The fundamental singularity in a shallow ocean with an elastic seabed^*

^*This research was supported in part by National Science Foundation through grant BES-9402539

Abstract

In this paper, the problem of constructing the acoustic pressure field excited by a time-harmonic point source in a shallow ocean over an elastic seabed is considered. This is a transmission boundary value problem for a system of prtial differential equations. Two different expansions for the propagating solutions are derived. The first expansion is obtained by using Hankel transformation. We symbolically compute the Hankel transform of the propagating solution and then perform inversion using Mittag-Leffler decomposition and other spectral analysis techniques. The second expansion is normal mode expansion. We find an appropriate inner product in a suitable function space, which permits us to compute the generalized Fourier coefficients. Numerical computations are presented to verify the orthogonality of the set of eigenfunctions with rewpect to this inner product, and to verify the equivalence of the two expansions.

Keywords:

• Acoustic
• elastic
• Hankel
• Mittag Leffler decomposition
• inner product

^*This research was supported in part by National Science Foundation through grant BES-9402539

^*This research was supported in part by National Science Foundation through grant BES-9402539

Notes

^*This research was supported in part by National Science Foundation through grant BES-9402539