# Seismological asperities from the point of view of dynamic rupture modeling: the 2007 Mw6.6 Chuetsu-Oki, Japan, earthquake

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## Abstract

We study the ground motion simulations based on three finite-source models for the 2007 Mw6.6 Niigata Chuetsu-oki, Japan, earthquake in order to discuss the performance of the input ground motion estimations for the near-field seismic hazard analysis. The three models include a kinematic source inverted from the regional accelerations, a dynamic source on a planar fault with three asperities inferred from the very-near-field ground motion particle motions, and another dynamic source model with conjugate fault segments. The ground motions are calculated for an available 3D geological model using a finite-difference method. For the comparison, we apply a goodness-of-fit score to the ground motion parameters at different stations, including the nearest one that is almost directly above the ruptured fault segments. The dynamic rupture models show good performance. We find that seismologically inferred earthquake asperities on a single fault plane can be expressed with two conjugate segments. The rupture transfer from one segment to another can generate a significant radiation; this could be interpreted as an asperity projected onto a single fault plane. This example illustrates the importance of the fault geometry that has to be taken into account when estimating the very-near-field ground motion.

## Keywords

Fault geometry Ground motions Seismic hazard Niigata Chuetsu-oki earthquake Dynamic rupture propagation## 1 Introduction

Predicting the ground motions for any given scenario of an earthquake is an important seismological task for seismic hazard evaluation (Douglas and Aochi 2008). Nowadays, the earthquake model is kinematically constructed based on the statistical analyses of past earthquakes obtained from various inversions or synthetic earthquake scenarios dynamically simulated (e.g., Mai and Beroza 2002; Irikura and Miyake 2011; Song et al. 2013). In some research projects, there have been attempts to carry out the ground motion simulations using the dynamically simulated earthquake models directly (e.g. Olsen et al. 2009). Indeed, for two decades, dynamic rupture models have been more commonly applied to reproduce the ground motions of recent earthquakes, such as the 1992 Landers earthquake (Olsen et al. 1997; Peyrat et al. 2001; Aochi et al. 2003). Furthermore, the characteristics of the ground motion based on the dynamic rupture models are synthetically studied in terms of rupture velocity, fault geometry, heterogeneity, and so on (e.g., Oglesby and Day 2002; Aochi and Olsen 2004; Aochi and Douglas 2006; Schmedes and Archuleta 2008; Dunham and Bhat 2008). Regardless of the progress in dynamic rupture modeling, the models are difficult to produce and calibrate. In this paper, we aim to show the applicability and the utility of the dynamic rupture models for the near-field ground motion simulations applied to the 2007 Mw6.6 Chuetsu-oki, Japan, earthquake.

## 2 Source models of the 2007 Chuetsu-Oki earthquake

## 3 Numerical simulations of ground motion

### 3.1 Simulation methods

The complexity of the 3D geological structure is well known in this region due to its complex tectonics. Aochi et al. (2013a) used the three available structure models of this region (Kato et al. 2008; Fujiwara et al. 2009; Sekiguchi et al. 2009) for ground motion simulations and discussed the validity of each model. Ground motion using the 3D structure obtained by tomography (Kato et al. 2008) shows a good coherence on rock sites that are situated close to each other. On the other hand, the models calibrated based on the geological map and the geophysical cross-sections (Fujiwara et al. 2009; Sekiguchi et al. 2009) are generally suitable for the soft sites. However, even when the models are good enough for the direct waves at certain stations, it is still difficult to obtain coherent phases for the later seismic arrivals. In this study, we adopt the 3D structure model by Sekiguchi et al. (2009) which has integrated geological layers, as shown in Fig. 1, and has a minimum shear velocity of *V* _{min} = 400 m/s.

For ground motion simulations, we use a fourth-order finite-difference method (Aochi et al. 2013a, b) with a grid spacing of *Δs* = 80 m for a dimension of 110 km (EW) × 120 km (NS) × 30 km (UD). The ground surface is approximated as flat, and the Sea of Japan is not taken into account. The maximum reliable frequency is estimated as *f* _{max} = *V* _{min}/(5 ⋅ *Δs*) = 400/(5 ⋅ 80) = 1.0 Hz. The time step is 0.004 s; the calculation is run for a duration of 60 s. The simulation procedure for generating ground motion is basically the same for both the kinematic and dynamic source models, as in Aochi and Dupros (2011) and Aochi et al. (2013a), but using finer grids in this study. Any finite source can be introduced as a series of point sources with a predefined slip function of any arbitrary shape (Aochi et al. 2013b).

The included source model has been previously presented; its characteristics are summarized in Fig. 2. We propose the following models: the kinematic model K has a large rupture area, while the dynamic rupture models AD and AK have shorter rupture dimensions. The slip velocity function is also smooth (lower peak and longer duration) in model K and is shaper in AD and AK.

### 3.2 Simulation results

It is difficult to capture the waveform characteristics precisely in the backward direction of the rupture propagation, namely, in the northeast area (NIG10 and NIG11). However, in the forward direction in the southwest area (NIG024 and NIG025), we find that the characteristic waveforms are better simulated by the dynamic model (AK) than by the kinematic model (K). This is an important feature. The kinematic model is based on an inversion that might have missed or underestimated significant behavior of the rupture process due to a priori constraints or smoothing of the inversion. Therefore, the source model might underestimate the strong ground motions that are closely related to the source process. The dynamic models AD and AK produce similar waveforms, in particular at NIG024, NIG025, NIG004, and NIG019, and seem to be closer to the observations than model K. The similarity of the resultant ground motions for the two models, AD and AK, indicates that the asperities inferred on a single fault plane can be represented by the geometrical irregularities of the fault system.

## 4 Criteria for ground motion estimation

This paper does not aim to improve the model parameters, but tries to show the performance of different earthquake models in generating the ground motion, in particular the performance of the two dynamic rupture models. Although inversion of dynamic rupture parameters has been done for a decade (Peyrat et al. 2004; Ruiz and Madariaga 2011; Douilly et al. 2015), the number of inverted model parameters is usually limited to about 10 due to the high nonlinearity of the system and computational costs. This means that one cannot expect the same degree of spatial or temporal resolution as found in kinematic inversions unless the model parameters of dynamic rupture are constrained by kinematic inversion results (e.g., Peyrat et al. 2004). For the purpose of the ground motion prediction for seismic hazard, the engineers are more interested in the ground motion parameters than in coherent waveforms. Aochi and Douglas (2006) proposed to compare statistically the ground motion parameters at numerous points from the simulations with the ground motion prediction equations in terms of peak ground acceleration (PGA), peak ground velocity (PGV), response spectral acceleration, Arias intensity, and relative significant duration.

*x*and

*y*are two sets of positive scalar metrics. By associating a weight on the GOF score calculated for each of the metrics, the average GOF score is obtained. Olsen and Mayhew (2010) used the metrics consisting of PGA, PGV, peak ground displacement (PGD), averaged response spectral acceleration (RS), Fourier spectrum (FS), energy duration (DUR), and cumulative energy (ENER) for broadband synthetics between 0.1 and 10 Hz for the 2008 Mw5.4 Chino Hills earthquake.

## 5 Discussion and summary

The aim of this paper was to examine the performance of the dynamically simulated earthquake ruptures in computing ground motion for the purpose of quantitative seismic hazard analysis. For the 2007 Mw6.6 Chuetsu-oki, Japan, earthquake, we compute ground motion in a 3D geological model using a kinematic source model and two dynamic source models. To quantify the performance of the models, we apply a GOF criterion to the simulated ground motions. From the comparisons, we find that the kinematic model does not always have the best performance in reproducing the characteristics of the strong ground motion. In particular, it does not work well in the very near field and in the forward direction of the rupture propagation. This is probably because an abrupt change in the rupture process (rupture onset and changes in rupture velocity) may not be well simulated by the kinematic description. Two dynamic rupture models produce a similar ground motion radiation. However, the model with the asperities distributed on a single fault plane might be a projection of the rupture process on conjugate fault segments. The rupture process changes the wave radiation naturally due to the geometrical irregularities. From this perspective, the dynamic rupture model on a complex fault geometry produces a reasonable rupture scenario and wave radiation for practical applications.

For the 2007 Chuetsu-oki earthquake, the conjugate segments might be a reasonable causal source model, as inferred from the geodetic analyses (Nishimura et al. 2008; Aoki et al. 2008). Although the model parameters could be calibrated better, the rupture process on each segment could be very simple, represented by three phases: first, rupture on the NW-dipping segment; second, a dynamic rupture transfer between conjugate segments (which changes the wave radiation); and third, rupture on the SE-dipping segment. These features correspond to the three asperities commonly found from the seismological finite-source inversions. It is not possible to distinguish between the two rupture scenarios. To allow for possible mechanisms, one has to consider the possibility of rupture transfer from one segment to another and be included in probable rupture scenarios used to estimate the ground motion. Indeed, recent improvements of the geophysical observations often reveal complex fault geometries even for moderate-magnitude earthquakes, such as the 2009 Mw6.4 Suruga Bay, Japan (Aoi et al. 2010), and the Mw6.9 Iwate-Miyagi Nairiku, Japan, earthquakes (Fukuyama, 2015). In the seismological analyses, these earthquakes were mostly studied as ruptures on a single fault plane, an approximation good enough for regional or teleseismic scales.

There remains a scientific debate on the different aspects of the dynamic rupture process because the dynamics are technically difficult to solve and the frictional component of the faulting is difficult to study. However, progress over the last two decades helps us to understand various aspects of the dynamics of the earthquake mechanism. Dynamic rupture scenarios have been used to compute the ground motions for high-seismic-hazard areas such as California (e.g., Olsen et al. 2009), Japan (Sekiguchi and Kase 2012), and Turkey (Aochi and Ulrich 2015). The parameter studies on dynamic rupture allow retrieving probable rupture scenarios and ground motions (e.g., Aochi et al. 2006; Aochi and Ulrich 2015). Moreover, these dynamic simulations provide insight about the variability of the phenomena and extreme ground motions (e.g., Andrews et al. 2007).

## Notes

### Acknowledgments

This study was launched during the French national project DEBATE (DEvelopment of Broadband Acceleration Time histories for Engineers, ended by 2012; grant ANR-08-RISK-001) funded by Agence Nationale de la Recherche. We thank the project partners, R. Madariaga, F. Bonilla, A. Pecker, and C. Gélis, who have encouraged us to finalize this work, and M. Y. for the one-year grant (2009–2010) of the Program for Overseas Research from the National Institute of Advanced Industrial Science and Technology (AIST) for his stay in France. All the calculations were carried out in 2015–2016 at the French national supercomputing centers, Grand Equipement National de Calcul Intensif/Centre Informatique National de l’Enseignement Supérieur (GENCI/CINES), and Très Grand Centre de Calcul (GENCI/TGCC), under grant no. 46700. We also benefited from the Grant-in-Aid for Scientific Research B (grant 15H02989) from Japan Society for the Promotion of Science and the Earthquake Research Institute cooperative research program (grant 2013-B-05). The data for the 2007 Chuetsu-oki earthquake are provided by K-NET and KiK-net of the National Research Institute for Earth Science and Disaster Prevention (NIED) and by Tokyo Electric Power Company (TEPCO), Japan. Figure 8 is calculated with the code TF_MISFIT_GOF_CRITERIA written by Kristekova et al. (2009). We thank S. Aoi and H. Sekiguchi for their source model and R. Archuleta, S. Das, R. Madariaga, and an anonymous reviewer for their comments to improve the manuscript.

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