Open AccessQuadrangle‐grid velocity–stress finite difference method for poroelastic wave equations
Author(s) -
Jianfeng Zhang
Publication year - 1999
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1046/j.1365-246x.1999.00938.x
Subject(s) - poromechanics , biot number , quadrangle , grid , finite difference , free surface , stress (linguistics) , geometry , mathematical analysis , finite difference method , mathematics , mechanics , geology , porous medium , porosity , physics , geotechnical engineering , linguistics , philosophy , geomorphology
A quadrangle‐grid velocity–stress finite difference method, based on a first‐order hyperbolic system that is equivalent to Biot’s equations, is developed for the simulation of wave propagation in 2‐D heterogeneous porous media. In this method the velocity components of the solid material and of the pore fluid relative to that of the solid, and the stress components of three solid stresses and one fluid pressure are defined at different nodes for a staggered non‐rectangular grid. The scheme uses non‐orthogonal grids, allowing surface topography and curved interfaces to be easily modelled in the numerical simulation of seismic responses of poroelastic reservoirs. The free‐surface conditions of complex geometry are achieved by using integral equilibrium equations on the surface, and the source implementations are simple. The algorithm is an extension of the quadrangle‐grid finite difference method used for elastic wave equations.