On the calculation of wave fields in elastic homogeneous media with plane parallel partitioning boundaries

Abstract At the present time, quantitative studies of exact solutions of dynamic problems in the theory of elasticity are usually conducted by means of approximate asymptotic methods. These methods vary depending on the portion of the disturbed layered medium being investigated. In a number of cases it is difficult to estimate the accuracy and region of applicability of the formulas that are obtained. For a more accurate and complete investigation which determines the entire wave field in a uniform manner, contour integrals are sometimes used (uniformity is very important here in order to have a simple standard scheme for numerical computations). The description of the solution is thereby reduced to integrals distributed along segments of the real axis which are evaluated by usual methods of numerical integration. As a point of departure, one can take any of the known forms of exact solutions [1–4] for concentrated excitations. The transition to distributed excitations, as is well known, can then be effected by application of the principle of superposition. It is convenient to use, for example, solutions in the form of formulas which are given in [3]. The present paper is addressed to the task of the reduction of these formulas to the simplest real integrals suitable for computation.