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Evaluation of accuracy of synthetic waveforms for subductionzone earthquakes by using a land–ocean unified 3D structure model
Earth, Planets and Space volume 70, Article number: 98 (2018)
Abstract
Seismic wave propagation from shallow subductionzone earthquakes can be strongly affected by 3D heterogeneous structures, such as oceanic water and sedimentary layers with irregular thicknesses. Synthetic waveforms must incorporate these effects so that they reproduce the characteristics of the observed waveforms properly. In this paper, we evaluate the accuracy of synthetic waveforms for small earthquakes in the source area of the 2011 Tohoku–Oki earthquake (M_{JMA} 9.0) at the Japan Trench. We compute the synthetic waveforms on the basis of a land–ocean unified 3D structure model using our heterogeneity, oceanic layer, and topography finitedifference method. In estimating the source parameters, we apply the firstmotion augmented moment tensor (FAMT) method that we have recently proposed to minimize biases due to inappropriate source parameters. We find that, among several estimates, only the FAMT solutions are located very near the plate interface, which demonstrates the importance of using a 3D model for ensuring the selfconsistency of the structure model, source position, and source mechanisms. Using several different filter passbands, we find that the full waveforms with periods longer than about 10 s can be reproduced well, while the degree of waveform fitting becomes worse for periods shorter than about 10 s. At periods around 4 s, the initial body waveforms can be modeled, but the later largeamplitude surface waves are difficult to reproduce correctly. The degree of waveform fitting depends on the source location, with better fittings for deep sources near land. We further examine the 3D sensitivity kernels: for the period of 12.8 s, the kernel shows a symmetric pattern with respect to the straight path between the source and the station, while for the period of 6.1 s, a curved pattern is obtained. Also, the range of the sensitive area becomes shallower for the latter case. Such a 3D spatial pattern cannot be predicted by 1D Earth models and indicates the strong effects of 3D heterogeneity on shortperiod (\({ \lesssim }\;10 {\text{s}}\)) waveforms. Thus, it would be necessary to consider such 3D effects when improving the structure and source models.
Introduction
Seismic wave propagation from shallow subductionzone earthquakes can be strongly affected by threedimensionally heterogeneous structures, such as oceanic water and sedimentary layers with irregular thicknesses (e.g., Okamoto 2002; Nakamura et al. 2012, 2015). In waveform analyses of earthquake sources and structural heterogeneities, these effects due to threedimensional (3D) heterogeneities must be properly incorporated in the synthetics, or otherwise the analyses could result in erroneous solutions (e.g., Okamoto and Takenaka 2009). Thus, we need to evaluate the accuracy of synthetic waveforms using a realistic 3D structure. Such studies require accurate source parameters and source locations. However, estimating these parameters for oceanic areas is often a challenge because of the presence of the abovementioned 3D heterogeneities and the onesided distribution of seismic stations with respect to a trench (e.g., Okamoto 2002; Takemura et al. 2016). It is not satisfactory to address the problem by using only longperiod waveforms, because surface waves are dominant in the longperiod records, and therefore, the body waves, which provide information such as Pwave travel times to deal with the biases, become insignificant. To deal with this problem, we recently developed a method called firstmotion augmented moment tensor (FAMT) analysis (Okamoto et al. 2017). FAMT analysis uses the initial part of the shortperiod waveforms in addition to the longperiod full waveforms in order to augment the information based on the body wave first motions. The detailed source time function can also be inferred by using shortperiod waveforms (4–40 s).
In this paper, we investigate the accuracy of synthetic waveforms for small suboceanic earthquakes in the Japan Trench area, in connection with the 2011 Tohoku–Oki earthquake (M_{JMA} 9.0: Fig. 1a), as the effect of 3D heterogeneities on the waveforms would be different depending on the source location on the vast fault plane of the 2011 Tohoku–Oki earthquake.
Data
We selected two events whose hypocentral parameters determined by the Japan Meteorological Agency (JMA) are: 01/11/2003, 22:10:08.33 (JST), 37.7742°N, 143.2713°N, depth of 46 km, \(M_{\text{JMA}}\) 6.2 (\(M_{\text{W}} 5.8\)), and 25/12/2007 23:04:32.85 (JST), 38.4833°E, 142.1537°N, depth of 40.29 km, \(M_{JMA}\) 5.6 (\(M_{W} 6.1\)), respectively (Fig. 1a; the \(M_{W}\) values were taken from the Global Centroid Moment Tensor (GCMT) catalog). Both events had interplate thrust mechanisms and occurred in the source region of the 2011 Tohoku–Oki earthquake. The waveforms from the 01/11/2003 event (referred to as EV2003 hereafter) and the 25/12/2007 event (referred to as EV2007), respectively, represent examples of “basic” waveforms from shallow and deep parts of the fault responsible for the 2011 Tohoku–Oki earthquake. We also note that, with the exception of EV2003, interplate thrust earthquakes with magnitudes of about 6 or greater are sparse around the GCMT location, which represents the major source region of the 2011 Mw9.1 Tohoku–Oki earthquake (Fig. 1a). We used local full waveform data recorded at the KNET, KiKnet, and Fnet stations (Fig. 1a) operated by the National Research Institute for Earth Science and Disaster Resilience (NIED).
FirstMotion Augmented Moment Tensor (FAMT) Analysis
In FAMT analysis, we combine a nonlinear waveform inversion method to estimate the moment tensor and the source time function of a point source simultaneously with a space–time grid search method to infer the best point source position and origin time correction that minimize the squared residual:
where \(D_{i} \left( {\varvec{x}_{i} ,t} \right)\) and \(S_{i} \left( {\varvec{x}_{i} ,t} \right)\) are the ith observed and synthetic waveforms, respectively, \(T_{i}\) is the length of the dataset, \(N_{\text{W}}\) is the number of waveforms, \(T = \mathop \sum \nolimits_{i = 1}^{{N_{\text{W}} }} T_{i}\), and \(w_{i}\) is weight on the ith datum (for details, see Okamoto et al. (2017) and its Additional file 1).
In the present analysis, as in Okamoto et al. (2017), passbands of 10–40 and 4–40 s are used for the “longperiod” and the “shortperiod” bandpassfiltered waveforms, respectively. The end time of the shortperiod waveforms is 10 s after onset of the Pwave, which is a sufficient duration to estimate the source time functions of the analyzed events. The weights (\(w_{i}\) in Eq. 1) are set to 3.0 for shortperiod waveforms and 1.0 for longperiod waveforms. The space–time grid searches are performed on 3528 spatial grid points for EV2003 (\(21 \times 21\) in horizontal and 8 in vertical), and 7938 points for EV2007 (\(21 \times 21\) in horizontal and 18 in vertical), and on seven time points from − 3 s to + 3 s with an increment of 1 s for the origin time corrections. The spatial increments are 2.4 km in horizontal and 1.2 km in vertical, respectively, for both cases.
The synthetic waveforms, \(S_{i} \left( {\varvec{x}_{i} ,t} \right)\) in Eq. (1), are composed of Green tensor generated with a triangular moment rate function with a width of 2 s. In order to incorporate the structural effects in the Green tensor, we use a land–ocean unified 3D structure model for the Japan Trench (Fig. 1b). This model was built from models of land–ocean topography (Kisimoto 2000), subsurface structures in the Japan Seismic Hazard Information Station V1 model (Fujiwara et al. 2009), the crust (Baba et al. 2006), the subducting Pacific plate (Baba et al. 2006), and the subducting Philippine Sea plate (Nakamura et al. 2010).
The Green tensor was computed using the same reciprocal method as in Okamoto et al. (2017), in which we applied our heterogeneity, oceanic layer, and topography (HOT)FDM scheme (Nakamura et al. 2012) with the correct fluid–solid boundaries. The spatial grid interval and maximum frequency of the FDM simulations were 150 m and 0.611 Hz, respectively. The simulations were performed on the TSUBAME2.5 and 3.0 supercomputers at the Tokyo Institute of Technology, Japan, using 150–640 graphic processing units (GPUs) as accelerators (Okamoto et al. 2010, 2013). For the details of the FDM parameters, see Additional file 1: Table S1.
Results of FAMT Analysis
We find that the best origin time correction to the JMA origin times is 0 s for both events (Additional file 1: Fig. S1). The inferred FAMT parameters are listed in Table S2 and S3 in Additional file 1. For both EV2003 and EV2007, the distributions of the residuals (F in Eq. 1) display welldefined spatial minimums (Fig. 2a, b). In the case of EV2003, the reddish area with small residuals is confined to layer 2 of the oceanic crust, and in the case of EV2007, the upper limit of the reddish area is nearly along the inclined plate interface: these features show the sensitivity of the waveforms to the source positions in the 3D model. In both cases, the FAMT locations are almost at the plate interface of the 3D model and are thus consistent with the interplate mechanisms of these events. Figure 2c, d compares various estimated source depths: the GCMT and the JMACMT are based on waveforms with periods of 40 s or longer, and the Fnet MT is based on waveforms with periods of 20 s or longer. Along with these routinely determined solutions are plotted the positions of LPMT (longperiod MT) that denote the best locations of the point moment tensor sources determined in this study by using the same procedure as in the FAMT analysis but with only the longperiod (10–40 s) data. The estimates based on the longperiod waveforms tend to be deeper than the plate interface (except the JMACMT of EV2003). It is unlikely that these differences in the estimated depths are the result of the source finiteness, as the fault planes are considered to be located along the plate interface. Thus, we consider that these differences are caused by the differences between the assumed structures of the respective analyses and by the degraded resolution of the longperiod (longwavelength) signals. The FAMT solutions demonstrate the importance of the 3D structure for ensuring the “selfconsistency” of the structure model, source locations, and source mechanisms. The horizontal scatter of the source locations is within a few kilometers for EV2003 and within 20 km for EV2007 (Additional file 1: Fig. S2).
Figure 3 compares the observed velocity waveforms with the synthetics determined in the FAMT analyses. The synthetic waveforms fit the observed waveforms generally well in both cases. The simple shortperiod waveforms (the initial Pwaves) of EV2003 are well reproduced with an approximately triangular source time function. On the other hand, a somewhat complex source time function is estimated for EV2007 on the basis of the multiple (split) peaks in the observed shortperiod waveforms.
We compare the observed waveforms with the synthetics computed using the 3D model and a flatlayered (1D) structure model for a period band of 10–40 s in Fig. 3c, d. The 1D synthetics were computed using the 1D structure model listed in Table 3 of Wu et al. (2008) and the discrete wavenumber method program (Takeo 1985) with the FAMT parameters. The 1D model was constructed for the analysis of the 1978 and 2005 Miyagi–Oki earthquakes that occurred near the coast; thus, the fit of the 1D synthetics to the observations is better for EV2007 (Fig. 3d) than for EV2003 (Fig. 3c). The landbased 1D structure model is not appropriate for EV2003, which occurred far off the coast; this can be seen from the large misfit of the 1D synthetic surface wave packets to the observations. Even for EV2007, the major phases (surface waves) show phase shifts and amplitude mismatches relative to the observations, even in the applied longperiod band (10–40 s).
Waveform fitting
To evaluate the degree of waveform fitting, we compare the observed and synthetic waveforms with several passbands. Figure 4a, b plots waveforms from two selected stations (TYS and HRO; all the waveforms are plotted in Additional file 1: Figs. S3 and S4). In these analyses, the FAMT parameters are used to generate synthetic waveforms; in so doing, the biases due to inappropriate source mechanisms and locations are minimized. For the shortest passband (2–4 s), the observed waveforms show prolonged ground motions in some components (e.g., HRO in Fig. 4b and MYGH06 in Additional file 1: Fig. S3a), but the corresponding synthetics do not reproduce such characteristics. For the passbands of 4–7 and 7–10 s, which are included in the passband of the “shortperiod” waveforms in the FAMT analysis, the later largeamplitude surface waves are not well reproduced by the synthetics, while the body waveforms of the initial Pwaves are reproduced (Fig. 3). The observed waveforms with periods of around 10 s or longer, especially the major part of the surface wave packets, are generally well reproduced, as shown in the fourth pairs of Fig. 4a, b.
Figure 4c, d plots the normalized residuals (F in Eq. 1) computed using the full waveforms of the 33 components in the case of EV2003 and the full waveforms of the 42 components in the case of EV2007, respectively. Here, we set all the weights to 1.0 in order that a residual value of 1.0 is assigned to a synthetic trace with “null” (zero) amplitude: that is, a residual larger than 1 (depicted with green lines in Fig. 4c, d) indicates a synthetic worse than the “null trace.” For both events, the residuals for passbands shorter than 10 s are larger than 1, while those for passbands longer than 10 s are smaller than 1: these values indicate that the synthetics with periods shorter than 10 s do not fit the corresponding observations, as described above. The residual of the 4–40 s passband also exceeds 1 for EV2003, while it is (slightly) smaller than 1 for EV2007, which shows that the synthetics with the 4–40 s passband fit the observations to some extent for the latter event. This fit can be visually verified in Fig. 4b (bottom pairs of traces) and in Additional file 1: Fig. S4e. We consider that this difference between EV2003 and EV2007 is due to the different source locations: the EV2007 event occurred close to land at a relatively deep plate interface, where the effect of heterogeneous shallow structures would be weaker than in the case of EV2003, which occurred far off the coast at a shallow plate interface.
We note that the normalized residual depends on the selected time window. Limiting the time window to the body wave part dramatically reduces the residuals (Additional file 1: Figs. S5 and S6), indicating that the Pwaves are reproduced well at short periods down to around 4 s. The residuals for the passband of 2–4 s are not sufficiently reduced in our analysis, because the passband is outside that of the FAMT analysis and the waveforms are not well constrained.
Discussion: sensitivity kernels
Through the FAMT analyses of the subductionzone earthquakes, we have concluded that the seismic waveforms cannot be reproduced in the periods shorter than about 10 s, and the degree of fitting depends on the source locations, with better fittings for deep sources near land. These results indicate the necessity of improving the 3D structure model, especially for shortperiod waveforms from shallow sources far off the coast like EV2003. For this purpose, it would be helpful to study the regions where the waves propagate in the heterogeneous structure. In order to gain insights into the characteristics of such wave propagations, we employ an analysis based on the sensitivity kernel.
The sensitivity kernel has been used to study heterogeneities in the Earth’s interior (Tarantola 1984; Tanimoto 1990; Tromp et al. 2005; Zhao et al. 2005; Yoshizawa and Kennett 2005). We use the method of Tanimoto and Okamoto (2014) to compute the waveform sensitivity kernels. The perturbation in a single component of the displacement in the frequency domain (\(\delta u\left( \omega \right)\)) can be expressed using the sensitivity kernels \(K_{\rho }\), \(K_{\lambda }\), and \(K_{\mu }\) as follows:
with
where \(\rho\) denotes the density, \(\lambda_{0}\) and \(\mu_{0}\) the reference elastic constants (relaxed moduli), \(\mu_{0}\) the rigidity, \(e_{ij}\) the strain tensor, and \(\Delta = \mathop \sum \nolimits e_{ii}\) (the above definitions are slightly different from that of Tanimoto and Okamoto (2014)). These kernels are computed from two wavefields: the forward wavefield computed with the earthquake source and the adjoint wavefield, which is denoted with the superscript \(A\) and computed with a single (impulsive) force placed at the station location (the direction of the force is the same as that of \(\delta u\)).
Here, we discuss the sensitivity kernels for the vertical component at station TYS for EV2003. We apply the FAMT parameters for the forward modeling of the seismic wavefield with a triangular moment rate time function with a base width of 2 s and a vertical single force with a triangular time function with a base width of 2 s at the station location for the adjoint wavefield. In computing the wavefield, we use the same method (GPUaccelerated HOTFDM) as in the FAMT analyses. To avoid the singularity at the source location, we use a cosinetapered finite source centered at the FAMT best location and distributed along the plate interface with a radius of 5 km for the forward wavefield. Further, we apply spatial smoothing to the raw kernels with a running average using a cell of \(11.7 \times 11.7\) km horizontally and 6.3 km vertically. We apply a Fourier transform to the full synthetic waveforms with a duration of 250 s from the onset of the source application to obtain the components in the frequency domain. The real parts of the smoothed, normalized kernels thus computed are shown in Fig. 5. The kernel for a period of 12.8 s (Fig. 5a) displays a horizontal distribution nearly symmetric with respect to the straight path between the source and the station. This feature suggests a moderate effect of the heterogeneous structure, which results in the synthetics having a good fit to the observations for the longperiod band (\({ \gtrsim }\,10 {\text{s}}\)) waveforms. Also, the sensitive area extends to a relatively deep part (about 21 km deep), while the sensitivity in the shallow part (about 2 km deep) is relatively weak. On the other hand, the shortperiod kernel (6.1 s) shows a bend and has a spatially asymmetric pattern, which indicates a strong effect due to the 3D heterogeneous structure. A strong, shallow sensitive area in the depth range from 2 to 11 km for the period of 6.1 s indicates that shallow structures, such as sedimentary layers, are important in modeling shortperiod waveforms. Such a spatial pattern of sensitivity cannot be predicted with 1D Earth models and indicates the strong effects of 3D heterogeneity on shortperiod (\({ \lesssim }10 {\text{s}}\)) waveforms. In addition, the crossbranch coupling between different mode branches would have a significant effect on the propagation of shortperiod surface waves in the period range treated in this study (e.g., Kennett and Nolet 1990; Marquering and Snieder 1995). Thus, it would be necessary to consider 3D effects such as curved paths and crossbranch coupling when improving the structure models. The finitedifferencebased adjoint kernels displayed in this study incorporate all these effects and would be suitable for the study of the Earth’s shallow structure.
Abbreviations
 FDM:

finitedifference method
 3D:

threedimensional
 JMA:

Japan Meteorological Agency
 FAMT:

firstmotion augmented moment tensor
 NIED:

National Research Institute for Earth Science and Disaster Resilience
 GCMT:

global centroid moment tensor
 GPU:

graphic processing unit
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Authors’ contributions
TN provided the model of the Philippine Sea plate. TO compiled the structure models for constructing the 3D structure model of the FDM simulations; coded the FDM program; performed the FDM simulation, inversion analysis, and sensitivity kernel analysis; and wrote the draft of the manuscript. HT and TN took part in discussions of the 3D structure model and the interpretation of the results of the inversion analyses. All authors contributed to the discussion and conclusions. All authors read and approved the final manuscript.
Acknowledgements
The authors are grateful to JMA, NIED, and GCMT project for providing the earthquake parameters, to K Kisimoto and T Baba for providing the structure models, to NIED for providing the waveform records of KNET, KiKnet, and Fnet, and to M Takeo for providing the discrete wavenumber program. Comments by K Yoshizawa (editor) and two anonymous reviewers were very helpful in improving the manuscript.
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
The waveform data used in this study are available on the NIED Web site.
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Funding
This study was supported by the Japan Society for the Promotion of Science (KAKENHI grant no.16K05535), HPCI System Research Project (Project ID: hp130118), and Joint Usage/Research Center for Interdisciplinary Largescale Information Infrastructures in Japan (JHPCN) (Project ID: jh170022NAJ).
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Additional file
Additional file 1: Table S1.
FDM parameters. Table S2. Estimated FAMT source parameters. Table S3. Estimated best double couples based on FAMT solutions. Figure S1. Residuals versus origintime correction. Figure S2. Horizontal source locations estimated by the FAMT and other analyses. Figure S3. Comparisons of the observed and synthetic velocity waveforms for EV2003. Figure S4. Comparisons of the observed and synthetic velocity waveforms for EV2007. Figure S5. Comparisons of the first body wave part of the observed and synthetic velocity waveforms for EV2003. Figure S6. Comparisons of the first body wave part of the observed and synthetic velocity waveforms for EV2007.
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Okamoto, T., Takenaka, H. & Nakamura, T. Evaluation of accuracy of synthetic waveforms for subductionzone earthquakes by using a land–ocean unified 3D structure model. Earth Planets Space 70, 98 (2018). https://doi.org/10.1186/s406230180871z
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DOI: https://doi.org/10.1186/s406230180871z
Keywords
 Japan Trench
 Subductionzone earthquake
 Waveform inversion
 GPU computing