Love waves propagated in an axially symmetric heterogeneous layer lying between two homogeneous halfspaces

Abstract

Propagation of Love waves in an axially symmetric heterogeneous layer lying between two homogeneous halfspaces is studied. The Lame's parameters and the density in the layer are supposed to vary according to the law $$\lambda /\lambda _0 = \mu /\mu _0 = 1/(1 + \alpha z), \varrho = \varrho _0 /(1 + \alpha z)^2 $$ where α is a constant andz is the distance measured from one of the interfaces into the layer. The vector wave equation is separable in this case and solution is obtained in terms of Whittaker's function. The frequency equation is solved for a particular model by using the asymptotic approximations for Whittaker's function. The results of the calculation are presented both in tabular and graphical forms.