Wave propagation theory in offshore applications

A frequency-wavenumber-domain formulation is presented in this paper for calculation of the Green's functions and wave propagation modes in a stratified fluid body underlain by a layered viscoelastic soil medium. The Green's functions define the solid and fluid displacements and fluid pressures due to uniform disk loads acting in either the soil or fluid media. The solution is in the frequency domain and is based on a Fourier expansion of the displacements in the azimuthal direction together with Hankel transform in the radial direction and analytical solutions in the vertical direction. The presented formulation uses the notion of layer stiffness matrices for the solid and fluid layers. Derivation of the expressions for the fluid layer matrices is presented, and a simple procedure for numerical integration of the Green’s functions is proposed. Two examples of the use of the presented model are presented. The first example deals with computation of the dynamic impedances of seabed foundations, and the second example concerns computation of fundamental modes of surface waves at the solid-fluid interface. This mode is often used in characterization of the seabed material from the direct seismo-acoustic measurements underwater.