A null field T‐matrix perturbation formalism for scattering from a fluid–elastic interface with random surface roughness

Abstract

A null field perturbation formalism for scattering a pressure wave from a fluid–elastic interface with random surface roughness is developed. Helmholtz–Kirchhoff integral equations and the elastic tensor boundary conditions are used to represent the unknown scattered and surface pressure and displacement fields. The null field hypothesis is used to obtain a system of coupled integral equations for the surface fields. Perturbative representations of the scattered and surface fields and of the matrix elements of the Helmholtz–Kirchhoff integral equations are constructed and used to develop equations for the nth‐order spectral amplitudes of the unknown fields. It is shown that the nth‐order spectral amplitude of a scattered field is coupled to the nth‐order spectral amplitudes of all scattered fields and to all lower‐order spectral amplitudes of all surface fields. Consequently, the nth‐order T‐matrix may be calculated recursively and expressed in terms of the zeroth‐order off‐shell T‐matrix elements. The T matrix for the nth‐order spectral amplitude of the scattered pressure field in the fluid is calculated, and it is shown that scattering process is mediated by excitation of all possible intermediate surface states created by mode conversion of all lower‐order surface field states.