Nonlinear magnetic inversion using a random search method

Abstract

A robust magnetic interpretation technique is described. It is based on the minimization of an objective function by a random search algorithm. Instead of just one estimate, this algorithm yields several points in parameter space, all producing objective function values below an assumed noise level. The centroid of the search points is in general a better estimate than each individual search point, especially when data are corrupted by noise. Since no derivatives are employed, even nondifferentiable objective functions, such as the [Formula: see text] norm of residuals, can be used. Computation of parameter covariance matrices and confidence ellipses is possible using simple formulas. The usefulness of R‐ and Q‐mode factor analysis applied to the correlation matrix is demonstrated. The R‐mode factor analysis can be used in parameter variance control, and the Q‐mode factor analysis provides means to find models which are extreme in some sense. The technique was applied to theoretical data and to field data from three different geologic settings. The results show that the algorithm produces accurate estimates of source parameters under different types of geologic constraints. The proposed technique has three main advantages. First, it attacks the multiple minima problem, which is always present in nonlinear inversion. A possible range of acceptable models consistent with a priori geologic information is computed. Second, when the multiple minima are not caused by the inherent ambiguity in potential field data, for example when presence of noise in data is significant or the wrong interpretation model is used, the technique provides parameter estimates which can be more significant than the estimates obtained by most optimization algorithms. Third, it can easily incorporate a priori geologic information, which is always available and should be used to reduce ambiguity. The technique can be applied at any stage of magnetic interpretation. However, its efficiency will depend upon the amount of a priori geologic and geophysical information available.