Development of Inversion Theory in Geophysics

Abstract

Geophysical models are generally estimated from observed data by using some criterion. In most cases observed data are inaccurate, insufficient and inconsistent. To deal with such data we must introduce a new criterion in place of the classical least-squares criterion. The history of the development of inversion theory in geophysics is the history of quest for the new criterion. From such a standpoint we review the development of inversion theory in the last score. In a series of papers published in 1967, 1968 and 1970, G. Backus and F. Gilbert introduced the concept of model resolution and formulated the geophysical inverse problem as the problem of compromising reciprocal requirements for model resolution and estimation errors in some natural way. This was the starting point of the fruitful development of inversion theory in geophysics. Various criteria to compromise model resolution and estimation errors have been proposed in the early part of the 1970s, but the objectivity of these criteria were not clear. At the end of the 1970s D. D. Jackson introduced the concept of prior information about unknown model parameters and combine two reciprocal criteria for model resolution and estimation erros in a natural way. Jackson's approach for linear inversion, which is based on the minimum variance criterion, has been soon exteded to nonlinear cases by A. Tarantola and B. Valette and also by D. D. Jackson and M. Matsu'ura on the basis of probability theory. The geophysical data inversion is now understood as the process of extracting new information from observed data, combining it with prior information about model parameters, and constructing the more clear image of a physical model.