Application of H-matrices method to the calculation of the stress field in a viscoelastic medium

In SW Japan, the Philippine Sea plate subducts from the south and the large earthquakes around M (Magnitude) 8 repeatedly occur at the plate boundary along the Nankai Trough, called as Nankai/Tonankai earthquakes. Near the rupture area of these earthquakes, the active volcanoes lines in the Kyushu region SW Japan, such as Sakurajima volcano. There are also distributed in the Tokai-Kanto region SE Japan, such as Mt. Fuji. The eruption of Mt. Fuji in 1707, called as Hoei eruption, have occurred 49 days after the one of the series of Nankai/Tonankai earthquakes, 1707 Hoei earthquake (M8.4). It suggests that the stress field due to the earthquake sometimes helps the volcanoes to erupt. When we consider the stress change due to the earthquake, the effect of viscoelastic deformation of the crust will be important. FEM is always used for modeling such inelastic effect. However, it requires the high computational cost of O(N3), where N is the number of discretized cells of the inelastic medium. Recently, a new method based on BIEM is proposed by Barbot and Fialko (2010). In their method, calculation of the stress field due to the inelastic strain is replaced to solve the inhomogeneous Navier's equation with equivalent body forces of the inelastic strain. Then, using the stress-strain greenfunction in an elastic medium, we can take into account the inelastic effect. In this study, we employ their method to evaluate the stress change at the active volcanoes around the Nankai/Tonankai earthquakes. Their method requires the computational cost and memory storage of O(N2). We try to reduce the computational amount and the memory by applying the fast computation method of H-matrices method. With H-matrices method, a dense matrix is divided into hierarchical structure of submatrices, and each submatrix is approximated to be low rank. When we divide the viscoelastic medium into N = 8,640 or 69,120 uniform cuboid cells and apply the H-matrices method, the required storage memory for the matrices of stress-strain greenfunction are reduced to 0.17 times or 0.05 times of those for the uncompressed original matrices with enough accuracy. In this study, using this method, we show the time development of the stress change at the volcanoes around the Nankai/Tonankai earthquakes, assuming the simple viscos structure.