Gaussian envelope for 3D geomagnetic data inversion

Abstract

We describe an inversion method for 3D geomagnetic data based on approximation of the source distribution by means of positive constrained Gaussian functions. In this way, smoothness and positivity are automatically imposed on the source without any subjective input from the user apart from selecting the number of functions to use. The algorithm has been tested with synthetic data in order to resolve sources at very different depths, using data from one measurement plane only. The forward modeling is based on prismatic cell parameterization, but the algebraic nonuniqueness is reduced because a relationship among the cells, expressed by the Gaussian envelope, is assumed to describe the spatial variation of the source distribution. We assume that there is no remanent magnetization and that the magnetic data are produced by induced magnetization only, neglecting any demagnetization effects. The algorithm proceeds by minimization of a (chi)2 misfit function between real and predicted data using a nonlinear Levenberg-Marquardt iteration scheme, easily implemented on a desktop PC, without any additional regularization. We demonstrate the robustness and utility of the method using synthetic data corrupted by pseudorandom generated noise and a real field data set.