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Validation of the Osaka basin velocity model by waveform simulation using sources inverted with reciprocal Green’s functions
Earth, Planets and Space volume 75, Article number: 69 (2023)
Abstract
To advance the methodology for validating velocity models by waveform comparison, we estimated source parameters for small magnitude earthquakes that can be approximated by point sources. Instead of using published source models, we used the reciprocity method to calculate 3D Green’s functions using the target velocity structure itself, and then inverted the earthquake sources. This method greatly reduces the calculations required compared to a full inversion of the source mechanism, depth, and source duration (risetime), making it possible to reproduce input ground motions in the target basin. Here, we validated the Japan Integrated Velocity Structure model of the Osaka basin using five earthquakes around the Osaka basin; these earthquakes allowed us to investigate the impact of the incident waves’ propagation directions. We first estimated source parameters using records at control bedrock sites surrounding the Osaka basin to reproduce the input ground motions. Then, we conducted a 3D finitedifference simulation for sites within the basin. By mapping the distributions of misfit values for individual waveforms, peak ground velocities, and response spectra, we were able to identify areas in the basin that require additional tuning of the velocity model.
Graphical Abstract
Introduction
The Osaka basin is a 2.5kmdeep sedimentary basin hosting the cities of Osaka and Kobe, as well as numerous structures vulnerable to longperiod ground motions, such as skyscrapers, oil tanks, and longspan bridges. Thick sedimentary cover, such as in the Osaka basin, is known to enlarge ground motion amplitudes. Since the 1985 Michoacan earthquake, realistic heterogeneous source models and 3D velocity structures have been widely and successfully used to simulate and predict damaging longperiod ground motions. Velocity structure models of the Osaka basin have been progressively developed as more data have become available (e.g., Iwasaki et al. 1994; Kagawa et al. 2004; Iwata et al. 2008). All these models have used spline interpolation for the bedrock depth (Koketsu and Higashi 1992) and a threelayer structure employing constant velocities within the layers and layer thicknesses proportional to the bedrock depth. Because they use just a few parameters, however, spline models are easily tuned; for example, Iwaki and Iwata (2011) used observed waveforms with periods > 3 s to improve waveform fit of the model of Iwata et al. (2008) by nonlinear inversion. Furthermore, Horikawa et al. (2003) and Sekiguchi et al. (2016) divided the spline interfaces with sheer planes to express steps along faults around and within the basin (Suehiro et al. 2003) and implemented velocity gradients within the structural layers. The increased detail in the model of Sekiguchi et al. (2016) is expected to better reproduce shortperiod waveforms compared to the spline model.
Further improvements in basin modeling require model validation to identify poorly modeled areas, followed by detailed and costly investigations of those areas. Validating velocity structure models by waveform simulation is straightforward and well suited to the problem of ground motion prediction. In many works this method is applied for validation of basin models, for example: San Bernardino basin, USA (Graves and Wald 2004); Santa Clara valley, USA (Hartzell et al. 2006); Los Angeles basin, USA (Lee and Chen 2016); Taipei basin, Taiwan (Lee et al. 2008); Mygdonian Basin, Greece (Maufroy et al. 2015); Southern California basins (Nweke et al. 2022); Po plain, Italy (Paolucci et al. 2015); Puget Sound basins, USA (Pitarka et al. 2004); Kanto basin, Japan (Takemura et al. 2015).
For this validation, it is necessary to estimate uncertain source parameters (e.g., source depth, source duration) for a mediummagnitude earthquake that is capable of generating longperiod waves but that can still be approximated by a point source. Here, we used the reciprocity method (e.g., Eisner and Clayton 2001) to tune source parameters. This method greatly reduces the cost of 3D finitedifference (FDM) simulations and allows for more parameters to be tuned, including the focal mechanism. We used the opensource Japan Integrated Velocity Structure model (JIVSM; Koketsu et al. 2012) that includes the Osaka basin model developed by Kagawa et al. (2004). We chose five target events around the basin and first estimated source parameters (depth, source duration, and mechanism correction) using records at bedrock sites. Then, we developed a 3D FDM simulation for sites within the basin.
Source tuning
To estimate site amplification effects, the ratio of amplitude spectra at sedimentary and nearby bedrock sites is often used, or spectral inversion is used to determine source–path–site effects if nearby bedrock sites are unavailable (e.g., Andrews 1986; Iwata and Irikura 1988). For modeling of waveforms, bedrock site approach was modified by Wen and Helmberger (1997). They propose using transfer function that can be calculated numerically in case of 3D basins (e.g., Yoshida 2011). In this approach, ground motions at a bedrock site are used as the motion input at a nearby sedimentary site. However, sedimentary basins have the additional complexity that they are affected by the basinedge generation of longperiod waves as well as wave amplification, reflection, and interference (e.g., Kagawa et al. 1992; Frankel 1994; Graves et al. 1998; Ayoubi et al. 2021, and references therein). In such cases, instead of ground motions at a single site, it is necessary to use the entire wavefield simulated for an earthquake outside the basin. The source model of the earthquake should be tuned to reproduce observed waveforms at bedrock sites located in front of the target basin (control points). Simulated input wavefield along segments between the control points are also assumed to reproduce wavefield from the natural earthquake source.
We note that observed waveforms at bedrock sites on the opposite side of the basin from the epicenter are strongly contaminated by basin waves, which produce delayed trailing waves that degrade the pulselike characteristic expected at bedrock sites (e.g., Ewald et al. 2006, their Fig. 3). Therefore, we exclusively used control sites between the basin and the epicenter for source tuning.
Most basins have complex shapes; the Osaka basin is elliptical, with steep edges on its northwestern and eastern sides and flat edges on its southern side (Figs. 1, 2). In this basin, therefore, the effects of basinwave generation, reflection, and interference depend on the azimuth of the incoming waves (e.g., Kagawa et al. 1992). For this reason, to validate the Osaka basin model, we used five mediummagnitude earthquakes with epicenters to the north, east, southeast, south, and west of the basin (see Fig. 1 and Table 1 for earthquake locations and parameters).
Published source parameters require tuning because available velocity structure models and the Green’s functions (GFs) used to estimate the source parameters have uncertainties that increase as the period of the target wave decreases. For example, the centroidmomenttensor (CMT) solutions from two major Japanese agencies, Fnet and JMA, differ because the agencies use different periods for their waveform inversions (Table 1). Thus, to avoid the effects of these uncertainties, longperiod waves are commonly used to obtain CMT solutions (e.g., 20–30 s for Fnet solutions; Aoi et al. 2020).
However, the objective of this study is to fit the shortperiod waveforms (as short as 2 s) that impact largescale engineering structures. By careful tuning of the source parameters using waveform fit at short periods, effect of uncertainties of velocity model can be reduced. This procedure is equivalent to hypocenter relocation in seismic tomography, but uses the full waveform and the full set of source parameters. We used a nonlinear simplex search (SS) method (Lagarias et al. 1998) based on the initial source parameters estimated by Fnet: source coordinates and depth, seismic moment, strike, dip, and rake. Target periods of the waveform misfit are 2–10 s.
We assumed symmetric bell functions for the time functions of the point sources. Bell functions require only one parameter, source duration Ts. To calculate waveforms over a large variety of source durations, we applied the spectral correction approach of Petukhin et al. (2017a). In the first step of the reciprocity method, we calculated GFs using bell functions and a dummy source duration value Ts^{*}. To calculate waveforms for the target source durations, which vary during the source inversion, we calculated the Fourier spectrum of each waveform for Ts^{*} and then converted it to the Fourier spectrum for the target Ts value using the equation:
where WS(f) is the spectrum of the target waveform, WS*(f) is the spectrum of the waveform for the dummy source duration, and S(f  Ts^{*}) and S(f  Ts) are the spectra of the source bell functions for the dummy and target source durations, respectively. Then, we performed an inverse Fourier transform to calculate the target waveform.
The initial models used for source tuning were Fnet CMT solutions (Table 2). Initial source duration values were estimated from the velocity pulse width at the bedrock site nearest the source when available, or calculated as:
where W is rupture width, and Vr = 2.4 km/s is the rupture velocity. For the 13 April 2013 earthquake, we used the model of Asano et al. (2016), in which the depth and source duration values were estimated by a grid search to fit the waveforms at the site nearest the source.
Methodology of the simplex search
The SS method is a derivativefree method developed by Lagarias et al. (1998); implemented in Matlab and ready to use) that allows us to stably search for the minimum of the target function. The SS method requires an initial model, in the vicinity of which it searches for a minimum of the target function. In this way, we could identify models that both fit the waveforms and conformed to the realistic Fnet solutions.
The waveform misfit (WM) adopted in the SS search is defined as:
where V_{obs}(t) and V_{sim}(t) are the observed and simulated velocity waveforms, respectively, and t_{d} the waveform duration. Before the misfit calculation, waveforms were adjusted to the common Pwave arrival time t_{P}, which was picked automatically and manually for the simulated and observed waveforms, respectively. For simulated waveforms, we used amplitude type t_{P} picker having threshold 1e−9 m/s. Considering that simulated waveform has zero amplitude before Pwave, this simple method works well.
The effectiveness of the SS method depends on the proximity of the initial model to the global minimum of the misfit function: that is, the search will identify the nearest minimum, be it a local or global minimum. For oscillating seismic waveforms, the WM will have many minima and maxima, depending on the waveform shift. It is thus necessary for the initial model to be in the vicinity of the global minimum of the WM in parameter space. As the minimum waveform period T_{min} decreases, the number of minima of the WM increases, decreasing the probability that the initial model is in the vicinity of the global minimum. To guide the search process toward identifying the global minimum for short target periods (T_{min} = 2 s), we applied the following procedure.
Step 1: We applied the SS method to a longperiod waveform with T_{min} = 5 s. This reduced the number of secondary minima, thus increasing the probability that the initial model was in the vicinity of the global minimum of the WM.
Step 2: We then repeated the SS twice, each time decreasing T_{min} by 1 s (i.e., once at T_{min} = 4 s, and again at T_{min} = 3 s) and using result of the previous search as the initial model.
Step 3: We performed a final SS at the target value T_{min} = 2 s.
This procedure allowed us to maintain the initial model in the vicinity of the global minimum at each step. The assumed tolerance of the model and the misfit was 0.01, which allowed us to finish the search in several hundred SS iterations.
Reciprocity method
The simulation approach, based on the scaled summation of precalculated GFs, is an effective way to calculate ground motions for many source models, which is necessary for nonlinear source tuning. To calculate longperiod GFs, we used the 3D FDM method, which is accurate but timeconsuming. For this reason, precalculating the GFs for all possible source locations and depths by forward 3D FDM became practically impossible. Therefore, to reduce the simulation time, we employed the reciprocity method, described in detail by Eisner and Clayton (2001) and Graves and Wald (2001), and adopted GF calculations used for source inversions (e.g., Matsushima and Kawase 2009) or probabilistic analyses of longperiod ground motions (e.g., Petukhin et al. 2017a, b).
In the first step of the reciprocity method, we calculated the responses of the three pointforces applied at the target site in the x, y, and z directions. Then, in the second step, the waveforms at each grid pair of the FDM doublecouple source (see Graves 1996) were combined to produce a moment tensor response at the site. It is necessary to run a number of simulations equal to 3 times the number of control sites to calculate the GFs for all source locations at all control sites. Although the first step requires a few days of time on a computer cluster, it can be run in advance and the results stored in memory. In contrast, the calculations in the second step are faster, requiring only an assumption of the focal mechanism; waveforms for hundreds of source models can be calculated in a few minutes on a desktop computer.
Source tuning results
We used the 2015 release of the JIVSM for 3D waveform simulations (Koketsu et al. 2012). The model consists of 23 constantvelocity layers, including crustal and subduction zone layers, that were previously validated and tuned around, but not within, the Osaka basin by waveform simulations (Petukhin et al. 2012). This model is thus ready to use for simulating ground motions. Parameters assigned within each layer are Vp, Vs, density, as well as frequencyindependent attenuation quality factors Qp and Qs. In this study we assumed for simplicity that Qp = Qs. Within sedimentary layers JIVSM model assumes that Qs = Vs/5, where Vs is in m/s. Our calculation area was 133.5–136.7° E and 33.6–35.8° N, with boundaries approximately 100 km beyond the basin; most of the calculation area is shown in Fig. 1. The depth of the calculation volume was 60 km, well below the Moho. Reflections from the Moho reduce the effects of possible reflections from the bottom of the calculation volume. We used the staggeredgrid method of Graves (1996). The FDM grid spacing was 280 m, allowing time steps 0.0085 s in the waveform simulations up to 2 s at the control sites. Within the basin, the grid spacing was refined to 140 m using a nonuniform grid (Pitarka 1999).
Our source tuning results are reported in Table 2. The tuned source locations and depths are compatible with the differences between the JMA hypocenters and the Fnet CMT solutions. Except for the 25 August 2001 earthquake, the differences between the tuned focal mechanisms and the initial CMT solutions were minor and compatible with the differences between the Fnet and JMA solutions. Because the source of the 13 April 2013 earthquake was just beneath the edge of the basin, we used the model previously tuned by Asano et al. (2016). An example of the improvement of the waveforms at bedrock sites is given for the 5 July 2011 earthquake (Fig. 3). In this example, our source tuning improved WM values at all target sites except HYG025, where only the E–W component was improved. The increased WM value for the N–S component at WKYH08 is due only to a waveform shift; the major pulse is better reproduced by the tuned source model than by the initial source model. The complete set of waveform comparisons is provided in Additional file 1. Overall, our tuning improved the WM values for 70% of the waveforms at the control sites.
Basin waveform simulation and validation results
The locations of the strongmotion stations used in our basin validation simulation are shown in Fig. 2. Osaka basin model comprises three sedimentary layers (V_{S} = 0.35, 0.6, and 1.0 km/s with increasing depth) with interfaces at 0.19 and 0.47 times the bedrock depth. These coefficients are subject for additional tuning by waveform modeling. For example, Iwaki and Iwata (2011) used values 0.12 and 0.41, respectively, while Guo et al. (2013) revised them to 0.08 and 0.39. Bedrock layers beneath the basin are from the JIVSM and have V_{S} = 2.4 and 3.2 km/s with increasing depth (for details, see Kagawa et al. 2004). The depth to bedrock is shown as contours in Fig. 2. For the 3D waveform simulations, we used the same FDM settings used for source tuning with a minimum simulated period of 2 s. Waveform comparisons for the 5 July 2011 earthquake are shown in Fig. 4; results for the other earthquakes are provided in Additional file 1. The distributions of WM values for the N–S component of each earthquake are mapped in Fig. 5. WM values are calculated with excluding later phases, i.e., for the 40s segment of waveform, starting from t_{P}. To indicate the azimuthal dependence of the goodnessoffit (lower WM values), WM values are plotted in segmented hexagons, with each segment roughly corresponding to the azimuth from which the incident waves propagated.
To facilitate our analysis, we classified the WM values as ‘Very good’ (< 1.0), ‘Good’ (1.0–2.0), ‘Bad’ (2.0–3.0), and ‘Very bad’ (> 3.0) (Fig. 6). We also calculated and classified the ratios of simulated to observed peak ground velocities (PGV) as ‘Good’ (1/1.5 to 1.5), ‘Bad, overestimated’ (1.5–3.0), ‘Bad, underestimated’ (1/3.0 to 1/1.5), and ‘Very bad’ (< 1/3.0 or > 3.0) (reported as log values in Fig. 7). Similarly, Figs. 8, 9, 10 and 11 show the ratios of simulated to observed response spectra (pseudo velocities, pSv) for wave periods of 2, 3, 5, and 7 s, respectively, classified based on the same ranges as the PGV ratios. Sites with especially bad fits are circled in Figs. 6, 7, 8, 9, 10 and 11; solid circles indicate sites with bad fits for multiple incident azimuths, dashed circles indicate sites with a bad fit for only one azimuth, and circle colors correspond to the misfits classification (black, ‘Very Bad’; red, ‘Bad’ or ‘Bad, underestimated’). We focus on underestimates because they are more likely to result in disaster than overestimates.
Analysis of Figs. 4, 5, 6, 7, 8, 9, 10 and 11 reveals that:

1.
Simulated Swave arrival times agree with the observations at most sites (Fig. 4), except those with unclear Swave arrivals (e.g., MRG and OSK005).

2.
Waveform fits for direct waves (~ 20 s after the Swave arrivals in Fig. 4) are good at many sites in terms of amplitude and phase, except those near the edges of the basin (e.g., OSK004, OSK010, OSKH01, OSK008, ABN), for which amplitudes are largely underestimated in one or both components. Detailed explorations may be necessary around those sites.

3.
Fitting later phases of basin waves is challenging. With few exceptions (N–S components at sites KRI and MRG, E–W component at site KPI), the later phases have different waveforms (Fig. 4). Nonetheless, the amplitudes of later simulated phases fit the observed amplitudes with errors of ± 50% at most of sites, which is acceptable. We note that the good fit of reflected and converted/interfered later phases, which appear ~ 40 s after Sarrival and later, depend on the accuracy of the modeling at the basin edges.

4.
The distributions of the WM misfits and the PGV and pSv ratios show that most sites with poor fits are near the basin edges, although there are also examples within the basin (e.g., sites FKS, ABN, and MRG). Asano et al. (2016) also reported large misfits for later phases at these sites during the 13 April 2013 earthquake using the basin model of Sekiguchi et al. (2016), especially for long periods of 6 s.

5.
Analysis of the misfits of the perioddependent parameter pSv indicates that misfits improve with increasing wave period. For example, the total number of azimuth sectors classified as ‘Bad’ or ‘Bad, underestimated’ in Figs. 8, 9, 10 and 11 decreases gradually from 42% at a period of 2 s to 30% at a period of 7 s. This is expected because uncertainties of velocity structure model decrease as the period of the target wave increases.
This analysis identifies sites in the Osaka basin that require detailed exploration and improvement.
Discussion
There are some issues with the method of basin model validation by waveform simulation for tuned sources. For example, the amplitudes of basin waveforms for the 31 October 2000 earthquake were systematically overestimated (Additional file 1: Fig. S5), probably because the source duration value used was too short (Ts = 0.88) for this M5.7 earthquake (Table 2). In addition to major effect of source duration to change frequency content of generated waves, there is an effect of waveform shift in time. For example, smaller source duration results in earlier arrival of waves. First effect is our target when we model waveforms. However, for calculation of WM value, second effect can be larger. In such cases, it may be necessary to manually correct short source durations to larger values, which does not affect the waveform fits at bedrock sites.
The predominant period of ground motions is an important parameter from an engineering standpoint. Miyakoshi et al. (2013) used a 1D approximation to compute and map theoretical site responses to Love waves in the Osaka basin. However, a preliminary analysis of predominant ground motion periods from simulated waveforms considering 3D effects (Petukhin et al. 2017a) indicates that multiple spectral peaks exist. Depending on numerous factors (e.g., depth to bedrock, distance to the basin edge), some spectral peaks become dominant, making interpretations of predominant ground motion periods difficult; improving these interpretations should be the focus of future work.
We limited our analysis of the basin waveforms to the 80 s following the Pwave arrival. At most sites, the largest amplitude waves arrive during that window. However, in some cases, large amplitude phases can arrive later. For example, Asano et al. (2016) reported the arrival of a large amplitude phase at 100 s after the Pwave arrival during the 13 April 2013 earthquake, which is difficult to reproduce with existing basin models. Further basin modeling is thus necessary, and should focus on critical areas like the Osaka bay area in the southwest part of the Osaka basin, where the late phase reported by Asano et al. (2016) was generated or amplified. In this area particularly, new seabed observations may be necessary.
Our results indicate that most of the poorly reproduced sites are near basin edges. This result is probably due to oversmoothing cause by the spline interpolation. Validation using the model of Sekiguchi et al. (2016) should be prioritized because their model includes detailed information on steps in the velocity model due to faults surrounding the basin.
Finally, we should notice that accuracy of waveform fitting depends on the accuracy of FDM waveform simulation, in addition to the accuracy of velocity structure model. Specifically, smaller grid spacing increases waveform accuracy. Moczo et al. (2011) analyzed effect of grid spacing and found that with increasing Vp/Vs ratio necessary grid spacing should be decreased. JIVSM model in this study has Vp/Vs = 4.86 in the shallowest layer. According to Moczo et al. (2011), this requires 8 grids per wavelength, i.e., 87.5 m for T_{min} = 2 s which is smaller than grid spacing 140 m (5 grids per wavelength) assumed in this study. To test effect of smaller grid spacing, waveforms in Fig. 4 additionally calculated with grid spacing 87.5 m. Results are compared in Appendix, Fig. 12. Although there is some waveform difference, we cannot conclude that smaller grid improves waveform fit: half of waveforms have improved WM value, while in another half WM value has degraded. Probable reason is that predominant periods inside Osaka basin are 3to7 s (e.g., Miyakoshi et al. 2013), which are larger than T_{min} = 2 s. From another side, smaller grid spacing is largely increasing computation cost largely; 6.5 times here. We will need to improve accuracy of waveform simulation in future work, as soon as getting improved velocity structures.
Conclusions
We applied the reciprocity method to tune the source models of mediummagnitude earthquakes around the Osaka basin. These source models were used to simulate 3D waveforms inside the basin, which we compared to waveforms observed at the same sites. Our comparison revealed that certain areas near the basin edges require detailed further exploration. We expect that future improvements to the basin model, especially near basin edges, will improve the waveform fit throughout the basin.
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Acknowledgements
This work was inspired by Asano et al. (2016). We used waveform data from the CEORKA, KNET, Kiknet, and PARI networks, and CMT solutions from Fnet and JMA. We are thankful to two anonymous reviewers and Associated Editor Fabrice Cotton for helpful comments that strongly improved manuscript.
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AP performed the simulations and inversion analysis. AP wrote the initial draft of the manuscript through discussion with YI, who proposed the study. Both authors have proofread the draft. Both authors read and approved the final manuscript.
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Additional file 1.
Auxiliary material: Waveform comparison for all analyzed earthquakes.
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Petukhin, A., Iwasaki, Y. Validation of the Osaka basin velocity model by waveform simulation using sources inverted with reciprocal Green’s functions. Earth Planets Space 75, 69 (2023). https://doi.org/10.1186/s40623023018245
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DOI: https://doi.org/10.1186/s40623023018245