Self-constrained inversion of potential fields through a 3D depth weighting

A new method for inversion of potential fields is developedusing a depth-weighting function specifically designed forfields related to complex source distributions. Such a weight-ing function is determined from an analysis of the field thatprecedes the inversion itself. The algorithm is self-consistent,meaning that the weighting used in the inversion is directlydeduced from the scaling properties of the field. Hence, thealgorithm is based on two steps: (1) estimation of the locallyhomogeneous degree of the field in a 3D domain of the har-monic region and (2) inversion of the data using a specificweighting function with a 3D variable exponent. A multiscaledata set is first formed by upward continuation of the originaldata. Local homogeneity and a multihomogeneous model arethen assumed, and a system built on the scaling function issolved at each point of the multiscale data set, yielding amultiscale set of local-homogeneity degrees of the field.Then, the estimated homogeneity degree is associated to themodel weighting function in the source volume. Tests on syn-thetic data show that the generalization of the depth weightingto a 3D function and the proposed two-step algorithm hasgreat potential to improve the quality of the solution. Thegravity field of a polyhedron is inverted yielding a realisticreconstruction of the whole body, including the bottom sur-face. The inversion of the aeromagnetic real data set, from theMt. Vulture area, also yields a good and geologically consis-tent reconstruction of the complex source distribution.