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# [SSS15-10] boundary integral equation method of dynamical elastic problems accelerated by H-matrix method, and its suggesting application to frictional properties of real fault systems

## ★Invited Papers

Keywords:fault forward modeling, dynamical boundary integral equation method, Hierarchical matrix method

On the other hand, handling of nonplanar fault geometries seen in inland faults and the like has caused a cost problem of simulation. In forward modeling, boundary integral equation method is standardly used in seismology as a highly accurate solution that can handle stress divergence at the fault breaking tip with high accuracy. Currently, the cost of the simulation increases significantly for non-planar faults when compared with planar fault shapes with a 90 degree tilt angle many simulation examples adopts. The cost ratio is roughly proportional to the number of boundary elements

*N*. In the current large scale simulation,

*N*is approximately several thousands to several tens of thousands. Because of this extreme cost increase, forward modeling of a system having a complicated fault geometry such as an inland fault remains as a big problem of earthquake science yet.

In order to solve this cost problem, we developed a new algorithm, the FDP = H-matrix method, which applies the fast domain partitioning method (FDPM) [Ando, 2016] and the Hierarchical matrix method (H-matrix method) [Hackbusch, 1999] to the dynamical boundary integral equation method. In this presentation, we present the outline of this algorithm and its application examples and discuss suggestions for fault friction estimation. FDP = H-matrix method is the method that the theoretical computational complexity of the stress convolution and the memory cost can be suppressed on the order of

*N log N*. Although its cost is lower cost than the conventional spectral method to the planar faults [Perrin et al., 1995], it can be applied to nonplanar fault geometries. This is an algorithm for potentially solving the conventional cost problem of the boundary integral equation method. FDP = H-matrix method by utilizing the FDPM which divides the stress integral kernel into P and S waves, the near-field term, and the secular term; the impulsive wave domain is thus efficiently treated, and FDP=H-matrix method has memory lightweight and computaional speed which could not be achieved by applying only the H-matrix method. Using this method, we will simulate fault motions on complex geometries as seen in the inland faults.