Garner C. Bishop
Naval Undersea Warfare Ctr. Div. Newport, Newport, RI 02840
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.