Spivack M., Rath-Spivack O.

A method is given for evaluating acoustic scattering by an arbitrary irregular surface with spatially varying impedance. This allows examination of the effects of impedance variation and the resulting modification of scattered field. Expressions are derived for the scattered field itself, and for the mean field when the impedance varies randomly. Many problems in acoustic propagation over irregular terrain (for example) are complicated by the presence of impedance variation, and it is often important to identify the scattering effects due to this, or to characterise the surface properties from the scattered field. We aim here to provide an efficient means to calculate such effects, and where possible to derive simple descriptions of the resulting coherent or mean field. In order to do this an operator expansion is used: Surface pressures (from which scattered fields are determined) are expressed as the solution of an integral equation, in which the influence of impedance variation is separated. The solution is written in terms of the inverse of the governing integral operator, and provided impedance variation is not too large this inversion can be expanded about the leading term. This provides convenient semi-analytical expressions for scattered fields and equivalent effective boundary conditions for the coherent fields.