### ASA 125th Meeting Ottawa 1993 May

## 5pPA2. Scattering from an elastic shell and a doubly infinite fluid--solid
interface with random surface roughness.

**Garner C. Bishop
**

**
Judy Smith
**

**
**
*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.