Raymond J. Nagem
Dept. of Aerospace and Mech. Eng., Boston Univ., 110 Cummington St., Boston, MA 02215
Ding Lee
Tien-Chay Chen
Naval Undersea Warfare Ctr., New London, CT 06320
A perturbation method is used to derive equations for wave propagation in an inhomogeneous elastic medium. The formulation is three dimensional, and is written explicitly in cylindrical coordinates so that it can include property variations in the depth, range, and azimuth directions. A factorization is used to convert the equations into an operator form which distinguishes outgoing waves from incoming waves. This factorization removes the requirement for a far-field boundary condition. For large-scale numerical problems, the factorization produces a tremendous reduction in computation time and in memory requirements. The elastic equations are written in a way that is directly analogous to previous work in ocean acoustics. With appropriate fluid--elastic interface conditions, the elastic and acoustic equations may be used to study the fluid--elastic interactions which are important in shallow-water environments, especially the propagation of shear waves in the ocean bottom. In this paper, the theoretical development of the elastic equations are presented and their merits and applications are discussed. [This work was jointly supported by the U.S. Office of Naval Research and the U.S. Naval Undersea Warfare Center.]