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

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 a inverse problem where the data are only the mass of the Earth and its moment of inertia. The solution of this inverse problem is based on a probabilistic philosophy and on the concept of entropy. It is defined an objective function which contains the relative entropy of the pdf (probability density function) of the model paxameters (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 with standard inversion techniques, showing that MRE gives a better agreement with the reference models considered (Bullen A, HB1). An extention is proposed using also the velocity distribution of body waves in the interior of the Earth.