Multiple scattering of waves by a half-space of distributed discrete scatterers with modified T-matrix approach

Abstract

In studying multiple scattering of waves by a half-space of distributed discrete scatterers, the approach of the quasi-crystalline approximation together with hole correction or pair distribution functions has been used extensively. In this approach a system of simultaneous equations must be solved to determine the effective propagation constant and the expansion coefficients of the coherent exciting field. In this paper, we analyse the same problem under Foldy's approximation by using the so-called modified T-matrix approach. Two simple and clear equations are obtained for determining the effective propagation constant and transmission coefficient of the coherent transmitted field when the scatterers are identical spheres. The expressions for the coherent reflected field and incoherent scattered intensity are also given. It is shown that, in the limit of low frequency and sparsely distributed scatterers, our solutions reduce to the well-known results. The numerical results for ka=0.2 also show that our results with the modified T-matrix and Foldy's approximation are better than Foldy's approximation alone, but are still worse than the quasi-crystalline approach with pair distribution functions and Monte Carte simulations because we have not incorporated the pair distribution functions into our modified T-matrix approach. It should be pointed out that the modified T-matrix approach can be generalized to the case of pair distribution functions in which the exciting field is also travelling with the effective propagation constant.