SOLUTION OF THE PROBLEM OF ELASTIC-WAVE RADIATION BY A SOURCE ACTING ON THE WALL OF A CASED BOREHOLE DRILLED IN AN ANISOTROPIC GYROTROPIC MEDIUM

Abstract

The subject of this paper is finding of a wave field from a source placed in a liquid-filled borehole cased by a metal pipe and cement stone. Outside of the case there is a medium which can be isotropic or anisotropic; moreover, it can be gyrotropic or nongyrotropic. Two types of elastic-wave sources are considered: 1 ) sources of the "directed force" type acting on the wall of a borehole and 2) a spherical source of the "center of expansion" type with a shell which does not touch the borehole wall. The problem is solved using the four-dimensional Fourier transform with respect to the variables t, x, y, and z. This enables one to present the boundary conditions in the form of algebraic equations for spectra. A system of equations is derived, which permits determination of the wave field at all points of media, including the points of contact between the source and the medium.