Waveform search for the innermost inner core

Transcription

1 Waveform search for the innermost inner core Vernon F. Cormier 1 and Anastasia Stroujkova 1,2 University of Connecticut Storrs, CT Abstract Waveforms of the PKIKP seismic phase in the distance range 150± to 180± are analyzed for evidence of an inner-most inner core of the type proposed by Ishii and Dziewonski [1] having an abrupt change in elastic anisotropy near radius 300 km. Seismograms synthesized in models having a discontinuity at 300 km radius in the inner core exhibit focused diffractions around the innermost sphere at antipodal range that are inconsistent with observed PKIKP waveforms. Successful models have either a transition in elastic properties spread over a depth interval greater than 100 km or an innermost sphere that exceeds 450 km radius. Evidence of a sharp discontinuity in the lower to mid-inner core is sparse in existing global seismic data. Some examples, however, can be found of PKIKP complexity near 161 o, consistent with a triplication created by a 475 km radius discontinuity. An abrupt change in either viscoelastic or scattering attenuation at this radius is also observed in PKIKP waveforms, suggesting the existence of an innermost sphere with low, regionally uniform, seismic attenuation. In contrast to the relatively uniform inner-most inner core, a 0 to 100 km thick region at the top of the inner core exhibits strong lateral variations in attenuation and velocity structure, suggesting lateral variations in the processes of solidification, flow and re-crystallization at the inner

2 core/outer core boundary. Analogous to the evidence for an abrupt fabric change in the upper-most inner core, the seismic evidence for an innermost inner core may represent another fabric change near 700 km depth from the inner core/outer core boundary. This last and deepest change may simply signify the end stage of solidification, flow and recrystallization, resulting in the highest ordering and largest grain sizes of intrinsically anisotropic crystals. Author Keywords: inner core, body waves, modeling, anisotropy, synthetic seismograms Submitted: Earth and Planetary Science Letters, January 27, Corresponding author: Vernon.F. Cormier Physics Department University of Connecticut 2152 Hillside Road, Storrs, CT Fax: (860) Ph. (860) co-author (current address): Anastasia Stroujkova Weston Geophysical 57 Bedford Street Suite 102 Lexington, MA Fax: (781)

3 1. Introduction Investigations of the uppermost 300 km of the inner core characterize this region as one of stronger lateral heterogeneity [2, 3. 4, and 5] and higher attenuation [6] and scattering [7] compared to the deeper portion of the inner core. Observations of PKIKP waveforms suggest one or more possibly sharp transitions in chemistry, phase, or fabric between the uppermost 100 km of the inner core and the lower inner core (e.g.,[8 and 9]). Taken together these observations may be indicative of effects associated with progressive solidification and fabric reorientation by flow and re-crystallization between 0 to 300 km depth in the inner core. Recently Ishii and Dziewonski [1 and 10] have proposed a much deeper sharp transition in anisotropic elastic constants at a radius of 300 km (depth of 900 km). At this depth it becomes difficult to argue that a sharp structural transition might still be an effect of solidification. Ishii and Dziewonski [1] suggest instead that it might be evidence of two separate episodes of inner core formation. They also noted that if its boundary were sharp, it would produce dramatic waveform effects beyond 165 o. Although they did not specifically search for these waveform effects, they predict the existence of either a triplication or shadow zone and caustic, depending on the azimuth of rays with respect to axes of anisotropic symmetry of the inner core. At the antipode, the existence of an innermost inner core might also be confirmed by observations of waves diffracting around the upper side and the interference head wave along the lower side of its boundary. This diffraction and head wave are strongly focused by constructive interference from all azimuths, analogous to the antipodal focusing of PKP-C diffracted

4 and PKIIKP [11]. A goal of the study described in the following sections was to search and model dense profiles of waveform data in the 160 o to 180 o range to find evidence of these waveform effects produced by an innermost inner core. 2. Models For a material with cylindrical symmetry the relationship between the elastic velocity and the direction of propagation is given by [12,13, and 1]: where d V p 2 2 V p 2 = e cos x + s sin x cos x, d V p V p is the perturbation of the compressional velocity given by PREM [14], and x is the angle between the propagation direction and the axis of anisotropy. The parameters e and s are related to Love s parameters A, C, F, L, and N [15] as: e C - A 2rV - A - C + 2F + 4L =. 2rV = and s 2 2 We synthesized waveforms predicted by both the preferred values of s and e and 300 km discontinuity depth obtained by Ishii and Dziewonski [10] by fitting PKIKP travel times and normal modes. For the innermost inner core their values of anisotropic parameters are: e = 3.7% and s = -19.7%, while for the bulk inner core the parameters are: e = 1.8% and s = -0.67%. We also investigated the effects of similarly parameterized models in which the magnitude of the maximum perturbation DV/V was varied as well as the depth of either one or two discontinuities in the inner core. Jumps in S velocity and density for the near grazing angles in our study produce only second order effects in PKIKP waveforms compared to the effects of the triplication and shadow zone

5 induced by the P velocity change. Hence, in all cases we assumed a constant S velocity and density across the discontinuities. The sign and the magnitude of the velocity change should depend on the ray direction as well as on the anisotropic parameters (Figs. 1 and 2). The rays whose angles with respect to the axis are less than about 20 o should experience a velocity increase, leading to a triplication of a travel time curve. The seismograms of waves traveling at angles between about o would see a velocity decrease at the boundary of the innermost inner core, exhibiting a shadow zone followed by a caustic and two closely spaced arrivals, the later arrival being a Hilbert transform of the first arrival. 3. Data analysis The data for this study come from the WILBER II database, which contains data from both global networks and temporary arrays. Only the broadband channels have been used in this study, providing a flat frequency response to particle velocity in the frequency band of interest (0.1-3 Hz). Events in the magnitude range between 5.6 and 6.8 were selected to ensure good signal-to-noise ratio, provided they had simple shortduration source functions. To eliminate contamination of the signal by surface reflections we used events with source depths of at least 100 km (with a few exceptions). The additional benefit of using deep events in this magnitude range is their typically simple source-time functions. Our data consists of 65 events (Table 1). Some of these events were used in other studies of core phases [4]. In addition we used several events with known source-time functions [6 and 16]. The event waveforms were grouped based on the angle between the

6 ray and an axis of anisotropy assumed to be coincident with the axis of rotation. In each group the waveforms were stacked within 0.5± intervals. These stacked waveforms are shown in Fig. 3 for cos x < 0. 3 (left panel), 0.3 < cosx < (middle panel), and cos x > 0.75 (right panel). We used particle motion considerations to eliminate some of the secondary phases arriving after PKIKP. This type of analysis cannot definitively prove the origin of the phase, but it can eliminate arrivals having different slowness than PKIKP. Examples of the secondary phases and particle motions are shown in Figs. 4 a-b. Fig. 4a shows waveforms for the event The rays go through the inner core at an oblique angle with respect to the axis. Therefore these rays should encounter a velocity decrease at the hypothetical boundary. The secondary phases in the distance range between o arrive parallel to the first P wave. Therefore they are consistent with being inner core phases. Fig. 4b shows the event , which occurred in the Sandwich Island area. The rays form this event are incident at an acute angle with respect to the axis (polar path), and therefore should experience a velocity increase. Some of the waveforms have spatially coherent secondary phases following PKIKP in the distance range between o. The particle motion in this time window, however, is not parallel to that of the PKIKP time window, suggesting that these secondary arrivals are probably due to scattering near the receiver. 4. Waveform modeling To predict the waveforms near the antipode for different angles between the ray direction and the anisotropy axis we performed waveform modeling using the full wave

7 techniques described by [17] together with the antipodal modifications described by [11]. The velocity model is defined as a radially symmetric medium with velocities specified by analytical functions of depth. We used PREM as a reference model, and included a frequency-dependent and depth-dependent viscoelastic attenuation model for the inner core based on the study by [6]. To model an innermost inner core we perturbed PREM as shown in Fig. 2 according to the Ishii and Dziewonski anisotropic model assuming a constant value of the angle x for profiles corresponding to three x ranges. We assume reflection/transmission coefficients for an isotropic solid, substituting only the perturbed P velocities predicted by Ishii and Dziewonski type models in the isotropic coefficients. This introduces errors in the amplitudes and particle motions of reflected and transmitted waves, but these errors are very small compared to the much larger effects on P waveforms due to the changes in P velocity. The assumption of a constant angle x in the syntheses is strictly valid only for rays lying in the equatorial plane for anisotropic models assuming a symmetry axis coincident with the rotational axis. We found that that x varies only by about 10 o in ray shooting experiments for the P wave critically reflected by the innermost discontinuity, which, as a diffracted phase, becomes the largest secondary phase following PKIKP at the antipode. This x variation is not large enough to affect our results for the predicted constructive interference of antipodal phases diffracted around the innermost boundary. Rays traveling either near 0 o or near 90 o angles x with respect to the anisotropy axis would experience a velocity increase through the discontinuity, which causes a triplication (Fig. 5). The position of this triplication depends on the radius of the proposed discontinuity. The effects of the triplication for a 2% velocity increase are subtle, but are

8 visible in the broadening of the first downswing of the PKIKP velocity waveform beginning around o for discontinuities between 300 to 500 km radius. Although there are occasional suggestions of this subtle effect in individual stacked intervals for equatorial and polar data (Fig. 3 right and left panels), spatial coherence is simply not strong enough to confirm the existence of a triplication. At the antipode, synthetics predict a strong constructive interference of the diffraction around the upper side of the innermost discontinuity and the underside interference head wave. These combined phases are predicted to arrive 3 to 8 seconds after PKIKP at 180 o, depending on the depth of the innermost discontinuity. In Fig. 3, we find no evidence of this phase near 180 o in the equatorial profile. In the polar profile, the particle motion of suggestive secondary phases following PKIKP near 180 o is consistent with near receiver scattering rather than an inner core origin. Rays with intermediate values of angle x would experience a velocity decrease through the discontinuity (Fig. 6). The shadow zone predicted by ray theory is expressed by a reduction of wave amplitudes. For small velocity decreases on the order of several percent, an accurate observation of an amplitude reduction in the shadow zone is made impossible by the interference of two closely spaced diffractions. An increase in the magnitude of the velocity jump across a negative discontinuity causes a sharp increase in the amplitude at the caustic. Fig. 7 shows this effect for d V V p p = - 4% (compared with d V V p p = - 2% ). We carefully searched for antipodal amplitude variations in PKIKP in one dense profile of a single source that was recorded along paths having the intermediate x values that are predicted to correspond to a velocity decrease in the innermost inner core. In this profile we could not see any evidence of amplitude variations exceeding

9 20%. We also did not see any strong evidence of an antipodally focused diffraction around the upper side of an innermost boundary (Fig. 3 middle panel). 5. Discussion and conclusions We examined PKIKP waveforms the recorded between 150 o and 180 o. The data were compared with synthetic seismograms predicted from the two-layered anisotropy model of Ishii and Dziewonski [10], having a sharp discontinuity in anisotropic elastic constants at 300 km radius. Data were also compared with similar models having smaller velocity jumps and higher discontinuities. Sharp discontinuities of several percent in P velocity at radii between 300 and 500 km were found to produce either a triplication or shadow zone in the 165 o to 175 o range and antipodal focusing of phases grazing the upper and lower side of the discontinuity. We found no convincing evidence of any of these waveform effects in data profiles sorted by paths into equatorial, intermediate, and polar profiles. Although the triplication and shadow zones for discontinuities of this magnitude are relatively subtle and can be easily masked by signal generated noise (scattering), our synthetics predict the antipodal focusing to be strong enough to be observed. We found no convincing evidence of this antipodal focusing in the profiles we collected. In a very few cases where a strong coherent secondary phase was found to follow 3 to 8 sec after PKIKP, its particle motion could be explained by near receiver scattering. An additional constraint on the radius of a possible sharp transition in inner core properties is provided by the behavior of the seismic attenuation of the inner core. [6 and 18] measured PKIKP attenuation by combined source and attenuation operator modeling

10 to match broadband waveforms. Using the results of that study, Fig. 8 plots the standard deviation of attenuation of PKIKP bottoming in an innermost inner core as a function of the radius assumed for its boundary. Starting at an assumed boundary of radius 500 km, lateral variations in attenuation for PKIKP waves sampling this region become uniformly small The sharp transition in the variation in measured inner core attenuation near 500 km may mark either a critical transition in crystal ordering responsible for scattering attenuation, an abrupt disappearance of partial melt, a sudden extinction of an unknown attenuation mechanism, or a combination of these effects. If the discontinuity in anisotropic elastic constants required to satisfy global PKIKP travel times could be moved up to 500 km radius or higher as suggested by attenuation measurements, then the magnitude of the required velocity jumps would decrease would also decrease by a factor of 2 or more. The antipodal focusing of phases grazing this discontinuity would decrease in amplitude and their travel times would be shifted further from PKIKP, both effects making it harder to identify antipodally focused waves in the scattered coda of PKIKP. Other scenarios are also possible to explain the observed lack of antipodal focusing of an innermost inner core. The change in anisotropic properties might be spread out over a transition zone of about 50 km, narrow enough to be consistent with a sharp transition to laterally-homogeneous attenuation, but wide enough to extinguish the higher frequency diffractions and interference head waves focused at the antipode. Finally, anisotropy of an innermost inner core starting with a transition zone at a radius between 400 to 300 km may be much stronger than that proposed by Ishii and

11 Dziewonski, strong enough to destroy the constructive interference of waves grazing the discontinuity at antipodal distances. Giving strong weight to our results for the behavior of PKIKP attenuation, coupled with the lack of observed antipodal focusing, makes us advocate a model of an innermost inner core transition starting at km. To satisfy observed PKIKP travel times this transition may be weaker by a factor of 2 compared to the model Ishii and Dziewonski and it may be spread out over a 50 km wide transition. Combining this result in modeling deeply penetrating PKIKP, with results of modeling PKIKP sampling the uppermost 100 km of the inner core [5 and 9] our preferred inner core model consists of 3 separate regions, which may differ only in fabric. These regions are (1) an uppermost region of 20 to 100 km thickness that highly attenuates PKIKP waves, nearly isotropic, with significant lateral variation that may be related to lateral variations in initial solidification process of the inner core, (2) a middle region from 100 km to 700 km depth from the inner core boundary, with weaker anisotropy, weaker attenuation, and smaller lateral variations in elasticity and attenuation, (3) an innermost inner core below 700 km depth (500 km radius) with stronger anisotropy, little or no attenuation or scattering, possibly consisting of a more perfectly aligned fabric of much larger iron crystals compared to the regions above it. The transitions between these regions may either be as sharp as 50 km or less or simply occasionally appear sharp due to the effects of heterogeneity on waves at grazing incidence to the transitions (e,g., [19]). These two transition zones in inner core structure may eventually be explained by as yet unknown processes of flow and re-crystallization in the inner core, and hence not require distinct episodes of inner core formation.

12 Waveform data cannot yet exclude quite different models, including models having stronger anisotropy or deep lateral heterogeneity. Advances in the synthesis of teleseismic wavefields for fully 3-D and anisotropic models at frequencies approaching 1 Hz, together with dense 3-component, broadband, arrays at antipodal ranges will assist in either confirming our preferred model of two transition zones (one at 20 to 100 km depth from the inner core boundary and another at km radius) or be able to better constrain the possible anisotropic constants of an innermost inner core at a different radius. Acknowledgements We thank Miaki Ishii and Adam Dziewonski for reprints, and Rhett Butler, whose continued enthusiasm for antipodal observations, helped call our attention to this problem. This work was supported by the National Science Foundation Grant EAR References 1. Ishii, M., and A.M. Dziewonski, The innermost inner core of the Earth: Evidence for a change in anisotropic behavior at the radius of about 300 km. Proc. Natl. Acad. Sci. U.S.A. 22 (2002), pp.14,026 14, Tanaka, S., and H. Hamaguchi, Degree one heterogeneity and hemispherical variation of anisotropy in the inner core from PKP(BC) and PKP(DF) times, J. Geophys. Res. 102 (1997), pp

13 3. Garcia, R., Constraints on upper inner core structure from waveform inversion of core phases, Geophys. J. Int. 150 (2002), pp Wen, L, and F. Niu, Seismic velocity and attenuation structures in the top of the Earth s inner core, J Geophys. Res. 107(B11) (2002) doi: /2001JB Cao, A, and B. Romanowicz, Hemispherical transition of seismic attenuation at the top of the earth's inner core, Earth and Planet. Sci. Lett., (in press), Li, X, and V.F. Cormier, Frequency dependent attenuation in the inner core: Part I.A viscoelastic interpretation, J. Geophys. Res. 107(B12) (2002) doi: /2002JB Vidale, J. E., and P. S. Earle. Fine-scale heterogeneity in the Earth's inner core, Nature 404 (2000), pp Song, X., and D. V. Helmberger, Seismic evidence for an inner core transition zone, Science 282 (1998), pp Stroujkova, A., and V.F. Cormier, Regional variations in the uppermost 100 km of the Earth s inner core, J. Geophys. Res. 109(B10) (2004) doi: /2004JB Ishii, M., and A.M. Dziewonski, Distinct seismic anisotropy at the center of the Earth, Phys. Earth Planet. Int., 140, (2003) pp

14 11. Rial, J.A., and V.F. Cormier, Seismic waves at the epicenter s antipode, J. Geophys. Res. 85 (1980), pp Backus, G. E., Possible forms of seismic anisotropy of the uppermost mantle under the oceans, J. Geophys. Res. 70 (1965), pp Crampin, S., A review of the effects of anisotropic layering on the propagation of seismic waves, Geophys.J. R. Astron. Soc. 49 (1977), pp Dziewonski, A.M. and D.L. Anderson, Preliminary Reference Earth Model (PREM), Phys. Earth Planet. Inter. 25 (1981), pp Love, A. E. H.,. A treatise on the theory of elasticity, 4 th ed., (1927), Cambridge Univ. Press, New York. 16. Persh, S., Seismic Investigations of Core-Mantle Boundary and Source Properties of Deep-Focus Events, Data (Ph. D. Thesis), University of California, Los Angeles, California, Cormier, V., and P. Richards, Spectral synthesis of body waves in Earth models specified by vertically varying layers, in Seismological Algorithms, edited by Doornbos, 2002, pp

15 18. Cormier, V.F., and X. Li, Frequency dependent attenuation in the inner core: Part II. A scattering and fabric interpretation, J. Geophys. Res. 107(B12) (2002), doi: /2002JB Mereu, R., The heterogeneity of the crust and its effect on seismic wide angl reflection fields, in Heterogeneity in the Crust and Upper Mantle, edited by J. A. Goff, and K. Holliger, Kluwer, 2003.

16 Figure Captions Figure 1. A comparison of P-velocity for the upper 920 km (dashed line) and the innermost 300 km of the inner core as a function of ray angle from the model of Ishii and Dziewonski, (2003). Figure 2. Changes in the compressional wave speed with radius depending on the ray direction with respect to the axis according predicted by the two-layered anisotropic model of the inner core of Ishii and Dziewonski (2003). Figure 3. Waveform profiles stacked in 0.5 distance intervals for different orientations of PKIKP rays with respect to the rotational axis ( polar cosx < 0.3, intermediate 0.3 < cosx < 0.75 (middle panel), and equatorial cosx > 0.75 ). Figure 4. (a) PKIKP waveforms and particle motion of (a) event whose rays are at oblique angles to the rotational axis and (b) event whose rays are nearly polar. Note that the particle motion of the phase following PKIKP in event (b) is not consistent with an inner core origin. Figure 5. Seismograms synthesized in inner core models having a +2% P velocity discontinuity at radii 300 km (left), 400 km (middle), and 500 km (right).

17 Figure 6. Seismograms synthesized in inner core models having a 2% P velocity discontinuity at radii 300 km (left), 400 km (middle) and 500 km (right). Figure 7. A comparison of seismograms synthesized in a model having a 4% velocity discontinuity at 300 km radius with a model having a 2% velocity discontinuity at 300 km radius. Note the more pronounced amplitude effects of the model having the 4% discontinuity. Figure 8. The standard deviation of measured PKIKP attenuation as a function of radius of an innermost inner core. These measurements are compiled from reported attenuation measurements from PKIKP waveforms and bottoming depths in the studies of Li and Cormier (2002) and Cormier and Li (2002). A minimum of a 20 inner core attenuation measurements are used for each standard deviation calculated for each assumed discontinuity radius. The low level of standard deviation for radii less than 475 km suggests that this region of the inner core has very little lateral variation in seismic attenuation.

18 Vp (km/sec) x (deg) Figure 1

19 Velocity profile if the ray is traveling parallel to the symmetry axis Velocity profile if the ray o is traveling at 45 to the rotation axis Velocity profile in PREM (Dziewonski and Anderson, 1981) km/sec Figure 2

20 Figure 3

21 a) Event b) Event Figure 4

22 dvp = +2% R = 300 km iic dvp = +2% R = 400 km iic dvp = +2% R = 500 km iic Figure 5

23 dvp = -2% R = 300 km iic dvp = -2% R = 400 km iic dvp = -2% R = 500 km iic Figure 6

24 dvp = -2% R = 300 km iic dvp = -4% R = 300 km iic Figure 7

25 s for 1/Qp x Radius of Proposed IC Discontinuity Figure 8

26 Table 1. Seismic events used for the antipodal study Event Latitude Longitude Depth, km Event Latitude Longitude Depth, km

27