In this paper the boundary integral equation method is used to solve a
scattering problem in a shallow ocean with an elastic seabed. The Han
kel transformation and Mittag-Leffler decomposition were used to const
ruct the propagating solution for both far-field and near-field. In pa
rticular, necessary and sufficient conditions are found for the existe
nce of the propagating solution. Using the propagating solution, the s
cattering problem is recast as a boundary integral equation. A numeric
al algorithm is developed for solving this boundary integral equation
and its implementation on a T3D parallel computer is used to compute a
n illustrative example.