Makiko Ohtani

Fast Computation of Quasi-Dynamic Earthquake Cycle Simulation with Hierarchical Matrices

Abstract In quasi-dynamic earthquake cycle simulations based on rate and state friction laws, we applied the method of Hierarchical-Matrices (H-matrices) to multiplicative computations of the N × N slip response function matrix and the slip deficit rate vector, where N is the number of divided cells on the plate surface. H-matrices, which are efficient low-rank compressed representations of dense matrices, enable more rapid arithmetic operations with less memory sizes. In this study, we constructed a friction model of quasi-dynamic earthquake cycles on a flat, dipping, plate interface in a semi-infinite homogeneous elastic medium, and investigated the effectiveness of H-matrices by changing N from 104 to 106. Construction of H-matrices involves several parameters controlling the structure and accuracy of the approximated matrix. With H-matrices using proper values for these parameters to maintain accuracy, except for smaller values of the parameter for suppressing the ranks of the outermost submatrices, the memory size of the matrix was reduced to about O( N ). The computational time in the multiplication was also reduced to O( N ) for a range of N values less than about 105, and to O( N ) ∼ O( N log N ) for a larger range. Thus, we found that the application of H-matrices greatly reduces the computational time and memory size in earthquake cycle simulations. This advance should enable the realization of large- and multi-scale simulations with a million order cells and the estimation of frictional parameters.

Improvement of Hierarchical Matrices with Adaptive Cross Approximation for Large-scale Simulation

We propose an improved method for hierarchical-matrices (H-matrices) using adaptive cross approximation (ACA) as the low-rank approximation. The improvement consists of a kind of normalization and a new stopping criterion for the ACA. By using the proposed method, we can avoid the trouble that ranks of approximated matrices increase rapidly as the matrix size increases when the conventional H-matrices with ACA are employed to an integral equation whose kernel function has high-order singularities. In particular, application of the proposed method enables us to perform large-scale simulations such that the conventional H-matrices with ACA fail to construct the low-rank approximation. Applicability of the proposed method is confirmed through numerical experiments on an earthquake cycle simulation.

Observed change in plate coupling close to the rupture initiation area before the occurrence of the 2011 Tohoku earthquake: Implications from an earthquake cycle model: A Cycle model for the 2011 Tohoku EQ.

Changes in plate coupling off the coast of Fukushima have been detected by GPS since 2000. These changes occurred close to the rupture initiation area of the Mw9.0 2011 Tohoku earthquake and possibly initiated the earthquake. We investigated these changes with quasi-dynamic earthquake cycle simulations using a hierarchical asperity model. We modeled the entire rupture region as rate weakening but conditionally stable, while areas with huge slips and Mw7 asperities were modeled as strong and ordinary rate-weakening unstable friction, respectively. The following observed characteristics were reproduced: long recurrence time, large rupture region (including a localized huge coseismic slip area and source area of recurring Mw7 earthquakes), and a Mw7 foreshock triggering the Tohoku earthquake. Off Fukushima, repeated aseismic slips propagating northward appeared in the last half of the cycle and possibly caused the decrease in plate coupling. However, it is not necessarily related to the immediate occurrence of the giant earthquake.