The Generalized Problem of Lamb I. The Reflection and Transmission of Pressure and Shear Waves Generated by an Explosion in a Two Layered Spherical Earth

Abstract

Summary A model of the Earth comprising a fluid core and an infinite elastic mantle is considered. An explosive sound source initiated at an arbitrary point in the fluid core generates reflected acoustic waves in the core, Stoneley waves at the interface, and transmitted P and S waves in the elastic mantle. The general solution in the Laplace transformed plane is composed of series of modified spherical Bessel and Hankel functions. Watson-type integral representations of the series are obtained and their asymptotic estimates are deduced by the method of Laplace. It is shown that the stress wave motion in the mechanical system is analogous to the geometrical optical system.