### ASA 125th Meeting Ottawa 1993 May

## 2aUW7. Limitations of the operator expansion method.

**Peter J. Kaczkowski
**

**
Eric I. Thorsos
**

**
**
*Appl. Phys. Lab., Univ. of Washington, Seattle, WA 98105
*

*
*
Preliminary studies of the operator expansion method applied to scattering
from rough surfaces satisfying the Dirichlet boundary condition [P. J.
Kaczkowski and E. I. Thorsos, J. Acoust. Soc. Am. 90, 2258 (A) (1991)] have
indicated that this relatively new method [D. M. Milder, J. Acoust. Soc. Am.
89, 529--541 (1991)] has a broad range of validity. For moderate rms surface
slopes, the method is accurate over almost all scattering angles, and
represents a vast improvement over the Kirchhoff approximation and small
perturbation methods. Further study of the operator expansion method has led to
new insights that establish a link between the formal validity of the method
and the validity of the Rayleigh hypothesis. While the Rayleigh hypothesis
appears to place a strict limit on the operator expansion, numerical examples
will be presented that illustrate that the accuracy of the scattering cross
section computed by the operator expansion method degrades only gradually as
the rms slope is increased beyond that limit. For scattering from surfaces
rough in one dimension, the accuracy of the operator expansion solution is
established through comparison with the solution to an integral equation.
Studies of the convergence of the terms in the operator expansion series
indicate how the convergence rate can be used to infer the accuracy of the
solution at any given order. This property will be useful when applying the
operator expansion method to scattering from surfaces rough in two dimensions,
for which exact solutions are still very costly. [Work supported by ONR.]