The problem of modelling thin layers in both elastic and acoustic scattering problems is addressed in the present paper. The layer is replaced by a single surface of discontinuity for the field variables, and the discontinuities are specified in such a manner that the influence of the original layer is reproduced to within O(h2), where h is the constant layer thickness. In essence, the layer is thus modelled by means of a set of ‘equivalent boundary conditions’, which are exact up to and including the first order in the layer thickness. Layers of fairly general shape, and at least five different configurations of materials, are considered. A numerical comparison of the approximate boundary conditions against an exact solution for scattering of P and S waves from a layered elastic sphere embedded in an elastic medium is included.
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Peter Bövik (1994) studied this question.