GREENS-FUNCTIONS FOR THE FULL-WAVE ACOUSTIC RADIATION-FIELDS DIFFUSELY SCATTERED BY ONE-DIMENSIONALLY AND 2-DIMENSIONALLY ROUGH SURFACES

Green's functions are derived for the acoustic radiation fields diffus ely scattered by rough surfaces. The media on both sides of the rough interface are characterized by their bulk modulus and equilibrium dens ity. Absorption is accounted for through the relaxation time parameter . The Green's functions are expressed as integrals over the rough surf ace variables, as well as the incident and scatter wave vector variabl es. Special forms of the Green's functions are obtained when the dista nces from the rough surface to the observation point and the source po int are large compared to the acoustic wavelength and when these dista nces are also much larger than the lateral dimensions of the excited r ough surface. In the appropriate limits, the full-wave solution is sho wn to be in good agreement with the small perturbation solution and th e physical acoustics solution for the acoustic pressure scattered by r andom rough surfaces. Thus, it accounts for specular point scatter as well as Bragg-type scatter in a unified self-consistent manner. An app roximate small-slope approximation, which is suitable for the sea surf ace, is also presented.