Numerical Applications of a Formalism for Geophysical Inverse Problems

Abstract

A gross datum of the Earth is a single measurable number describing some property of the whole Earth, such as mass, moment of inertia, or the frequency of oscillation of some identified elastic-gravitational normal mode. We prove that the collection of Earth models which yield the physically observed values of any independent set of gross Earth data is either empty or infinite dimensional. We exploit this very high degree of non-uniqueness in real geophysical inverse problems to generate computer programs which iteratively produce Earth models to fit given gross Earth data and satisfy other criteria. We describe techniques for exploring the collection of all Earth models which fit given gross Earth data. Finally, we apply the theory to the normal modes of elastic-gravitational oscillation of the Earth.