Response of an elastic half-space to finite sized sources

Abstract

Analysis of the transient response of an isotropic, homogeneous and elastic half-space due to the application of a point, a finite line, and areal sources are presented in this thesis. The source is either buried or on the surface while the receiver is always taken on the surface. Solutions are obtained for vertically and radially oriented sources and for different values of zo depth of the source and ro radial distance from the source to the receiver. The response due to finite sized line and areal sources are obtained by integrating numerically the point source results along the line and over the area respectively. The results obtained in this work can be used to explain the effect of the size of the transducers used in Nondestructive Testing of materials. Here, the solution gives the response of a half-space for a Heaviside's step input function. In the numerical calculations, using the generalized ray theory, the. response of the half-space is expressed in terms of the contributions from individual rays. Each ray is ·expressedin terms of integrals in the complex Laplace transform space, and the Cagniard's method is used to take the inverse transform of the expressions. As each ray has a distinct path and a certain arrival time, only the rays that arrive prior to the time of interest are considered.