鉛直方向任意不均質弾性媒質における平面波入射問題の時間領域差分解法

Abstract

Plane-wave responses of vertically heterogeneous structure models (1-D media) are often computed in seismology. For horizontally layered media, they can be calculated by semi-analytical methods such as the propagator matrix method. However, for gradient velocity or randomly heterogeneous structures, we have to use numerical methods such as the finite-difference method. Conventional codes for the 2-D or 3-D finite-difference method require huge computer memory and long computation time even for calculating plane-wave responses of 1-D media. In this study we propose an efficient procedure to calculate plane-wave responses of arbitrary 1-D media using the finite-difference method in the time domain (FDTD). We first derive an elastodynamic equation of plane-wave incidence problem for vertically heterogeneous media by applying the Snell's law to 3-D elastodynamic equation. We then discretize the velocity-stress formulation of the derived elastodynamic equation using a staggered-grid finite-difference scheme of fourth-order accurate in space and second-order accurate in time. We also investigate the implementation of the stress-free surface condition for the scheme, and perform a stability check of the total scheme through actual computations. We computed plane-wave responses of a structure model with a velocity gradient using the derived finite-difference method. We focused on the PS-converted phase and found a “offset” phase appearing between the PS-converted phases generated at the top and bottom boundaries of the velocity-gradient layer on the surface responses of the structure model with the velocity gradient due to a P-wave incidence. This phase can be emphasized by calculating the receiver function from the radial and vertical waveforms. In this study we also investigate the “offset” phase attributed to the velocity gradient by numerical computations using the derived finite-difference method.