Love waves due to a point source in an axially symmetric heterogeneous layer between two homogeneous halfspaces

Abstract

Propagation of Love waves due to a point source in an axially symmetric heterogeneous layer lying between two homogeneous half-spaces is studied. The variation of Lame's parameters and the density in the layer is assumed to be of the type $$\frac{\lambda }{{\lambda _0 }} = \frac{\mu }{{\mu _0 }} = \frac{1}{{(1 + \alpha z)}},\frac{\varrho }{{\varrho _{_0 } }} = \frac{1}{{(1 + \alpha z)^2 }}$$ 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 the solution is obtained in terms ofWhittaker's function. Using the asymptotic approximation forWhittaker's function, an approximate solution is obtained to the first power in α. This agrees with the solution obtained directly by neglecting the squares and higher powers of α at each stage.