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

In 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.