THE INVERSION OF VERTICAL MAGNETIC DIPOLE SOUNDING DATA

Abstract

It is demonstrated that the generalized linear inverse theory may be applied to vertical magnetic dipole sounding problems. An analysis of inversion of theoretical data for a two‐layer model illustrates the method and indicates certain features not inherent in the commonly practiced curve‐matching method of interpretation. In particular, the standard deviations of the layered model parameters may be estimated. Also the data may contain varying degrees of information about individual model parameters. Indeed, the information density matrix may be used to optimize the data information distribution by choosing only data that contributes information above some minimal level. The relative importance of the information distribution to the determination of individual model parameters may be assessed using both the structure of the information density matrix and the size of the estimated parameter standard deviations. Data may be removed until the estimated standard deviations of the parameters exceed some critical values. This process may be viewed as a method of experimental design such that information/cost ratios may be maximized. Also, if the economy of the interpretation is a serious consideration, then the same process could be used to eliminate those data that have minimal information and whose exclusion does not significantly effect the parameter resolution. This process would tend to maximize interpretation/cost ratios. Inversion analyses of four sets of data previously interpreted by the curve‐matching method illustrate the inherent features of the inverse method. Results of the inverse method of interpretation may be used to make a statistical evaluation of both the fit between observed and predicted data and the resolution of the model parameters.