WAVE-PROPAGATION IN HETEROGENEOUS, POROUS-MEDIA - A VELOCITY-STRESS, FINITE-DIFFERENCE METHOD

A particle velocity-stress, finite-difference method is developed for the simulation of wave propagation in 2-D heterogeneous poroelastic me dia. Instead of the prevailing second-order differential equations, we consider a first-order hyperbolic system that is equivalent to Blot's equations. The vector of unknowns in this system consists of the soli d and fluid particle velocity components, the solid stress components, and the fluid pressure. A MacCormack finite-difference scheme that is fourth-order accurate in space and second-order accurate in time form s the basis of the numerical solutions for Blot's hyperbolic system. A n original analytic solution for a P-wave line source in a uniform por oelastic medium is derived for the purposes of source implementation a nd algorithm testing. In simulations with a two-layer model, additiona l ''slow'' compressional incident, transmitted, and reflected phases a re recorded when the damping coefficient is small. This ''slow'' compr essional wave is highly attenuated in porous media saturated by a visc ous fluid. From the simulation we also verified that the attenuation m echanism introduced in Blot's theory is of secondary importance for '' fast'' compressional and rotational waves. The existence of seismicall y observable differences caused by the presence of pores has been exam ined through synthetic experiments that indicate that amplitude variat ion with offset may be observed on receivers and could be diagnostic o f the matrix and fluid parameters. This method was applied in simulati ng seismic wave propagation over an expanded steam-heated zone in Cold Lake, Alberta in an area of enhanced oil recovery (EOR) processing. T he results indicate that a seismic surface survey can be used to monit or thermal fronts.