- Open Access
The effect of heterogeneous crust on earthquakes: a case study of the 2004 Chuetsu, Japan earthquake
© Miyatake; licensee Springer. 2014
- Received: 7 August 2013
- Accepted: 26 November 2013
- Published: 24 April 2014
The cause of asperities (i.e., high-slip regions) remains the subject of much debate in seismology. Several tomography studies have reported previously that high-velocity bodies coincide with asperities. However, it remains unclear whether the heterogeneity of the crust generates these asperities. This can be addressed by conducting stress analysis. The 2004 Chuetsu, Japan earthquake is one of the best examples, since a detailed 3D seismic velocity structure was elucidated. For the resulting structural model, we calculated the heterogeneous stress distribution numerically, adding tectonic loading. Then, we calculated the distribution of the stress drop on the fault based on a frictional coefficient μd, the pore fluid factor λv, and the tectonic loading ratio c. We assumed λv to be 0.85 based on a previous study and calculated the corresponding slip distributions and seismic moment. To have been responsible for this Mw6.6 earthquake, the parameters μd and c must have been located somewhere along a particular line in c - μd space; this constrains the possible range of these parameters. We found that the asperity region for the above slip distribution corresponds approximately to that of the kinematic model, which suggests that the asperity may have been created by heterogeneity in the crustal structure.
- Stress Drop
- Seismic Moment
- Slip Distribution
- Seismic Velocity Structure
- Heterogeneous Crust
The causes of asperities or high-slip areas on faults remain unclear. An asperity was defined originally as the protrusion of a frictional surface in rock mechanics and an asperity model was proposed to explain various types of seismicity along plate boundaries (Kanamori 1981). In this model, asperities are represented as regions of high strength and can accumulate high stress (Das and Kostrov 1983; Lay and Kanamori 1981). Conversely, asperities are often considered to be regions of high slip (e.g., Somerville et al. 1999). In the present study, we adopt the latter definition and omit any discussion of strength. Regardless of the particular meaning preferred, it is generally believed that fault processes (and thus asperities) are controlled by the frictional properties on faults. The inherent variability of fault’s frictional properties has allowed the emergence of a wide variety of fault rupture processes; yet coincidence between asperities and bodies with high seismic velocity has been reported previously for several source regions (Michael and Eberhart-Phillips 1991; Chiarabba and Amato 2003; Kato et al. 2010), suggesting that the stress field itself may cause asperities. However, it remains unclear whether the frictional properties of fault surfaces or stress field characteristics are the primary factors controlling the development of asperities. In the present study, we attempt to address this gap in knowledge by investigating the effects of the stress field on asperities. The 2004 Chuetsu earthquake in Japan and its source region provide an excellent case study in this regard. The highly resolved velocity structure of this earthquake has been inferred from the arrival times of aftershocks, observed by an extremely dense network of temporary seismic stations (Kato et al. 20062009) that detected the presence of a high-velocity body that coincided approximately with an asperity (Kato et al. 2010). For this heterogeneous structural model, we calculate the heterogeneous stress distribution on the fault numerically using the finite difference method (FDM). If the asperity (i.e., high-slip region) can be shown to have been created by the stress field in our stress analysis, it can be considered likely that the asperity was caused by this heterogeneous stress field generated by a heterogeneous crustal structure.
Stress on the fault
where λ and μ represent Lamé constants whose distributions were obtained using a previously developed 3D velocity model (Kato et al. 2006) and from the relationship between P wave velocity and density (Birch 1961), respectively.
In our computation, L x = L y = L z = 50 km. The displacement u0 in Equation 4 may relate to a plate motion. Because the absolute value of the boundary condition (i.e., u0) in Equation 4 was not known, we tentatively assumed , where . Moreover, the resultant stress field had to be adjusted by multiplying with a constant, c ().
We obtained the stress field for c = 1 using the FDM in which grid sizes are taken as 0.4 km for z-axis and 0.3 km for horizontal axes. This ratio corresponded approximately to the dip angle of the fault. We also applied the successive over-relaxation (SOR) iterative method (Press et al. 1992) in our computation.
In system-2, we considered both lithostatic stress and fluid pressure. Thus, σ xx = σ yy = σ zz = σ V = ρgz, where ρ, g, and z are density, gravitational acceleration, and depth, respectively.
It should be noted that the above stress drop is not a true stress drop; rather, it is a potential value based on the assumption that the rupture occurred along the entire region of positive stress drop on the fault. Therefore, this can be considered an approximation of the stress drop that can be used as an initial model for dynamic rupture simulation.
The stress drop distribution described above is controlled by the tectonic loading imposed by the heterogeneity of the crustal structure. To ascertain whether such a stress drop could have generated the mainshock of the 2004 Chuetsu earthquake, we calculated the slip distribution due to the stress drop distribution, described in Equation 7, and compared it with the kinematic model slip distribution (Hikima and Koketsu 2005). Three primary parameters are required (either given or assumed) to calculate the stress drop and estimate the slip distribution according to Equation 7: μd, c, and λv. However, the computation of the slip distribution due to stress drop on a fault in a heterogeneous structure is extremely time-consuming because it requires more than several thousand computations to constrain the parameters.
where Δu L and Δσ L are slip and shear stress drop at fault element L of (ξ i , η j ). L is given by L = i + (j - 1) M, where i = 1,…, M and j = 1,…, N. To reduce computation time, we calculated the slip on the size of the twice longer fault than the kinematic model. For a given shear stress drop distribution Δσ L , we were able to solve the slip distribution Δu L . In this computation, we assumed that , and ρ = 2.8 g/cm3 and used the code of Okada (1992) for computation of Gij. The differences in slip distribution between our method and the heterogeneous model are presented in Appendix B.
As Sibson (2007) estimated λv to be between 0.75 and 0.95 for our study region, we assumed a constant λv of 0.85. Typically, lower values of λv correspond to a requirement for higher loading stress, which corresponds to higher values of c. Through additional computations, we found c to increase by about 30% for a given value of μd when we set λv = 0.8, although the stress drop distribution was found to be very similar to that for λv = 0.85. Thus, it is clear that the value of λv does not affect the overall distribution of the stress drop, although heterogeneity of λv may have some effect on stress distribution. Heterogeneous distributions of λv have not been reported extensively, although Terakawa and Miller (2012) tried to estimate the regional variation in pore fluid pressure in Basel, Switzerland, using Centroid Moment Tensor (CMT) inversion results based on the assumption that tectonic stress is uniform. Both the heterogeneity of fluid pressure and structure are known to be important for earthquake rupture. However, based on the coincidence of the asperity and the zone of high seismic velocity in the present study, the main features of the particular event studied here (e.g., the size and location of the asperity) appear to have been controlled primarily by the heterogeneous seismic velocity structure.
Shibazaki et al. (2008) used finite element analysis to demonstrate that the loading processes of large inland earthquakes in northeastern Japan are determined by the nonuniform thermal structure of the deeper crust and uppermost mantle. However, it has been demonstrated that coincidence between an asperity and high elastic properties (i.e., a high-seismic-velocity structure) cannot always be attributed to rheological properties. An asperity is a region of high moment release, which typically corresponds to large stress drop or high stress; thus, asperities can support strain energy. Therefore, the heterogeneity of elastic properties in the upper crust may create the initial conditions required for a given event, thus controlling the faulting process (i.e., the size and stress drop of asperities). Accordingly, we considered only the elasticity in our stress analysis.
We compared the slip distribution caused by crustal heterogeneity with that indicated by a previously developed kinematic slip model. Our crustal heterogeneity data were inverted using the DD tomography method (Zhang and Thurber 2003) and utilizing a huge dataset of aftershock arrival times observed by the dense seismic network deployed after the mainshock of the 2004 Chuetsu earthquake. Conversely, the kinematic model was inverted from the permanently strong ground motion station. Thus, the small offset (i.e., a few kilometers) between the asperity and the high-velocity body may have resulted from differences in the datasets and modeling parameters used or from differences in inversion method.
We investigated the effects of heterogeneous crustal structure on earthquake rupture, using the 2004 Chuetsu earthquake and its source region as a case study. In particular, we calculated the stress distribution numerically using a 3D crustal structure model of the source region. A region exhibiting a high ratio of shear to normal stress, which can be considered as an indicator of stress drop, was found to coincide approximately to the fault area of the 2004 Chuetsu earthquake. Then, we assumed values for several unknown parameters (frictional coefficient μd, pore fluid factor λv, tectonic loading ratio c) to estimate the potential stress drop distribution. Using the grid search technique, we obtained the relationship between c and μd for the occurrence of an earthquake with a seismic moment of 8.8 × 1018 Nm. Under these conditions, we were able to reproduce the localized rupture area at a location that almost coincides with that of the asperity of the 2004 Chuetsu earthquake, suggesting that the asperity of the mainshock of this earthquake could have been created by a heterogeneous stress field generated from heterogeneous crustal structure. Overall, our results demonstrate that although the dynamic rupture of this asperity is controlled by the frictional properties of the fault surface, the stress field is also an important factor in asperity creation.
The effects of heterogeneous crust on slip distribution
The computations were conducted by the parallel computer of the Earthquake Information Center in the Earthquake Research Institute, University of Tokyo. I thank Dr. K. Hikima and Dr. A. Kato for providing their inversion data. I thank Dr. Shibazaki for valuable comments. I also acknowledge two anonymous reviews for helpful comments.
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