Reduction of the Memory Consumption in the Aki-Larner Method

Abstract

Aki-Larner method (ALM) is a very powerful technique to calculate the seismic responses of layered media having irregular interfaces. However, it is necessary to solve complex simultaneous equations with very large full matrices so that it takes very long time and consume much memory. Recently, Ohminato et al. (1990) proposed a Galerkin method and suggested that wavenumber coupling between far separated elements in the submatrices of the full matrices are very week if the lateral irregurality is gentle. Their idea seems to be applicable to the analyses of ALM, too. Therefore, in this paper, we estimated possible reduction of the memory consumption in the ALM by neglecting most of non-diagonal elements of the submatrices. Through the 2-dimensional (2-D) analyses, we calculated responses due to vertically incident plane SH-wave and studied the effect of the neglect of non-diagonal submatrix elements on the accuracy of results. Six types of alluvial valleys with different shape were used and the error caused by the neglect was evaluated in comparison with results obtained by the conventional ALM. As a result, we can treat submatrices as band matrices with 1/4 or 1/6 width if the lateral irregularity is gentle, and this leads to reduction of the memory consumption in the Aki-Larner method for the simulation in high frequencies or 3-D problems.