An optimized staggered-grid finite-difference operator for seismic wave simulation in poroelastic media

Abstract

Most of the finite-difference methods for simulating seismic wave propagation in poroelastic media compute the spatial derivatives using fixed-length, which is the 2Mth-order operator. An optimized staggered-grid finite-difference (SGFD) method, which uses mixed operator length to approximate spatial derivatives, is derived from Biot’s equations to improve accuracy and stability. The numerical stability and dispersion of our optimized scheme are derived using the dispersion relation for the poroelastic equations. We have compared the dispersion curve plots for the developed and the conventional method. We introduce evidence that the developed scheme is comparatively more stable and accurate than the existing conventional method. The numerical solutions obtained using our optimized scheme closely approximate the analytical solution, and all wave types predicted by Biot’s theory are generated. Our scheme is used to simulate seismic wave propagation in a 2D homogeneous model, a two-layered model, a moderately complex model derived from the Utsira Formation, Sleipner North Sea, where a large amount of CO2 is being sequestrated, and a 3D homogeneous model. The developed scheme takes less computational time than the conventional SGFD method without compromising the accuracy or the stability.