### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 4aUW6. A numerical solution of the parabolic elastic wave equation.

**Raymond J. Nagem
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*Dept. of Aerospace and Mech. Eng., Boston Univ., 110 Cummington St.,
Boston, MA 02215
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**Ding Lee
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*Naval Undersea Warfare Ctr., New London, CT
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**Gongquin Li
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*Univ. of New Orleans
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Based on the parabolic equation approximation, a set of equations has been
developed for three-dimensional time-harmonic wave propagation in an elastic
medium. The elastic equations for the scalar and vector potentials are written
in a matrix form which is a direct counterpart to previous work on the scalar
wave equation for a fluid medium. An ordinary differential equation (ODE) method
in conjunction with a finite-difference scheme leads to a stable marching
procedure. One feature of this approach is that every finite-difference
discretization results in a tridiagonal system of equations; these equations can
be solved efficiently by recursive formulas. This paper reports the
computational results which are used to check (1) the stability of the marching
scheme, and (2) the accuracy of the elastic model. Accuracy and validity are
verified by comparing the numerical results of the finite-difference method with
a far-field analytic solution in an unbounded medium.