3‐D inversion of magnetometric resistivity data

Abstract

†Summary We develop algorithms to forward model and invert magnetometric resistivity (MMR) responses over an arbitrary 3-D conductivity structure. The observed data can be at the surface or in the borehole. In the forward modelling algorithm, the secondorder partial differential equations for the scalar and vector potentials are discretized on a staggered-grid using the finitevolume technique. In the inversion method, we discretize the 3-D model into a large number of rectangular cells of constant conductivity, and the final solution is obtained by minimizing a global objective function composed of the model objective function and data misfit. All minimizations are carried out with the Gauss-Newton algorithm and model perturbations at each iteration are obtained by a conjugate gradient least squares method (CGLS), in which only the sensitivity matrix and its transpose multiplying a vector are required. A depth weighting and a sensitivity-based weighting are respectively applied to inversion of surface and down-hole MMR data. The inversion method has been tested with a field data set from Western Australia.