3D inversion of potential field data using a marginalizing probabilistic method

Abstract

Probabilistic inversion methods have proven effective in solving many geophysical inverse problems. Structural orientation and spatial extent information can be efficiently incorporated the probabilistic inversion by the use of parameter covariances to produce a geologically realistic model. However, the use of a single model covariance matrix, with the underlying assumption of the presence of only one type of feature (e.g., similar size, shape, and orientation) in the subsurface, limits the ability of probabilistic inversions to recover geologically sound models. An approach based on marginalizing the probabilistic inversion is presented, which makes it possible to partition the inverse domain into various zones, each of which can have its own covariance matrix depending upon the features and/or depths of the sources. Moreover, a spatial gradient weighting function is introduced to enhance or attenuate the structural complexity in different zones. Thus, sources with different shapes, sizes, depths, and densities (or magnetic susceptibilities) can be simultaneously reconstructed. The sensitivity of the solutions to uncertainties in the a priori information, including the orientation, depth, and horizontal position as well as subdivision of the inversion domain, is analyzed. We found through synthetic examples and field data that the developed inversion method was a valid tool for exploration geophysics in presence of a priori geologic information.