Spectral representation of the love wave operator

Abstract

In many geophysical problems of diffraction of Love waves at a laterally discontinuous change in elevation or in material properties of layered structures, we need to express the displacements on either side of the discontinuity, in terms of a complete set of functions, proper or improper, associated with the Love wave operator in order to be able to apply such powerful tools as integral equations and variational principles. Kazi [1976] presented a method for obtaining the spectral representation of the two-dimensional Love wave operator, associated with the propagation of monochromatic SH waves in a laterally uniform layered strip or a half-space. Kazi [1976] found such a representation for a two-layer model of an infinite strip, overlying another infinite strip or a half-space, with constant rigidity and density within each layer. This thesis seeks to determine the spectral representation of the two dimensional Love wave operator associated with the propagation of monochromatic SH waves in three-layer models of two infinite strips, overlying another infinite strip or a half-space, with constant rigidity and density within each layer. This representation will be of considerable use in tackling Love wave diffraction problems in horizontally discontinuous structures involving three layers.