On a fast method for computing the field of waves reflected by a thin elastic layer

A method for computing the field of waves reflected by a thin elastic layer is proposed. The method takes into account all kinds of exchange type reflections and is based on the summation of kinematic and dynamic analogues.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Vol. 179, pp. 152–162, 1989.