Inversion in rough surface scattering via the frequency-difference autoproduct

Abstract

The forward scattering of acoustic waves, with wavenumber k, from a rough surface is a well-known problem in underwater acoustics. A random rough surface, statistically characterized by its root-mean-square roughness h and its correlation length L, exponentially reduces reflected field coherence as kh increases. The frequency-difference autoproduct is a nonlinear mathematical construction that recovers field coherence in rough surface scattering by down shifting recorded signal frequencies, thereby minimizing apparent surface roughness. Salient features of frequency-difference-autoproduct forward-scattering results, including the dependence on both h and L, are shown. Further, this presentation describes the unique capability afforded by the frequency-difference autoproduct to approach the inverse problem in a rough surface scattering environment. In particular, inference of a random rough surface's root-mean-square height and correlation length is accomplished via autoproduct-based signal processing methods. The work implements an isotropic surface roughness profile corresponding to in-band roughness values of 1.25 < kh < 3.5. Using the same scattered signals, conventional in-band inversion techniques are compared to the results obtained via the frequency-difference autoproduct. Experimental results from a laboratory water tank may be discussed as well. [Work supported byONR.]