Estimation of S-wave scattering coefficient in the mantle from envelope characteristics before and after the ScS arrival

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 30, NO. 24, 2248, doi: /2003gl018413, 2003 Estimation of S-wave scattering coefficient in the mantle from envelope characteristics before and after the ScS arrival Won Sang Lee Seismological Observatory, School of Earth and Environmental Sciences, Seoul National University, Seoul, Korea Haruo Sato Department of Geophysics, Graduate School of Science, Tohoku University, Sendai, Japan Kiehwa Lee Seismological Observatory, School of Earth and Environmental Sciences, Seoul National University, Seoul, Korea Received 14 August 2003; revised 23 October 2003; accepted 29 October 2003; published 18 December [1] Examining seismogram envelopes of regional earthquakes in Central Asia with focal depths deeper than 150 km in 1s 20s periods for a wide lapse time range up to 2000s, we found an offset in each coda envelope before and after the ScS arrival at 10s and 15s periods. The ScS wave has its own tail, that is, scattered waves of ScS waves sometimes dominate over the original coda waves composed of scattered S waves and scattered surface waves. For 1s, 2s and 4s periods, such an offset is not clear. However, there is a change of coda decay gradient associated with the ScS arrival. In a layered velocity and attenuation structure according to the PREM, scattering process of S-waves can be simulated by using the Monte Carlo method based on the radiative transfer theory for isotropic scattering process. Comparing numerical simulation for a two-layered scattering model with observed envelopes, we estimated the total scattering coefficients as km 1 and km 1 at 4s, and km 1 and km 1 at 10s, for the lithosphere and upper mantle and for the lower mantle, respectively. In the lower mantle, scattering loss is dominant in the total attenuation of S waves. INDEX TERMS: 7207 Seismology: Core and mantle; 7218 Seismology: Lithosphere and upper mantle; 7299 Seismology: General or miscellaneous. Citation: Lee, W. S., H. Sato, and K. Lee, Estimation of S-wave scattering coefficient in the mantle from envelope characteristics before and after the ScS arrival, Geophys. Res. Lett., 30(24), 2248, doi: / 2003GL018413, Introduction [2] The excitation level of coda waves and the temporal decay gradient of coda amplitudes characterize the scattering strength and attenuation of the real earth medium. There 1 have been a lot of measurements of coda attenuation Q C and total scattering coefficients over the world [e.g., Sato and Fehler, 1998]; however, most of coda measurements reported were done for lapse times shorter than a few hundred seconds and for periods shorter than 1s. That is, most of these values characterize the heterogeneity of the lithosphere. There were some exceptions: Biswas and Aki Copyright 2003 by the American Geophysical Union /03/2003GL018413$05.00 SDE 5-1 [1984] Q C 1 reported in Alaska for periods from 1s to 10s, and Sato and Nohechi [2001] reported the excitation of Rayleigh-wave coda of periods for 100s 200s for longer lapse times. Rautian and Khalturin [1978] reported that coda envelopes of local earthquakes have a few lapse time segments characterized by different attenuation parameters. Assuming the decrease of g 0 with depth, Gusev [1995] theoretically predicted the decrease of Q C 1 with increasing lapse time. [3] Since the most prominent velocity contrast deep in the earth is the CMB, reflected phase ScS clearly appears in long period seismograms. Reflected phases associated with mantle discontinuities also appear on seismograms; however, there have been no reports on the envelope characteristics before and after these arrivals. [4] Having interests in the mantle heterogeneity, we examine the coda decay characteristics of regional deep focus earthquakes recorded at an IRIS station in Central Asia. We measure the decay of coda envelopes in several period bands from 1s to 20s for lapse times as long as 2000s. This lapse time range includes ScS and ScS 2 arrivals. For events deeper than 150 km in depth, we estimate especially the total scattering coefficient g 0 for 4s and 10s period bands using the direct simulation Monte Carlo (DSMC) method [Yoshimoto, 2000]. 2. Observation Data [5] Broadband velocity seismograms of regional earthquakes registered by the AAK station of the IRIS network in Central Asia were used for the analysis. From the data collected during the period from 1992 to 2001, 15 NScomponent seismograms were chosen for this study. Their magnitudes range from 5.3 to 6.5, epicentral distances are less than 1000 km, and focal depths are deeper than 150 km up to 250 km (Figure 1). [6] Second-order Butterworth band-pass filters having center periods of 1s, 2s, 4s, 10s, 15s and 20s are applied to data. Smoothing the square of band-pass filtered trace, we compute mean square (MS) envelopes. As an example, in Figure 2, gray traces exhibit the logarithmic plot of band-pass filtered MS envelopes. In order to correct the source-size differences, we plot these traces normalizing the average coda level at lapse time ranging from 650s to 750s as marked by a bold solid bar at the bottom. Vertical

2 SDE 5-2 LEE ET AL.: ESTIMATION OF S-WAVE SCATTERING COEFFICIENT simulation, we considered only S wave and assumed isotropic scattering consistent with an acoustic model with point scatterers. We use the velocity structure of S-wave having a positive gradient with depth as illustrated in Figure 3, which is a slight modification of the original PREM model [Dziewonski and Anderson, 1981]. According to the PREM, total attenuation profile chosen mostly from body wave studies can be approximated by a two-planelayered model where the boundary is 670 km in depth. We neglected the narrow low Q zone at km in depth: total attenuation Q m of the upper layer (Layer 1) and the lower layer (Layer 2) are 143 and 312, respectively. The scattering power per unit volume is given by g 0 value in each layer for each period. The total attenuation Q m works as a strong constraint for the range of variation of g 0 value. Figure 1. Epicenters (stars) of 15 deep focus earthquakes used for this study and an IRIS network station (AAK, triangle) in Central Asia. dashed lines indicate theoretically calculated S and ScS arrivals based on the IASP91 model. The black trace is a stacked trace for each period band. As seen in these plots, at 1s, 2s and 4s periods, the decay gradient is smooth irrespective of the ScS arrival and there is little difference in envelope levels before and after the ScS arrival. At 10s, 15s and 20s periods, however, the ScS phase is clear, the envelope decay gradients are different before and after the ScS arrival, and there is an offset of the envelope level around the ScS arrival. That is, the ScS wave has its own tail. We examined envelopes of shallow earthquakes; however, this characteristic is more prominent for MS envelopes of earthquakes with focuses deeper than 150 km. Thus, we confine our attention to deep focus events only in this study. Some phases arriving after the ScS arrival have been explained as reflections from the mantle discontinuities, the CMB and the earth s surface [Revenaugh and Jordan, 1989]. Similar offset and tail appearing in coda envelopes of local earthquakes in Kanto, Japan were reported by Obara and Sato [1988], and they interpreted the offset by the reflection on the surface of the subducting Pacific plate. Considering the similarity of the stacked envelopes with those observed for coda waves of local earthquakes, we propose to explain the envelope characteristics by the scattering of S-waves due to distributed heterogeneities in the mantle and the reflection at the CMB. 3. Numerical Simulation [7] We use the direct simulation Monte Carlo (DSMC) method [Yoshimoto, 2000] for the simulation of S wave envelopes in scattering media based on the radiative transfer theory with a complex spatial variation of velocity. For the Figure 2. Plots of the logarithmic MS band-pass filtered envelopes from 1s to 20s period bands at AAK in Central Asia. Gray traces are for 15 regional earthquakes within 1000 km in epicentral distances and 250 km in depths. MS envelopes of each period band are normalized by coda amplitude at lapse time ranging from 650s to 750s as indicated by a bold bar at the bottom. Black traces are stacked MS envelopes. Vertical dashed lines indicate theoretical S and ScS arrivals according to the IASP91 model.

3 LEE ET AL.: ESTIMATION OF S-WAVE SCATTERING COEFFICIENT SDE 5-3 Figure 3. The velocity structure (solid line) and the attenuation structure (dashed line) used in the synthesis. The velocity structure is modified after the PREM model for SV wave velocity. We use a two-layered scattering model for scattering and attenuation, where total attenuation Q m values of Layer 1 (shallower than 670 km in depth) and Layer 2 (up to the CMB) are 143 and 312, respectively. When g 0 value is given, the intrinsic attenuation term can be calculated by 1/Q i ( f ) = 1/Q m g 0 V s /(2pf ) for a given frequency f in Hz. [8] In the numerical calculations of particle tracing, we adopt a time step of t( f ) = 0.2/f in second, which is roughly less than one hundredth of mean free time (1/g 0 ( f )V(z)). One million particles are shot from the source. The number of energy particles contained in a receiver volume is counted every 10s. The source is put at a depth of 218 km and the receiver is put at a distance of 759 km according to the average of the observed events. At the ground surface and the CMB we assume total reflection. 4. Analysis of the Observed Data [9] We found changes in coda envelope decay gradient before and after the ScS arrivals in the MS envelopes for the period bands from 4s to 20s. In Figure 2, we could not see any offset and the envelopes have just small coda decay gradient change around the ScS arrivals for 1s, 2s and 4s period bands. The vertical offset, however, appears after the ScS arrival on 10s, 15s and 20s periods and coda decay gradient change around the ScS arrival is also much clear for the events deeper than 150 km. We carried out the grid search analysis to seek g 0 values that minimize the squared log residual between the observed data and the synthetic MS envelopes. In the grid search analysis, the maximum and the minimum boundary values of g 0 ( f ) are 98% and 2% of g 0m ( f ) calculated from Q m for each layer in the simulation. [10] The residual takes a minimum value at g 0 = ( for ±20% in error) km 1 for Layer 1 and g 0 = ( for ±20% in error) km 1 for Layer 2 at 4s. g 0 = ( for ±10% in error) km 1 and g 0 = ( for ±10% in error) km 1 at 10s for Layer 1 and Layer 2, respectively. In Figure 4, we show the stacked observation data by gray curves and the best-fit synthetic envelopes by black curves for the period bands 4s and 10s. It exhibits good coincidence between them except lapse time around 250s for 10s period. The discrepancy before 250s could be explained by the influence of surface waves. We can find a small offset with a small coda decay gradient for 4s and a clear offset with a big change of coda decay gradient for 10s after the ScS arrival in the simulation. For period bands, 15s and 20s, the influence of the surface waves is too strong in observed data, however, our model is for S-wave scattering and is not able to simulate surface wave scattering. For 1s and 2s period bands, the synthetic envelopes based on a two-layered scattering model are not able to explain simultaneously the strong ScS peak observed and the smooth decay of envelopes. [11] The Seismic Albedo (B 0 ), the ratio of scattering loss to the total attenuation in Layer 2 is higher than 74% and 80% for 4s and 10s periods, respectively. It means that the scattering mainly controls the seismic attenuation when the seismic waves pass through the lower mantle. Therefore, much stronger scattering than intrinsic attenuation might cause the offset behavior and coda decay gradient change after the ScS arrival for 4s and 10s period bands beneath Central Asia. 5. Discussion [12] Scattered S-waves or scattered surface waves are dominant in coda before the ScS arrival; however, scattered waves of ScS waves sometimes dominate over those scattered waves in later coda. It might mean that coda envelopes after 1000s in lapse time are mostly excited by the ScS waves. There is a bend of envelope decay and a level change around the ScS arrival, which is more than 5 db for 10s 20s. We could not find such anomaly, however, in smaller period bands. The change of coda decay gradient associated with the ScS arrival becomes smaller as the period becomes shorter. [13] Aki and Chouet [1975] and Rautian and Khalturin [1978] concluded that coda waves of periods longer than 1s were thought to be mostly composed of scattered surface waves. From our result, however, even at periods longer than 1s (at least up to 15s), envelopes of deep focus earthquakes at lapse times longer than 1000s are mostly composed of scattered S-waves associated with the ScS arrival rather than scattered surface waves. Rautian and Khalturin [1978] reported that coda envelopes show a systematic step-like change in decay rate with lapse time; however, we could not find such a systematic decay rate change, except only change once around the ScS arrival, up to lapse time 2000s. Sipkin and Jordan [1979] pointed out the importance of scattering loss due to random velocity inhomogeneities from the observed increase in Q 1 ScS with decreasing period from 100s to 1s. Our result is in harmony with their interpretation.

4 SDE 5-4 LEE ET AL.: ESTIMATION OF S-WAVE SCATTERING COEFFICIENT Figure 4. Gray curves show the observed MS envelopes for (a) 4s and (b) 10s period bands. The best-fit synthetic MS envelopes are represented by bold black curves and the best-fit total scattering coefficients are shown at the right-upper corner. The calculation window for the grid search analysis is from 300s to 1500s in lapse time. [14] The total scattering coefficient of S-waves in the lithosphere has been widely measured over the world for short periods and that of Rayleigh waves was measured for long periods. In Figure 5 we plot our results with those measurements. We believe that the scattering coefficients estimated in this study are quite reliable especially to understand the medium heterogeneity of the lower mantle. [15] From a preliminary survey of seismograms of regional deep focus earthquakes over the world [Lee et al., 2002], we found similar characteristics in S wave envelopes before and after the ScS arrival and the change in coda level varies from station to station. We note a contribution of surface wave scattering in addition to S-wave scattering especially before the ScS arrival. It suggests that it is necessary for us to discriminate the contribution of surface wave scattering and reflection and conversions at the mantle discontinuities in order to measure the spatial variation of mantle heterogeneity. 6. Conclusion [16] Examining seismogram envelopes of regional earthquakes in Central Asia in periods from 1s to 20s for a wide lapse time range up to 2000s, we found that the change of coda decay gradient becomes smaller as the period becomes shorter after the ScS arrival. We also found that envelopes have clear offsets around the ScS arrivals especially at 10s and 15s periods for earthquakes with focuses deeper than 150 km. That is, the ScS phase has its own decaying tail. These observations suggest that scattered waves of the ScS waves sometimes dominate over scattered S waves and scattered surface waves. As a result of grid search by using the DSMC method for synthesizing S wave envelopes, we estimated the scattering coefficients using total attenuation of the PREM as a restriction. For the two-layered scattering model, the resultant total scattering coefficients are km 1 and km 1 at 4s, and km 1 and km 1 at 10s, for Layer 1 and Layer 2, respectively. The scattering mainly controls the seismic attenuation when the seismic waves pass through the lower mantle. Thus we can imagine that much stronger scattering than intrinsic attenuation might cause the offset Figure 5. Resultant total scattering coefficients of S-waves in the mantle from the analysis of ScS records observed in Central Asia are marked by open and solid diamonds for Layer 1 and Layer 2, respectively. Total scattering coefficients of S-waves for short periods in the lithosphere (Modified after Figure 3.10 of Sato and Fehler [1998]) and those of Rayleigh waves for the lithosphere and the uppermost mantle [Sato and Nishino, 2002] are also plotted.

5 LEE ET AL.: ESTIMATION OF S-WAVE SCATTERING COEFFICIENT SDE 5-5 behavior and coda decay gradient change after the ScS arrival for 4s and 10s period bands. [17] Acknowledgments. The authors would like to thank K. Yoshimoto for his kind support for the use of DSMC. We would like to express our gratitude to V. I. Khalturin for his helpful comments on coda envelopes. We also thank A. Zollo and two reviewers for their critical comments that helped us to improve the manuscript. W. S. Lee is grateful to the BK21 Project of the Korean Government for their support for his long-term stay at Tohoku University as a visiting graduate student. References Aki, K., and B. Chouet, Origin of coda waves: Source, attenuation and scattering effects, J. Geophys. Res., 80, , Biswas, N. N., and K. Aki, Characteristics of coda waves: Central and south central Alaska, Bull. Seismol. Soc. Am., 74, , Dziewonski, A. M., and D. L. Anderson, Preliminary reference Earth model, Phys. Earth Planet. Inter., 25, , Gusev, A. A., Vertical profile of turbidity and coda Q, Geophys. J. Int., 123, , Lee, W. S., H. Sato, and K. Lee, A classification of the coda based on the envelope characteristics before and after the ScS arrival, Eos Trans., AGU, 83(47), Fall Meet. Suppl., Abstract S51A-1037, Obara, K., and H. Sato, Existence of an S wave reflector near the upper plane of the double seismic zone beneath the southern Kanto district, Japan, J. Geophys. Res., 93(B12), 15,037 15,045, Rautian, T. G., and V. I. Khalturin, The use of the coda for determination of the earthquake source spectrum, Bull. Seismol. Soc. Am., 68, , Revenaugh, J., and T. H. Jordan, A study of Mantle Layering Beneath the Western Pacific, J. Geophys. Res., 94(B5), , Sato, H., and M. C. Fehler, Seismic wave propagation and scattering in the heterogeneous earth, AIP Press/Springer Verlag, New York, 1 308, Sato, H., and M. Nohechi, Envelope formation of long-period Rayleigh waves in vertical component seismograms: Single isotropic scattering model, J. Geophys. Res., 106(B4), , Sato, H., and M. Nishino, Multiple isotropic-scattering model on the spherical Earth for the synthesis of Rayleigh-wave envelopes, J. Geophys. Res., 107(B12), , Sipkin, S. A., and T. H. Jordan, Frequency dependence of Q ScS, Bull. Seismol. Soc. Am., 69, , Yoshimoto, K., Monte Carlo simulation of seismogram envelopes in scattering media, J. Geophys. Res., 105(B3), , W. S. Lee and K. Lee, Seismological Observatory, School of Earth and Environmental Sciences, Seoul National University, Seoul, Korea. (daffodil@snu.ac.kr) H. Sato, Department of Geophysics, Graduate School of Science, Tohoku University, Sendai, Japan.