Sound propagation over the ground with a random spatially-varying surface admittance

Abstract

Sound propagation over the ground with a random spatially-varying surface admittance is investigated. Starting from the Green's theorem, a Dyson equation is derived for the coherent acoustic pressure. Under the Bourret approximation, an explicit expression is deduced and an effective admittance that depends on the correlation function of the admittance fluctuations is exhibited. An asymptotic expression at long range is then obtained. Influence of the randomness on the amplitude of the reflection coefficient and on the wavenumbers of the surface wave component is analyzed. Afterwards, numerical simulations of the linearized Euler equations are carried out and the coherent pressure obtained by an ensemble-averaging over 200 realizations of the admittance is found to be in good agreement with the analytical solution. In the considered examples of grounds, the mean intensity is shown to be similar to the intensity in the non-random case, except near interferences that are smoothened out due to randomness. It is however exemplified that the intensity fluctuations can be large, especially near destructive interferences.

Random Scattering by Rough Surfaces With Spatially Varying Impedance

“…The total field E along the surface is then given by the solution of a Helmholtz integral equation (see also [1,17]) as follows:…”

“…We now consider the special case of a planar surface ζ(x) ≡ 0 with variable impedance, using the above operator expansion. We should mention here the elegant method of [1] and that of [2] which also considers ensemble averages and could be alternatively employed. To simplify notation we will denote the operators in this case by A 0 and A 1 so that Equation (2) becomes…”

“…Many applications of wave scattering from rough surfaces are complicated by the involvement of further scattering mechanisms [1][2][3][4][5][6]. Radar propagating over a sea surface, for example, may encounter spatially varying impedance due to surface inhomogeneities [7][8][9], or refractive index variations in the evaporation duct [10,11].…”

“…Roughness is often the dominant feature, but impedance variation may produce further multiple scattering. The great majority of theoretical and numerical studies nevertheless treat such effects in isolation [1,2,[13][14][15]. Of particular note are the elegant studies of admittance variation by [1], which obtain analytical solutions by applying Bourret approximation to a Dyson equation, and of impedance variation by [2] which derive intensity fluctuation statistics.…”

“…The great majority of theoretical and numerical studies nevertheless treat such effects in isolation [1,2,[13][14][15]. Of particular note are the elegant studies of admittance variation by [1], which obtain analytical solutions by applying Bourret approximation to a Dyson equation, and of impedance variation by [2] which derive intensity fluctuation statistics. Experimental validation of scattering models in complex environments remains a major difficulty, exacerbated by the lack of detailed environmental information, and it is therefore crucial to distinguish and identify sources of scattering.…”