SOME ASPECTS OF THE PHYSICS AND NUMERICAL MODELING OF BIOT COMPRESSIONAL WAVES

Abstract

We investigate the problem of wave propagation in a porous medium, in the framework of Biot's theory, computing the numerical solution of the differential equations by a grid method. The problems posed by the stiffness of the equations are circumvented by using a partition (or splitting) time integrator which allows for an efficient explicit solution as in the case of nonstiff differential equations. The resulting algorithm possesses fourth-order accuracy in time and "infinite" (spectral) accuracy in space. Alternatively, a second-order algorithm, based on a Crank–Nicolson method, provides similar stability properties, although lower accuracy. The simulations correctly reproduce the wave forms of the fast and slow compressional waves and their relative amplitudes. Moreover, we observe the static slow mode, particularly strong when the source is a bulk perturbation or a fluid volume injection. The numerical results are confirmed by the analytical solution.