. Helens (Figures 1, and 2). The earthquakes in Parkfield consist of 25 events located on the San Andreas fault, and 11 earthquakes located on various 141 secondary faults with magnitudes ranging from 1.4 to 3.7. We used the double difference relocated catalog for Parkfield to obtain events located both on and off the active San Andreas fault strand. Those off of the main strand are assumed to be located on secondary faults (Rymer 2007, personal communication) [Thurber et al., 7

8 ]. The earthquakes at Mount St. Helens consist of 40 events located at the base of an extruding solid rock spine in the crater of the volcano in February and March of 2005 (when station MIDE was operational). We calculate magnitudes ranging from 0.4 to 1.4 for the set of events. The earthquakes were found by cross-correlation of larger master events over both low- and high-gain channels of Pacific Northwest Seismographic Network (PNSN) stations MIDE and NED in order to find co-located events below the catalog threshold. Because we obtain source time functions via a spectral division method, we are limited to co-located event pairs with a magnitude unit or more difference in size. We begin by deconvolving an empirical Green s function (the event with the smaller magnitude in each pair) from the entire waveform of the larger co-located event in order to obtain the source-time function for all of the events in our data set. Once we obtain the source-time function, we calculate the source spectra of each event. Only two seismic stations were both operational in February and March of 2005, and located close enough to the crater to record the small earthquakes associated with the solid rock spine extrusion at Mount St. Helens. The two stations, MIDE and NED, of the PNSN are short-period, vertical component seismometers peaked at 1 Hz, having sample rates of 100 sps. For the earthquakes located in Parkfield, we use all available station recordings from the High Resolution Seismic Network (HRSN). The HRSN consists of 13, 3-component borehole stations with depths ranging from m, an average depth of 236 m, and a sampling rate of 250 sps. For each event, we stack all of the available source time function files determined at each station in order to have a spatially averaged source time function. For specific details of the source time function spectral calculation, such as the width of the time windows used 8

9 for the Fourier transforms, station averaging, and magnitude determination, we refer the reader to Harrington and Brodsky [2007] and Harrington and Brodsky [2009]. Using the spectra along with the modeled, and f c values, we can calculate other source parameters such as the energy moment ratio ( E R ), seismologically observable fracture energy moment ratio ( E G ), and static stress drop ( σ). A comparison of all source parameters between populations permits us to make inferences regarding how the fault maturity affects their relative scaling. We model the source spectra for each event using a Brune spectral model with spectral falloff n = 2 [Brune, 1970; Abercrombie, 1995]. 178 Ω(f) = Ω 0 (1 + ( f f c ) n ) (1) We calculate a least-squares fit to the spectral data using the Brune spectral model in order to calculate the values for the corner frequency (f c ) and the long period spectral amplitude (Ω 0 ) from which we calculate the moment Harrington and Brodsky [2007, 2009]. Out of the 40 earthquakes in the Mount St. Helens edifice, 36 come from one earthquake family (recorded at station MIDE), meaning that we were able to use a single empirical Green s function to determine the source time function for the 36 events. We determined the seismic moment of the empirical Green s function using the long period portion of the earthquake spectrum. The event was extremely small (estimated magnitude of 0.07), and therefore only recorded on a single station located 150 m from the source. Estimating the absolute moment error is therefore difficult, however, the error between relative values of the 36 events should be negligible because of the use of a single empirical Green s function. The moment and corner frequency 9

10 for the remaining four events recorded at station NED follow the same scaling as those events recorded at MIDE. The earthquakes in Parkfield however, are not clustered at a single location as are those at Mount St. Helens. Therefore, each source time function requires a separate empirical Green s function, and calculating the relative seismic moment from a single event is not possible. We therefore rely on the magnitude calculations provided by the NCSN catalog, as the instrument coverage in the area is dense, and magnitude errors in the region are estimated to be as low as magnitude units [Eaton, 1992; Bakun, 1984]. We also estimate the error in NCSN magnitude calculations by calculating the seismic moment using only the HRSN stations for the earthquakes in our data set and converting them to magnitude using the standard relation which converts seismic moment to moment magnitude (M w ) [Hanks and Kanamori, 1979]. Our magnitude estimates have a standard deviation of 0.3 magnitude units from the NCSN catalog values. Given that our magnitude estimations come only from the 13 HRSN stations, and the values estimated by Eaton [1992]; Bakun [1984] are lower, we take 0.3 magnitude units as an upper bound to the catalog magnitude error for the earthquakes located in Parkfield. The error bars in Figures 3, 4,and 5 reflect the upper bound error estimate for the catalog values. Given the modeled f c values, the calculated moment values at Mount St. Helens, and the moment values converted from the catalog in Parkfield, we calculate the radiated seismic energy (E R ) of the two populations following similar methods to Prieto et al. [2004]. We use the fitted f c and long period amplitude (Ω 0 ) values in 10

11 213 combination with a Brune spectral model to calculate the integrated velocity, I. 214 { } 2 2πfΩ 0 I = 1 + ( f df (2) f c ) n 215 We then use I in the calculation of E R [Prieto et al., 2004]. 216 E R = U 2 θφ 4πρβ 5 M 2 0 I Ω 2 0 (3) Where U 2 θφ = 2/5 is the mean S-wave radiation pattern over the focal sphere, β = 3500 m s kg is the shear-wave velocity, and ρ = 2700 m 3 We use values of β = 650 m s, and ρ = 2000 kg m 3 is the density for Parkfield. for the loosely consolidated volcanic rock and ash in the Mount St. Helens edifice. We base the calculations on S-waves values because the S-wave energy accounts for more than 97% of the total radiated energy [Kanamori et al., 1993]. Equation 3 is independent of geometrical spreading and radiation pattern terms, and is therefore appropriate for source-time function spectra. We now discuss how we calculate the remaining source parameters using the values of moment and corner frequency obtained from the spectral model. We can relate the static stress drop for a circular, two-dimensional fault to the scalar moment using the following equation [Burridge and Knopoff, 1964]: 229 = 16 7 σa3 (4) 230 where a is the fault radius. We then relate f c to a using the following relationship 11

12 [Madariaga, 1976]: a = 0.32β f c. (5) By combining Equations 4 and 5, we have the stress drop in terms of the quantities estimated using our source spectra. ( fc ) 3 (6) 235 σ = β We discuss in the Observations section how we use E R E G. and σ to estimate values of Observations The ratio of radiated seismic energy to moment, E R may be considered as the amount of energy radiated per unit fault area per unit slip in an earthquake. It characterizes the dynamic properties of rupture, and provides indirect information about the rup- ture process [Wesnousky, 2006; Kanamori and Rivera, 2004; Choy and Kirby, 2004; Wyss and Brune, 1968]. Given the physical differences in surface geometry between young and old faults, it follows that earthquakes might rupture differently, depending on the faulting environment in which they occur. For example, one might expect to observe differences in rupture speed and seismologically observable fracture energy, depending on differences in surface roughness. The group of earthquakes on immature faults, i.e. those on secondary faults in Parkfield, and in the Mount St. Helens crater, occur presumably on rougher fault surfaces. We assume the immature faults are rougher based on the fieldwork of Sagy et al. [2007]; Sagy and Brodsky [2009], and because their cumulative displacement is 12

13 negligible in comparison to the San Andreas fault. Similarly, the events on the San Andreas fault, i.e. the earthquakes comprising the mature population, occur presum- ably on a smoother fault surface. If we can assume that differences in fault surface geometry cause the observed differences in the radiated energy to moment ratios ( E R ) between the immature and mature earthquake populations, then the differences demonstrate how differences in faulting environment might influence properties of rupture (Figure 3). A least-squares fit for both the mature and immature populations indicates a slope of 0.8 and 0.02 respectively in the variation of E R with seismic moment (Figure 3). The fit suggests a negligible variation of the E R fault surfaces, and a much stronger dependence of E R ratio for the immature (rougher) on moment for the mature (smoother) fault surface. Figure 4 suggests that the amount of seismologically ob- servable fracture energy per moment ( E G ) is directly related to the radiated seismic energy per moment value. The relationship between E G and E R can be understood by considering an earthquake rupture model which assumes no overshoot or under- shoot. Using such a model, one can show that E R is directly proportional to the sum of stress drop and seismologically observable fracture energy E G [Kanamori and Heaton, 2000; Abercrombie and Rice, 2005; Kanamori and Brodsky, 2004]. The pro- portionality becomes apparent when considering the total elastic energy release in an earthquake, W. Consider that the total energy release in an earthquake is parti- tioned into radiated energy, E R, seismologically observable fracture energy, E G, and constant component of friction, E f. 274 W = E R + E G + E f (7) 13

14 The total energy can also be written in terms of the average stress, the fault area, and the average slip on the fault, 277 W = σ 1 + σ 0 Ad (8) where σ 1 and σ 0 are the final and initial stresses respectively. If one assumes that the frictional stress on the fault surface is equal to the final stress (i.e. no overshoot or undershoot), then the frictional energy can be written in terms of the final stress. 281 E f = σ 1 Ad (9) Equation 9 can then be substituted into the in the energy equation, producing the following relation σad = E R + E G E G = 1 2 σad E R (10) 285 If we use the equation for scalar moment, 286 = µa D (11) 287 then we can write Equation 10 in terms of the energy moment ratios, 288 E G = 1 σ 2 µ E R (12) where µ is the rigidity [Keilis-Borok, 1959; Kanamori and Anderson, 1975]. Using Equation 12 to calculate E G, we obtain values which are on average 7 times a large 14

15 as values of E R using Equation 6. calculated using source spectra (Figures 3 and 4). We calculate σ Comparison with faults from the literature The earthquakes in both our mature and immature populations occur in non-typical 295 faulting environments. The events comprising the mature population occur near the creeping/locked transition of the San Andreas fault, and the majority of those comprising our immature population occur in a volcanic edifice, rather than a tectonic fault. We consider the possibility that our observations result from using earthquakes in a unique environment by comparing our energy-moment ratios and static stress drop values to those of other studies. Figures 6, 7, and 8 plot our observations shown in Figures 3, 4, and 5 along with the results of Prieto et al. [2004], Abercrombie [1995], and Abercrombie and Rice [2005] for comparison. They show that our earthquakes follow the same trend as other populations of mature and immature events elsewhere 304 on more typical faults in southern California. The analogous immature events consist of those analyzed by Prieto et al. [2004], while the mature events consist of those analyzed by Abercrombie [1995], and Abercrombie and Rice [2005]. The measurements of energy and stress drop in Prieto et al. [2004] come from earthquakes originating near Buckridge on the Anza section of the San Jacinto fault in southern California. We consider the Prieto et al. [2004] data set an analog to the immature population, as the earthquakes in their data set occur on a fault segment which has an estimated cumulative displacement of approximately 6 km according to Sharp [1981] [Sharp, 1981; U.S. Geological Survey, California Geological Survey, 2006]. The total estimated slip on the Parkfield section of the San Andreas fault is 15

16 approximately 310 km by comparison [Sims, 1993; U.S. Geological Survey, California Geological Survey, 2006]. The events analyzed in the preferred model (2) by Abercrombie [1995], and those re-analyzed in Abercrombie and Rice [2005] are analogous to the mature population, as they occur near the Cajon Pass section of the San Andreas fault, which has a cumulative displacement similar to Parkfield. The cumulative displacement on the San Andreas fault at in Parkfield and the Cajon Pass is nearly two orders of magnitude larger than that in Anza, and therefore great enough to consider the events of Abercrombie [1995]; Abercrombie and Rice [2005] as belonging to a mature population. The results of Abercrombie [1995] use a Brune source model 323 with a seismic Q S = Q P = 1000 to estimate the source parameters, rather than a spectral ratio approach. However, we assume that the comparison of our results is valid due to the high-quality borehole seismic data used, and the consistency of their results with the later analysis of Abercrombie and Rice [2005], which uses a spectral ratio approach similar to the one used here. The similarity of the scaling between mature and immature populations therfore suggests that the observed features of the earthquakes in the mature population near Parkfield and the immature population near Parkfield and at Mount St. Helens in our data set may be a general feature of earthquakes outside of our study areas, and not the result of some unusual faulting environment Discussion The comparison of the ratios of energy to moment ( E R, E G ) between populations of earthquakes occurring on both mature and immature faults suggest that fault maturity affects the dynamics of rupture. More specifically, the energy relations in 16

17 Figures 3 and 4 suggest that at least for smaller earthquakes, less energy is radiated away and less energy goes into forming new fractures on smoother, more mature faults compared to rougher, less mature faults. While the mature population obeys the self-similar scaling observed for the duration-moment scaling of the earthquakes in Parkfield, the decreasing energy-moment ratios also likely results from the unchanging source area observed [Harrington and Brodsky, 2009]. The roughly constant fault area observed may be dictated by the asperity size, meaning that the smallest patch of the mature fault surface that might rupture in 345 typical earthquake may be limited by the size of the elliptical bump. Immature faults have scale invariant roughness, which would imply that earthquake rupture might result from asperity rupture at a variety of length scales. In such a scenario, one would expect to observe a population of earthquakes with a wide distribution of rupture areas, leading to an observation of self-similarity, or constant stress drop ( σ), and an invariant energy-moment ratio ( E R ). In fact, we observe a nearly constant value of σ for the earthquakes in the immature population (Figure 5). We speculate that once the rupture length of a particular earthquake exceeds the elliptical bump (i.e. asperity) dimension by a significant amount, that fault slip and length may scale once again according to constant stress drop. Furthermore, we speculate that the minimum asperity size on a fault asymptotically tends toward a fixed value. Such a hypothesis is supported not only by our observation of a fixed fault area. Studies of fault zone damage suggest that when a fault is first formed, the width of the damage zone increases with fault displacement up to a certain offset, after which the rate of damage formation decreases [Savage and Brodsky, 2010; Chester and Chester, 2005]. Savage and Brodsky [2010] argue using observations of fracture density that 17

18 the amount of displacement at which the damage rate decreases is 100 m, after which, the observed damage formation rate becomes roughly constant, because the fault damage zone with is no longer determined by larger asperities (see Savage and Brodsky [2010], Figure 4). They interpret the decline in damage formation dependence on asperity size as the result of slip being distributed throughout a wider patch on the fault surface, making it easier for the slipping patches to get around large asperities without damaging host rock. Consequently, they claim that earthquakes on less mature faults which accommodate more slip past asperities should have higher radiated energy values compared to their counterparts on mature fault surfaces. (We claim in such a scenario that seismologically observable fracture energy values should be higher as well, if more asperities are being damaged). Figures 3 and 4 indicate a higher E R, and E G per unit for the immature population, and are consistent with their claim. Although our observations suggest that absolute energy values may differ between mature and immature populations, we examine what portion of the energy associated with the slip on the fault surface goes into seismologically observable fracture energy. Consider the energy partitioning model discussed in the Observations section where the final stress on the fault surface is assumed to be the frictional sliding stress (i.e. 379 no overshoot or undershoot). Such a model is commonly used to describe energy partitioning during rupture, and is effectively the model described in Figure 18 of Kanamori and Brodsky [2004] [Chester and Chester, 2005; Kanamori and Brodsky, 2004; Kanamori and Heaton, 2000]. We use such an example to describe the energy portioning in the mature population and immature population of earthquakes (Figure 9). Let the total energy associated with the dynamic stress drop be defined as 18

19 E dyn. E dyn is the sum of E R, and E G, and is given in terms of the static stress drop, fault area, and slip in the left side of Equation 10. Alternatively in terms of moment, E dyn can also be written as the following. 388 E dyn = 1 2µ σ (13) The fraction of the total energy associated with the stress drop taken up by the seismologically observable fracture energy is then given by 391 E G E dyn = 2µE G σ, (14) and is shown in Figure 10. Interestingly, the fraction of seismologically observable fracture energy, or the portion of the energy associated with the slip dependent stress, 394 is roughly constant for both populations. Stated alternatively, the seismologically observable fracture energy scales with the total energy associated with the stress drop, regardless of fault geometry. If the assumed model sufficiently describes the energy 397 partitioning process, one can estimate using Figure 10 that E G is approximately % of E dyn. As discussed in detail by Tinti et al. [2005], some portion of E G may actually be dissipated via frictional heating, and may not be used entirely for fracture formation. One might illustrate such additional slip-dependent frictional heating by 401 modifying the energy model depicted in Figure 9 to have a line separating E f and E G which is no longer straight, and may be above the line shown. They therefore refer to the seismologically observable fracture energy as breakdown work (W d ). If, as they suggest, only some small portion of E G is directly related to damage, then we might conjecture, based on the observations of Savage and Brodsky [2010] which 19

20 record similar damage patterns regardless of fault maturity, that the percentage of energy going into damage formation is the same regardless of whether the earthquake happens on an immature or mature fault. Such a conjecture would also be consistent with their hypothesis stating that off-fault damage patterns for all types of faults can be straightforwardly described as being inversely proportional to the distance from the fault surface. The implication would also mean that the poorly understood E G term is a measure of fracture formation both on the fault surface and in the surrounding host rock, in addition to a slip-dependent frictional dissipation Conclusions A comparison of E R, E G, and σ between earthquakes on immature fault surfaces in Parkfield, California, and Mount St. Helens Volcano, Washington, and on a ma- ture fault surface, namely the San Andreas fault near Parkfield, CA, indicates that the values are roughly constant for immature faults, while the values decrease with decreasing magnitude for mature fault surfaces. The decrease in the energy-moment ratio results from an unchanging fault area, for earthquakes smaller that M 3.3 on the San Andreas fault. The implications for an unchanging fault area are that fault length and slip do not scale as expected for a constant static stress drop ( σ). The static stress drop for the mature faults does not remain constant as expected for cases of constant stress drop, but rather decreases with magnitude. Therefore E G decreases as expected given the direct dependence on σ, and E R, assuming that the final stress on the fault surface equals the frictional stress (σ 1 = σ H ). Although both the radiated energy and the fracture energy values scale differently 20

21 for the immature and mature populations, the fraction of the total energy associated with the dynamic stress drop (i.e. the energy not going into frictional heating) used by the fracture energy remains constant, independent of faulting environment. Stated alternatively, the fracture energy scales with the total dynamic energy. In addition, the energy model used suggests that the seismologically observable fracture energy accounts for about 70% of the dynamic energy budget. A constant seismologically observable fracture energy fraction is consistent with a model of off-fault damage formation which invokes a single mechanism, and suggests that the seismologically observable fracture energy term in common energy models (E G ) is a measure of fracture formation both on and near the fault surface. The difference in source parameter scaling between immature and mature earthquake populations suggests that the ordinary scaling relationships resulting from a commonly assumed constant stress drop are not generally valid for each earthquake population individually. However, while moment-area scaling might differ depending on fault surface geometry, the energy going into fracture formation, into slip dependent frictional dissipation, and into generating seismic waves seems to be partitioned in the same way, independent of fault maturity Acknowledgments The Mount St. Helens seismic data used here was collected by the Cascades Volcano Observatory, and the Pacific Northwest Seismograph Network, and distributed by the Incorporated Research Institutions for Seismology (IRIS). The IRIS DMS is funded through the National Science Foundation and specifically the GEO Direc- 21

22 torate through the Instrumentation and Facilities Program of the National Science Foundation under Cooperative Agreement EAR Data on fault locations and displacements was collected from the U.S. Geological Survey, California Geological Survey, 2006, Quaternary fault and fold database for the United States, accessed Sept. 15, 2009, from USGS web site: http//earthquakes.usgs.gov/regional/qfaults/. Parkfield waveform data is provided by Berkeley Seismological Laboratory, University of California, Berkeley and accessible through the Northern California Earthquake Data Center (NCEDC) website. The projected Landweber deconvolution code was provided by Hiroo Kanamori, and the FDDECON deconvolution code was provided by Thorne Lay. This work was supported by the National Science Foundation grant EAR , and the Alexander Von Humboldt foundation. 22

23 References Abercrombie, R. E., Earthquake source scaling relationships from -1 to 5 M(L) using seismograms recorded at 2.5-km depth, J. Geophys. Res., 100, 24,015 24,036, Abercrombie, R. E., and J. R. Rice, Can observations of earthquake scaling constrain slip weakening?, Geophys. J. Int., 162, , Bakun, W. H., Seismic moments, local magnitudes, and coda-duration magnitudes for earthquakes in central California, Bull. Seismol. Soc. Am., Brune, J. N., Tectonic stress and the spectra of seismic shear waves from earthquakes, J. Geophys. Res., 75, , Burridge, R., and L. Knopoff, Body force equivalents for seismic dislocations, Bull. Seismol. Soc. Am., 54, , Chester, F. M., and J. S. Chester, Fracture surface energy of the Punchbowl fault, San Andreas system, Nature, 437, , Choy, G. L., and S. H. Kirby, Apparent stress, fault maturity and seismic hazard for normal-fault earthquakes at subduction zones, Geophys. J. Int., 159, Eaton, J. P., Determination of amplitude and duration magnitudes and site residuals from short-period seismographs in northern California, Bull. Seismol. Soc. Am., 82, , Hanks, T. C., and H. Kanamori, Moment magnitude scale, J. Geophys. Res., 84, , Harrington, R. M., and E. E. Brodsky, Volcanic hybrid earthquakes that are brittlefailure events, Geophys. Res. Lett., 34 (L06308), Harrington, R. M., and E. E. Brodsky, Source duration scales with magnitude differently for earthquakes on the San Andreas Fault and on secondary faults in Parkfield, CA, Bull. Seismol. Soc. Am., 99, , Ide, S., G. C. Beroza, S. G. Prejean, and W. L. Ellsworth, Apparent break in earthquake scaling due to path and site effects on deep borehole recordings, J. Geophys. Res., 108 (2271), 2271, Imanishi, K., and W. L. Ellsworth, Source scaling relationships of microearthquakes at Parkfield, CA, determined using the SAFOD pilot hole seismic array, in Earthquakes: Radiated Energy and the Physics of Faulting, edited by R. E. Abercrombie, 23

24 A. McGarr, H. Kanamori, and G. Di Toro, Geophysical Monograph Series, pp , AGU, Kanamori, H., and D. L. Anderson, Theoretical basis of some empirical relations in seismology, Bull. Seismol. Soc. Am., 65, , Kanamori, H., and E. E. Brodsky, The physics of earthquakes, Reports On Progress In Physics, 67, , Kanamori, H., and T. H. Heaton, American Geophysical Union Geophysical Monograph 120, chap. Microscopic and macroscopic physics of earthquakes, American Geophysical Union, Kanamori, H., and L. Rivera, Static and dynamic scaling relations for earthquakes and their implications for rupture speed and stress drop, Bull. Seismol. Soc. Am., 94, , Kanamori, H., J. Mori, E. Hauksson, T. Heaton, L. K. Hutton, and L. M. Jones, Determination of earthquake energy-release and M(L) using Terrascope, Bull. Seismol. Soc. Am., 83, , Keilis-Borok, V., On estimation of the displacement in an earthquake source and of source dimensions, Ann. Geofis. (Rome), 12, , Madariaga, R., Dynamics of an expanding circular fault, Bull. Seismol. Soc. Am., 66, , Mayeda, K., L. Malagnini, and W. R. Walter, A new spectral ratio method using narrow band coda envelopes: Evidence for non-self-similarity in the Hector Mine sequence, Geophys. Res. Lett., 34 (11), Ohnaka, M., A constitutive scaling law and a unified comprehension for frictional slip failure, shear fracture of intact rock, and earthquake rupture, J. Geophys. Res., 161 (9-10), Prejean, S. G., and W. L. Ellsworth, Observations of earthquake source parameters at 2 km depth in the Long Valley caldera, eastern California, Bull. Seismol. Soc. Am., 91, , Prieto, G. A., P. M. Shearer, F. L. Vernon, and D. Kilb, Earthquake source scaling and self-similarity estimation from stacking P and S spectra, J. Geophys. Res., 109,

25 Sagy, A., and E. E. Brodsky, Geometric and rheological asperities in an exposed fault zone, J. Geophys. Res., 114 (B02301), Sagy, A., E. E. Brodsky, and G. J. Axen, Evolution of fault-surface roughness with slip, Geology, 35 (3), , Savage, H., and E. E. Brodsky, Collateral damage: Capturing fault strand formation in fracture profiles, Submitted to Geology, Sharp, R. V., Variable rates of late quaternary strike slip on the San-Jacinto fault zone, Southern-California, 86 (NB3), , Shearer, P. M., G. A. Prieto, and E. Hauksson, Comprehensive analysis of earthquake source spectra in southern California, J. Geophys. Res., 111 (B06303), Sims, J. D., Chronology of displacement on the San Andreas fault in central California evidence from reversed positions of exotic rock bodies near Parkfield, California, in Powell, R.E., Weldon, R.J., II, and Matti, J.C., in The San Andreas fault system Displacement, palinspastic reconstruction, and geologic evolution: Geological Society of America Memoir 178, pp , Geol. Soc. Am., Thurber, C., H. Zhang, F. Waldhauser, J. L. Hardebeck, A. Michael, and D. Eberhart- Phillips, Three-dimensional compressional wavespeed model, earthquake relocations, and focal mechanisms for the Parkfield, California, region, Bull. Seismol. Soc. Am., 96, S38 S49, Tinti, E., P. Spudich, and M. Cocco, Earthquake fracture energy inferred from kinematic rupture models on extended faults, J. Geophys. Res., 110 (B12303), B12,303, U.S. Geological Survey, California Geological Survey, Venkataraman, A., and H. Kanamori, Observational constraints on the fracture energy of subduction zone earthquakes, J. Geophys. Res., 109 (B05302), Venkataraman, A., G. C. Beroza, and J. Boatwright, A brief review of techniques used to estimate radiated seismic energy, Geophysical Monograph, 170, 15 24, 2006a. Venkataraman, A., G. C. Beroza, S. Ide, K. Imanishi, H. Ito, and Y. Iio, Measurements of spectral similarity for microearthquakes in western Nagano, Japan, J. Geophys. Res., 111, 2006b. Wesnousky, S. G., Predicting the endpoints of earthquake ruptures, Nature, 444, , doi: ,

26 Wyss, M., and J. N. Brune, Seismic moment, stress, and source dimentions for earthquakes in the California-Nevada region, J. Geophys. Res., 73, 4681,

27 Figure 1: Parkfield study area. The map shows the location of the mature (circles), and immature (diamonds) events used in our study. Symbols are scaled according to earthquake duration as determined from the source time function pulse width. Source time functions for these earthquakes are obtained by projected Landweber deconvolution of a co-located earthquake that is at least one magnitude unit smaller than the events shown. The large stars represent the epicenters of the 1966 and 2004 earthquake epicenters. Symbol shapes and colors follow the same convention in the subsequent figures. 27

28 Figure 2: Mount St. Helens study area. The map shows the location of cataloged earthquakes occurring from 2/26/2005 to 3/8/2005 (the time of our data set). Note that events shown here are meant to give an indication of the location of cataloged seismicity during the time period of our data collection. They do not correspond to the exact location of the events in our data set. The earthquakes in our data set are below the catalog threshold. S-P wave arrival times, as well as a lack of seismicity elsewhere in the volcanic edifice indicate that their locations are in the crater. 28

29 Figure 3: Radiated energy to moment ratio ( E R ) vs. earthquake size. Earthquakes on immature faults are represented by red diamonds, black X s and + s. Earthquakes on a mature fault are represented by blue circles. A constant value of E R with respect to moment would represent constant stress drop scaling. Long dashed line (least-squares fit) indicates that earthquakes on the immature faults exhibit roughly constant stress drop scaling, while those on mature faults have a decreasing E R with moment (short-dashed line). Error bars on the Parkfield earthquake data indicate our estimated upper bound of catalog magnitude error of 0.3 magnitude units (see text). 29

30 Figure 4: Ratio of seismic fracture energy vs. seismic moment ( E G ) vs. Earthquake size. Earthquakes on immature faults are represented by red diamonds, black X s and + s. Earthquakes on a mature fault are represented by blue circles. A comparison between values from earthquakes on mature, vs. immature faults indicate that the ratio remains roughly constant for earthquakes on mature, or rougher faults, (as expected for constant stress drop scaling) and decreases with moment for earthquakes on mature, smoother faults. Error bars on the Parkfield earthquake data indicate our estimated upper bound of catalog magnitude error of 0.3 magnitude units. 30

31 Figure 5: Seismic moment vs. stress drop. A comparison between values from earthquakes on mature, vs. immature faults. Earthquakes on immature faults are represented by red diamonds, black X s and + s. Earthquakes on a mature fault are represented by blue circles. A least squares fit indicates stress drop remains roughly constant for earthquakes on immature, or rougher faults (slope = 0.06), and decreases with moment for earthquakes on mature, smoother faults (slope = 0.93). Error bars on the Parkfield earthquake data indicate our estimated upper bound of catalog magnitude error of 0.3 magnitude units. 31

32 Figure 6: Figure 3 shown together with the data points of Prieto et al. [2004], Abercrombie [1995], and Abercrombie and Rice [2005] for comparison, suggesting that our results are a general feature. Events analyzed by Prieto et al. [2004] are representative of an immature population, while those from Abercrombie [1995], and Abercrombie and Rice [2005] are representative of a mature population. 32

33 Figure 7: Figure 4 shown together with the data points of Prieto et al. [2004], Abercrombie [1995], and Abercrombie and Rice [2005] for comparison, suggesting that our results are a general feature. Events analyzed by Prieto et al. [2004] are representative of an immature population, while those from Abercrombie [1995], and Abercrombie and Rice [2005] are representative of a mature population. 33

34 Figure 8: Figure 5 shown together with the data points of Prieto et al. [2004], Abercrombie [1995], and Abercrombie and Rice [2005] for comparison, suggesting that our results are a general feature. Events analyzed by Prieto et al. [2004] are representative of an immature population, while those from Abercrombie [1995], and Abercrombie and Rice [2005] are representative of a mature population. 34

35 Figure 9: Schematic representation of the energy partitioning in an earthquake on a mature fault surface (right) and an immature fault surface (left). For two earthquakes of comparable seismic moment, the lower stress drop and slip values would be consistent with a weaker fault. σ S 0, σ W 0, and σ 1 represent initial stress on a strong fault, initial stress on a weak fault, and the final sliding stress respectively. D c, termed critical slip, represents the amount of slip required for the stress as a function of slip to go from the initial to the sliding stress. Values for the radiated energy (E R ), and seismically observable fracture energy (E G ) are indicated schematically as the the area of the shaded regions. 35

36 Figure 10: Figure indicates that the ratio of fracture energy to total energy associated with the stress drop ( 2µE G σ ) is approximately constant for both mature and immature populations. The seismologically observable fracture energy is proportional to the total energy associated with the dynamic stress drop (E dyn = E R +E G ), and accounts for about 70% of E dyn (see text). Considering the constant energy ratio in the context of a damage model requiring a single mechanism for damage formation suggests that the E G term accounts for fracture formation both on the fault surface and in the surrounding rock. 36