Green's function for a harmonic acoustic point source within seawater overlying a saturated poroelastic seabed

Abstract

In this paper, Green's function for an acoustic source within half-space seawater overlying a porous seabed is established. The half-space seawater is described using the Helmholtz equation, while the seabed is considered as a saturated porous medium and characterized by Biot's theory. Green's function of the half-space seawater has two components: the principal and complementary parts. The principal part of Green's function is the solution for a conventional acoustic point source in an infinite medium, while the complementary part corresponds to the general solution of the Helmholtz equation for the half-space. Green's function of the half-space seabed is obtained by solving Biot's dynamic equations via the Hankel transform method. Using the continuity conditions at the interface between the seawater and the seabed, the closed-form Green's functions for the seawater and the seabed in the frequency–wavenumber domain are determined. The frequency domain Green's function is recovered by the inversion of the Hankel transform. A parametric study is carried out for Green's function in the frequency domain, and a time domain example is presented in terms of frequency domain Green's function. Numerical results show that the permeability of the porous seabed has very little influence on the response of the seawater, while Biot's modulus has a pronounced influence on the wave field.