### ASA 126th Meeting Denver 1993 October 4-8

## 2aUW11. A null field T-matrix perturbation formalism for scattering from a
fluid--elastic interface with random surface roughness.

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