### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 2pUW1. Propagation in range-dependent poro-elastic media.

**Michael D. Collins
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*Naval Res. Lab., Washington, DC 20375
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**W. A. Kuperman
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*Scripps Inst. of Oceanogr., La Jolla, CA 92093
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**William L. Siegmann
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*Rensselaer Polytech. Inst., Troy, NY 12180
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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.