Seismic wavefield modelling in two‐phase media including undulating topography with the modified Biot/squirt model by a curvilinear‐grid finite difference method

Abstract

ABSTRACTIn this paper, we deduced the corresponding first‐order velocity–stress equation for curvilinear coordinates from the first‐order velocity–stress equation based on the modified Biot/squirt model for a two‐dimensional two‐phase medium. The equations are then numerically solved by an optimized high‐order non‐staggered finite difference scheme, that is, the dispersion relation preserving/optimization MacCormack scheme. To implement undulating free‐surface topography, we derive an analytical relationship between the derivatives of the particle velocity components and use the compact finite‐difference scheme plus a traction‐image method. In the undulating free surface and the undulating subsurface interface of two‐phase medium, the complex reflected wave and transmitted wave can be clearly recognized in the numerical simulation results. The simulation results show that the curvilinear‐grid finite‐difference method, which uses a body‐conforming grid to describe the undulating surface, can accurately reduce the numerical scattering effect of seismic wave propagation caused by the use of ladder‐shaped grid to fit the surfaces when undulating topography is present in a two‐phase isotropic medium.