Michael D. Collins
Naval Res. Lab., Washington, DC 20375
W. A. Kuperman
Scripps Inst. of Oceanogr., La Jolla, CA 92093
William L. Siegmann
Rensselaer Polytech. Inst., Troy, NY 12180
Biot's theory of poro-elasticity is derived for heterogeneous media and reduced to a system of three coupled equations. Previous formulations of this problem include a redundant fourth equation. The reduced system factors into incoming and outgoing wave equations and may therefore be solved with the parabolic equation (PE) method, which is useful for range-dependent problems. The operator square root is approximated using rational-linear functions that were originally designed for the elastic PE and provide accuracy and stability. An initial condition for the poro-elastic PE is obtained with the self-starter, which has been generalized to handle compressional and shear sources in poro-elastic media. Qualitative tests involving the propagation and reflection of slow and fast compressional wave beams and shear wave beams demonstrate that the poro-elastic PE handles all wave types. A solution based on the wave-number spectrum has been developed to test the poro-elastic PE quantitatively. The PE and spectral solutions are nearly identical for problems involving a water column overlying a poro-elastic sediment. A nonlinear relationship involving the coefficients of the wave equation and the Biot moduli has been worked out so that the natural parameters (i.e., porosity, density, wave speeds, and attenuations) may be used as inputs to propagation models.