Scattering from an elastic shell and a rough fluid–elastic interface: Theory

A null-field T-matrix formalism is developed for scattering a pressure wave from a stationary elastic shell immersed in a homogeneous and isotropic fluid half-space and in proximity to a rough fluid–elastic interface. Helmholtz–Kirchhoff integral representations of the various scattered pressure and displacement fields are constructed. The surface fields are required to satisfy the elastic tensor boundary conditions and the scattered fields are required to satisfy the extended boundary condition. Spherical basis functions are used to construct a free-field T-matrix for the elastic shell and rectangular vector basis functions are used to construct a representation of the free-field T- matrix for the rough fluid–elastic interface. The free-field T-matrices are introduced into the Helmholtz–Kirchhoff and the null-field equations for the shell-interface system and a general system of equations for the spectral amplitudes of the various fields is obtained. The general system of equations is specialized to scat...