Author(s)

G.D. Manolis & R.P. Shaw

Abstract

In this work, a fundamental solution is derived for the case of time harmonic seismic waves originating from a point source and propagating in a three-dimensional, unbounded heterogeneous medium with a Poisson's ratio of 0.25. The first step in the solution procedure is to transform the displacement vector in the Navier equations of dynamic equilibrium through scaling by the square root of the position- dependent shear modulus. Following imposition of certain constraints that are subsequently used to derive the depth profile of the elastic modulii and of the density, it becomes possible to employ Helmholtz's vector decomposition so as to generate two scalar wave equations for the dilational and rotational components of the wave motion, a process which again generates additional constrai

Keywords