Beschreibung:
<jats:p>In the present article we give a general three-dimensional formalism for scattering in two half spaces, one of which contains a bounded inhomogeneity. Our formalism consists of an extension of the transition matrix method which has been given by Waterman, a method which applies equally well to acoustic, electromagnetic, and elastic scattering. The formalism is here developed in detail for the case when the source and inhomogeneity are situated in different half-spaces. However, the same method works for other source positions as well, and the basic equations are given also for the case when the source and the inhomogeneity lie in the same half space. In the final expression for the total scattered field, that part (the so-called anomalous scattered field) which depends on the presence of the inhomogeneity, can be separated, and the physical meaning of the various quantities which determine this anomalous scattered field can be identified. The inhomogeneity enters through its T matrix, and previous results on various bounded configurations of scatterers can therefore be inserted and used in the present formalism. Numerical results are given for inhomogeneities consisting of one or two spheres.</jats:p>