Long-Period Ground Motion Simulation Based on Three-dimensional Centroid Moment Tensor Inversion Solutions in the Kanto Region, Japan

We conducted centroid moment tensor (CMT) inversions of moderate (Mw 4.5–6.5) earthquakes in the Kanto region, Japan, using a local three-dimensional (3D) model. We then investigated the effects of our 3D CMT solutions on long-period ground motion simulations. Grid search CMT inversions were conducted using displacement seismograms for periods of 25–100 s. By comparing our 3D CMT solutions with those from the local one-dimensional (1D) catalog, we found that our 3D CMT inversion systematically provides magnitudes smaller than those in the 1D catalog. The Mw differences between 3D and 1D catalogs tend to be signicant for earthquakes within the oceanic slab. By comparing ground motion simulations between 1D and 3D velocity models, we conrmed that observed Mw differences could be explained by differences in the rigidity structures around the source regions between 3D and 1D velocity models. The 3D velocity structures (especially oceanic crust and mantle) are important for estimating seismic moments in intraslab earthquakes. The seismic moments directly affect the amplitudes of ground motions. Thus, 3D CMT solutions are essential for the precise forward and inverse modeling of long-period ground motion. We also conducted long-period ground motion simulations using our 3D CMT solutions to evaluate reproducibility of long-period ground motions at stations within the Kanto Basin. The simulations of our 3D CMT inversion well-reproduced observed ground motions for periods longer than 10 s, even at stations within the Kanto Basin.

high-rise buildings, oil storage tanks, and suspension bridges. The characteristics of long-period ground motions were have been summarized in Koketsu and Miyake (2008). In the Kanto region, Japan, longperiod ground motions with predominant periods of 5-10 s have frequently been observed during shallow moderate-to-large earthquakes (e.g., Kinoshita et al. 1992 Recent advances in numerical simulation codes (e.g., Gokhberg and Fichtner 2016;Maeda et al. 2017) and local/regional three-dimensional (3D) velocity structure models (e.g., Koketsu Miyoshi et al. 2017). In forward and inverse modeling of long-period ground motion and structural properties along propagation paths, an assumption of a double-couple point source is usually assumed. The centroid moment tensor (CMT) solutions based on displacement for periods longer than 20 s are generally considered robust against structural heterogeneities, compared to rst-motion solutions (e.g., Takemura et al. 2016). As such, onedimensional (1D) velocity models are adopted in local/global CMT inversion systems (e.g., Kubo et al. 2002; Bernardi et al. 2004;Vallée et al. 2011;Ekström et al. 2012); these solutions are typically used in ground motion simulations. However, in regions with strong heterogeneities, such as thick sediments and subducting oceanic plates, focal mechanisms could be incorrectly estimated using conventional 1D CMT methods. To address this issue, the CMT inversion based on Green's functions using the local/regional 3D model has been developed in such regions (e.g., Lee Takemura et al. (2020) demonstrated that the differences in centroid depths and focal mechanisms between 1D and their 3D CMT solutions were signi cant for offshore earthquakes due to offshore heterogeneities. These differences could affect ground motion simulations (e.g., Takemura et al. 2019c). To achieve precise forward and inverse modeling of long-period ground motions in the Kanto region, where large sedimentary basin and two subducting plates exist, accurate CMT solutions should be required.
In this study, we conduct CMT inversions of moderate earthquakes in the Kanto region using the 3D Green's function dataset. We evaluate differences in source parameters between 1D and 3D CMT solutions. We conduct ground motion simulations using 3D CMT solutions to discuss the effects of CMT solutions on long-period ground motion modeling in the Kanto Basin. To accurately model phases and amplitudes of long-period ground motion, we demonstrate that the adjusted source model should be incorporated in the used 3D model (e.g., 3D CMT solution).

Method
In this study, we used the F-net broadband seismograms of the target earthquakes. At each F-net station ( lled triangles in Fig. 1 Science and Disaster Resilience 2019). Our target earthquakes were shallow (≤ 50 km) earthquakes with moment magnitudes (Mw) between 4.5-6.5, listed in the F-net moment tensor (MT) catalog. The F-net 1 D velocity structure model has been used in the F-net MT catalog (Fukuyama et al. 1998;Kubo et al. 2002). Target earthquakes (focal mechanisms in Fig. 1) occurred within the area of assumed source grids (crosses in Fig. 2a) between April 2017 and March 2020. The data of the Metropolitan Seismic Observation Network (MeSO-net) was also available from the NIED website in the analyzed period (e.g., Kasahara et al. 2009; Sakai and Hirata 2009). As MeSO-net stations were densely deployed around the Tokyo metropolitan area in Japan (inverse triangles in Fig. 1), we also evaluated long-period ground motion in the Kanto Basin using earthquakes that occurred after April 2017. Table 1 Physical parameters of each layer in JIVSM. The air and seawater layers were treated as being the same, following Maeda et al. (2017). The P-wave velocity (V P ), S-wave velocity (V S ), density (ρ), rigidity (µ) and inelastic attenuation (Q P and Q S ) are listed. We choose F-net stations within epicentral distances between 100-400 km from the initial epicenter, obtained from the F-net MT catalog. A set of Green's functions at the source grids, which were located in ± 0.4° grids from the initial epicenter and distributed at depths between 6-60 km, were selected for grid search inversion. A 200 s time window for each CMT inversion at every 1 s was adopted to determine the centroid time. Time shifts were not permitted during grid search inversion, despite typical 1D MT routines such as the F-net MT system, enabling time shifts at each station between synthetic and observed seismograms. After CMT inversions, we obtained seismic moments and focal mechanisms at all times and selected source grids. Then, we evaluated variance reductions (VRs) between the observed and synthetic displacement seismograms for periods of 25-100 s. If there was a perfect match between the observed and synthetic seismograms, the VR is 100%. The maximum VR solution was considered the optimal solution, providing the optimal centroid location, depth, time, focal mechanism, and seismic moment. Other technical details of 3D CMT inversions and the evaluation of Green's functions are described in Takemura    Cross-sections of pro les A and B are also plotted at the bottom of Fig. 3a. Along with pro le B, many earthquakes occurred just below the upper surface of the Paci c Plate. This seismicity was also con rmed in the hypocenter distribution determined by temporal ocean bottom seismometers (Ito et al. 2017b, a). However, these aligned intraslab earthquakes were not con rmed in the F-net catalog (Fig. 3b).
As such, although the resolution of centroid depth is not very high, the 3D CMT inversion is also considered to work well in the Kanto region.

Differences between 3D CMT and F-net MT catalogs
The F-net solutions of corresponding earthquakes are also plotted in Fig. 3b. Spatial distributions of both catalogs seem to be similar. To quantitatively evaluate differences between the 3D CMT in this study and the F-net MT catalogs, we calculated cross-correlation coe cients of P-wave radiation patterns (e.g., Kuge and Kawakatsu 1993;Helffrich 1997), depth, and Mw differences between the 3D CMT and F-net MT catalogs (Fig. 4). With the exception of this event, differences in focal mechanisms and centroid depths were not signi cant compared to offshore earthquakes along the Nankai Trough (Fig. 8 of Takemura et al. 2020).
On the other hand, we found that the Mw values based on the 3D CMT were systematically smaller than those of the F-net MT catalog (Fig. 4c). The Mw values are very important for ground motion simulations because values of seismic moments are directly related to the amplitude of the simulated ground motion.
Using the 3D CMT catalog along the Nankai Trough (Takemura et al. 2020; https://doi.org/10.5281/zenodo.3674161), we also evaluated the differences in the Mw between 3D CMT and F-net MT solutions. We found both larger and smaller Mw values compared to the F-net catalog in the Nankai region (Fig. 5). In the Kanto and Nankai regions, the differences in Mw for offshore earthquakes were larger than those of onshore earthquakes; these differences may be caused by 3D heterogeneities.
To investigate the cause of these Mw differences, we conducted ground motion simulations for earthquakes on November 17, 2017 (Event a) and August 4, 2018 (Event b). Using the 3D CMT method, Events a and b were located just below the upper surface of the oceanic crust layer 2 and the boundary between oceanic crust layers 2 and 3 of the Paci c Plate, respectively. The Mw differences for events a and b were − 0.31 and − 0.25, respectively, and the estimated seismic moments of the 3D CMT solutions were approximately 35% and 42% of the F-net 1D solutions, respectively. We conducted simulations using the same source models and three different heterogeneous models; the JIVSM (Koketsu et al. 2012), the JIVSM without sediments, and the F-net 1D model (Kubo et al. 2002). The source models were the optimal solutions of 3D CMT inversion for two earthquakes (Events a and b in Table 3). On the other hand, the amplitudes of simulation seismograms with a similar source and the F-net 1D model were approximately 35-45% of the observed amplitudes. The effects of the Kanto Basin have a minor in uence on ground motion at outcrop rock sites (F-net), and differences in mechanisms and depths compared with F-net solutions that are not signi cant. This difference could be explained by differences in heterogeneities around the seismic source. The 3D CMT solutions of events a and b were located just beneath the upper surface of the oceanic crust layer 2 and near the boundary between oceanic crust layers 2 and 3 of the Paci c Plate, respectively. In the JIVSM (Table 1), the rigidities of source areas for both events were 20.4-34.3. In contrast, the rigidity at depths between 33-100 km was a uniform value (63.7 GPa; Table 2) in the F-net 1D model. The differences in rigidities around source regions between the JIVSM and the F-net 1D model correspond to differences in seismic moments between the 3D CMT and F-net MT solutions (34-42%). As such, it may be concluded that the major cause of differences in seismic moments between the 3D CMT and F-net 1D MT solutions is the difference in rigidity around the source areas. For the Nankai Trough, both overestimations and underestimations of seismic moments compared to the F-net catalog were observed (Fig. 5). Large Mw differences only appeared in the offshore region, where many intraslab and interplate earthquakes occurred. In particular, intraslab earthquakes along the Nankai Trough occurred within the low-velocity oceanic crust and high-velocity oceanic mantle (see Figs. 5 and 6 of Takemura et al. 2020), not modeled in the F-net 1D model. The difference in Mw values along the Nankai Trough could also be explained by the differences in heterogeneous structures between the 3D and 1D models.
In the F-net routine system, the origin times and epicenters were xed as those in the JMA uni ed hypocenter catalog, and time shifts between observed and synthetic seismograms at each station were enabled. Miyoshi et al. (2017) notes that prior to estimating structural properties, the re-evaluation of centroid times for F-net MT solutions should be required to obtain suitable waveform inversion results. In this study, we found that the estimation of seismic moments was affected by the rigidity structure around the source region. The difference in the estimation of seismic moments directly impacts the amplitude of ground motion simulations. The amplitude of ground motion simulation is important to evaluate seismic hazards and estimate structural properties along propagation paths. For 3D forward and inverse modeling of seismic ground motion, the adjusted source model observed and synthetic seismograms in the assumed local 3D model should be used, such as the 3D CMT solution.
Long-period ground motion simulations in the Kanto region By using our the 3D CMT solutions based on the JIVSM, we conducted numerical simulations of longperiod ground motions and compared with the observed seismograms. For the SNR of the MeSO-net for periods longer than 5 s, three earthquakes were selected with an Mw equal to or larger than 5.5 for simulations of long-period ground motion in the Kanto Basin. The source parameters of selected events (A-C) are listed in Table 3. Complete les of simulated velocity waveforms and wave elds are available online https://doi.org/10.5281/zenodo.3926888. Figure 7 shows an example of simulated vertical velocity wave elds for the simulation of Event A at 40, 60, 80, 100, 120, 140, 160, and 180 s from the earthquake origin (movie le is also available from https://doi.org/10.5281/zenodo.3926888). The seismic waves radiated from the source complicatedly propagate through the Kanto region. In the Kanto, Niigata, and offshore regions, the wavelengths and propagation speeds of the Rayleigh waves became shorter and slower due to low-velocity sediments. The energy of these shorter-wavelength components (i.e., long-period ground motion) was trapped within lowvelocity sediments. Thus, the duration of long-period ground motion was elongated in the Kanto, Niigata, and offshore regions (lapse time of 180 s). Peak ground velocities (PGVs) were calculated by the vector sum of three-component ltered seismograms at the F-net and MeSO-net stations; the passband period was 5-30 s. Figure 8 shows the spatial distributions of PGVs for each event. With the exception of Event C, the simulations were able to roughly reproduce the observed features of PGVs. Large PGVs appeared in regions with bedrock depths greater than 3 km. ground motion for 10-20 and 5-16 s periods were affected by the Kanto sedimentary basin oceanic sediments from the epicenter to coastal regions. Thus, these sedimentary structures in the offshore region may decrease waveform tness for this event. The overestimation of PGVs (Fig. 8c) may also be attributed to the models of the Kanto Basin and the oceanic sediments along propagation paths.

Conclusions
We conducted CMT inversions of moderate earthquakes in the Kanto region from April 2017 to March 2020. The estimated focal mechanisms and depths using the 3D CMT method were not signi cantly different from the corresponding F-net MT solutions. However, the Mw values were systematically smaller than those in the F-net catalog. Earthquakes with large Mw differences tended to be located within the subducting plate, i.e., intraslab earthquakes. Using numerical simulations with 3D and 1D velocity models, we concluded that the major cause for the Mw differences is the difference in rigidity between the 1D and 3D velocity models. The 3D subducting oceanic crust and mantle could not be modeled in the 1D CMT system. The differences in the estimation of seismic moments directly affect the amplitude of ground motion simulations. The 3D simulation of an intraslab earthquake using the 1D CMT catalog could cause overestimations in the amplitude, even at outcrop rock sites. The 3D CMT solutions should be adopted for precise forward and inverse modeling of long-period ground motion simulations.
Simulations using the 3D CMT solutions in this study and the JIVSM were able to reproduce ground motion for periods longer than 5 s at outcrop rock sites. This means that the 3D CMT inversion works well in the Kanto region, and 3D CMT solutions are suitable for modeling long-period (> 5 s) ground motion. However, while simulations at stations within the Kanto Basin reproduced observed seismograms for periods longer than 10 s, the reproducibility of these simulations decreased for periods shorter than 10 s.
In the Kanto region, because the predominant period of long-period ground motion is approximately 6 s, a well-constrained sedimentary model is required to evaluate long-period ground motion for observed and anticipated large earthquakes. Recently, other regional/local velocity structure models of the sedimentary basin and subducting oceanic plate have been released (e.g., Hirose Table 1

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