Scattering from an elastic shell and a doubly infinite fluid–solid interface with random surface roughness

Abstract

A null field T-matrix formalism similar to that of Kristensson and Strom [J. Acoust. Soc. Am. 64, 917–936 (1978)], is used to obtain a formal solution for scattering from a stationary elastic shell immersed in a homogeneous and isotropic fluid half-space and in the vicinity of a doubly infinite fluid–solid interface with random surface roughness. The full elastic tensor boundary conditions are applied at each fluid–solid interface and equations that follow from the application of the Helmholtz–Kirchhoff integral and the null hypothesis to the various regions are used to construct the T matrix for the shell-interface system and the free-field T matrices for the elastic shell and the randomly rough fluid–solid interface. Spherical basis functions are used to construct the conventional free-field T matrix for the elastic shell. However, rectangular vector basis functions are used to construct a formal representation of the T matrix for the randomly rough fluid–solid interface. The free-field T matrices are introduced into the Helmholtz–Kirchhoff and the null field equations for the shell-interface system and it is shown that the T matrix for the system is simply related to the free-field T matrices for the shell and the randomly rough fluid–solid interface. Therefore, a perturbation theory T matrix for the randomly rough surface can be introduced in a relatively simple manner. An explicit representation for the scattered pressure field in the fluid is constructed. It is also shown that the formalism contains multiple-scattering effects between the surface and the shell and also on the rough interface.