Renormalization group analysis of rough surface scattering

An acoustic field of wavelength much larger than the largest scale of a scattering body is considered. A renormalization group equation has been developed to find an easier way of calculating the ensemble averaged scattered fields, with the renormalized parameter being impedance constant introduced to describe the behavior of the boundary under insonification. The results suggest that rough surface scattering is, in fact, an asymptotic theory, under the limit that the surface structure has no lower cutoff and the scatterer has a power-law surface spectrum. Also, a fundamental difference in the renormalization scheme between the two extreme boundary conditions (von Neumann and Dirichlet) is pointed out. a)Currently at Naval Research Laboratory, Washington, DC 20375-5000.