ABSTRACT

The maximum entropy approach to inversion appears at its best when conclusions are to be drawn from very limited information. An example is the estimation of the density profile of the earth (assumed to be spherically symmetric) on the basis of only its mean density and its relative moment of inertia. With conventional methods giving rather unsatisfactory results, the maximum entropy method provides a density profile which agrees surprisingly well with the one presently considered to be the best.

INTRODUCTION

Inverse problems in geophysics frequently confront us with one of two extreme situations. While we generally have a large number of unknowns to estimate, we may also have a tremendous amount of data – actually, more data than we can reasonably process – and more or less elaborate data reduction schemes are employed to reduce the wealth of data to a more manageable size. Of course, this reduction is performed in a way which improves the quality of the retained data in some sense (e.g., increases the signal-to-noise ratio).

At other times we may still have large numbers of unknowns to contend with but very few data. In fact, the data may be so inadequate that any attempt at estimating the unknowns appears bound to fail. It is this situation which I now want to address by means of an example.