Inversion of the Earth's Radial Density Distribution by an Information Theory Approach

Abstract

A new formulation called Minimum Relative Entropy (MRE) is applied to the determination of the density profile within the Earth. The question is defined as an inverse problem where the data are only the mass of the Earth and its moment of inertia. The solution ofthis inverse problem is based on aprobabilistic philosophy and on the concept ofentropy. It is defined an objective function that contains-thê relative entropy ofthe probability density function ofthe model parameters (density distribution). The objective function is then minimized under adequate constraints in order to give the output estimate of the model parameters. The results are compared to a standard inversion technique, showing that MRE gives a much better agreement with the reference models considered (Bullen A, HB I and PREM).