WAVE-PROPAGATION IN ANISOTROPIC, SATURATED POROUS-MEDIA - PLANE-WAVE THEORY AND NUMERICAL-SIMULATION

Porous media are anisotropic due to bedding, compaction, and the prese nce of aligned microcracks and fractures. Here, it is assumed that the skeleton (and not the solid itself) is anisotropic. The rheological m odel also includes anisotropic tortuosity and permeability. The poroel astic equations are based on a transversely isotropic extension of Blo t's theory, and the problem is of plane strain type, i.e., two dimensi onal, describing qP-qS propagation. In the high-frequency case, the (t wo) viscodynamic operators are approximated by Zener relaxation functi ons that allow a closed differential formulation of Biot's equation of motion. A plane-wave analysis derives expressions for the slowness, a ttenuation, and energy velocity vectors, and quality factor for homoge neous viscoelastic waves. The slow wave shows an anomalous polarizatio n behavior. In particular, when the medium is strongly anisotropic the polarization is quasishear and the wave presents cuspidal triangles. Anisotropic tortuosity affects mainly the slow wavefront, and anisotro pic permeability produces strong anisotropic attenuation of the three modes. The diffusive characteristics of the slow mode are predicted by the plane-wave analysis. As in the single-phase case, it is confirmed that the phase velocity is the projection of the energy velocity vect or onto the propagation direction. Moreover, some fundamental energy r elations, valid for a single-phase medium, are generalized to two-phas e media. Transient propagation is solved with a direct grid method and a time-splitting integration algorithm, allowing the solution of the stiff part of the differential equations in closed analytical form. Th e snapshots show that the three waves are propagative when the fluid i s ideal (zero viscosity). It is confirmed that, when the fluid is visc ous, the slow wave becomes diffusive and appears as a static mode at t he source location. The modeling confirms the triplication (cusps) of the slow wave and the polarization behavior predicted by the plane ana lysis. (C) 1996 Acoustical Society of America.