R. A. Stephen
Dept. of Geol. and Geophys., Woods Hole Oceanographic Inst., Woods Hole, MA 02543
``Shallow'' water means water depth less than an acoustic wavelength and implies by definition strong interaction with the bottom. However since most ocean bottoms are rough and laterally heterogeneous many of the assumptions used to simplify the elastodynamic equations are invalid. On the other hand, since the depths and ranges of interest are considerably less (in terms of wavelengths) than deep water problems, direct numerical solutions of shallow water problems are quite tractable. Finite difference approaches, for example, have the following advantages over alternative methods: (a) They include all shear wave (rigidity) effects in the bottom including body and interface waves. (b) They can be applied to pulse beams at low grazing angles (less than 20(degrees)). (Methods based on ``infinite plane waves'' have conceptual problems at low angles.) (c) Both forward scatter and backscatter are included in the solutions. (d) Multiple interactions between scatterers are included. (e) Arbitrary range-dependent topography and volume heterogeneity, can be treated simultaneously in the same formulation. (f) Problems are scaled to wavelengths and periods so that the results are applicable to a wide range of frequencies. (g) The method considers scattering from structures with length scales on the order of acoustic wavelengths.