A parabolic equation for poro-elastic media

Abstract

The parabolic equation (PE) method is extended to handle problems involving poro-elastic layers [M. A. Biot, ‘‘Theory of propagation of elastic waves in a fluid-saturated porous solid,’’ J. Acoust. Soc. Am. 28, 168–191 (1956)]. The equations of motion are derived for heterogeneous poro-elastic media. Interface conditions that are appropriate for the PE method are derived for coupling to fluid and elastic layers. For the two-dimensional geometry (range and depth) that is representative of many problems in ocean acoustics, the equations of motion reduce to three coupled equations that factor into outgoing and incoming wave equations (the standard formulation has a redundant equation). The outgoing wave equation is solved with the PE method using rational approximations. The poro-elastic PE, which is a generalization of the elastic PE, is an efficient approach for solving range-dependent propagation problems involving an ocean overlying a poro-elastic sediment. The self-starter is generalized to handle compressional and shear sources in poro-elastic layers. The coefficients of the poro-elastic wave equation are derived from a set of natural parameters.