Three component 1D viscoelastic FDM for plane-wave oblique incidence

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, and SH 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. Q_P and Q_S 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.