An analytical solution for wave propagation in a semi-infinite medium with a fluid layer subjected to a buried arbitrary cylindrical line source

Abstract

This paper develops an analytical solution for the transient response of a semi-infinite solid with a fluid surface subjected to an arbitrary line source in the solid. The line source is first decomposed into P and Spulses, and the wavefields for transient responses of the fluid and semi-infinite solid are presented. Applying the Fourier and Laplace transform methods, the analytical solution in the transform domain, which is an integral solution, is obtained. Using de Hoop's method, a suitable distortion of the contour is provided to change the path of integration and the positions of the singularities and branch points, and a new form of integration is obtained. As the new integration has a form similar to that of the Laplace transform pair, the inverse Laplace transform is directly obtained, and the analytical solution in the time domain is developed. In practice, the compressional wave velocity in the solid is usually larger than that in the fluid. For the cylindrical S-pulse line source, the head wave can always be observed in the fluid–solid system. For the cylindrical P-pulse line source, the head wave can be observed in the fluid–solid system only when the wave is refracted from the solid to the fluid. Numerical examples are provided to discuss the behaviour of the fluid–solid system.