Ray-theoretical approach to torsional oscillations of a two-layered spherical shell and application to an inversion problem.

Abstract

A ray-theoretical approach was adopted to obtain an asymptotic frequency equation for torsional oscillations of a spherically symmetrical Earth consisting of a two-layered solid shell, that is, the crust and mantle. It is shown that the equation is utilized for the inversion problem of getting the shear wave velocity distribution in the mantle from torsional eigenfrequencies. Two different methods of solving the problem are then presented. Numerical experiments for a model Earth confirm the validity of these methods and show the necessity of taking the Moho discontinuity into consideration for this kind of inversion method.