THREE-COMPONENT 1D VISCOELASTIC FDM FOR PLANE-WAVE OBLIQUE INCIDENCE

Abstract

We propose a very efficient scheme for modeling three-component seismic plane waves in vertically heterogeneous attenuative media using the finitedifference (FD) method in the time domain. The scheme is able to represent P , SV ,a ndSH waves incoming from different direction. The algorithm can also calculate the plane-wave responses of media for different incident angels. In the algorithm, neglecting lateral heterogeneity, the wave equation is rewritten for plane waves by applying a 2D Radon transform to the 3D general wave equation. QP and QS are incorporated via generalized Zener body rheological models for viscoelasticity to represent anelastic attenuation. Our FD scheme uses a 1D grid, which leads to a significant reduction in computation time and memory requirements as compared to the corresponding 3D or 2D computations. It may be an efficient tool for pre- or post-analysis of local structural effects including anelastic attenuation, before or after the large-scale seismic wave simulation. To demonstrate the ability and efficiency of the scheme, we calculate a synthetic vertical seismic profile (VSP) for a borehole with a highly heterogeneous velocity model and frequency dependent attenuation model in the Kanto area of Japan.