Finite difference modeling of Biot's poroelastic equations at seismic frequencies

Abstract

Across the seismic band of frequencies (loosely defined as <10 kHz), a seismic wave propagating through a porous material will create flow in the pore space that is laminar; that is, in this low‐frequency “seismic limit,” the development of viscous boundary layers in the pores need not be modeled. An explicit time stepping staggered‐grid finite difference scheme is presented for solving Biot's equations of poroelasticity in this low‐frequency limit. A key part of this work is the establishment of rigorous stability conditions. It is demonstrated that over a wide range of porous material properties typical of sedimentary rock and despite the presence of fluid pressure diffusion (Biot slow waves), the usual Courant condition governs the stability as if the problem involved purely elastic waves. The accuracy of the method is demonstrated by comparing to exact analytical solutions for both fast compressional waves and slow waves. Additional numerical modeling examples are also presented.