Three-dimensional numerical modeling of Sub-Audio Magnetic data

Abstract

A rapid numerical method for evaluating Total Field Magnetometric Resistivity (TFMMR) responses of arbitrary three-dimensional structures located between two point current sources has been developed. Finite-difference equations are derived from the Poisson equation which governs electric potential distribution within a given conductivity model. Solution of the resulting matrix equation is made using the Successive Over-Relaxation (SOR) technique combined with matrix pre-conditioning. Computation of current density from the potential and conductivity models is then made. A new, rapid Fourier domain method for evaluating the magnetic field arising from the sub-surface current flow is developed. The new method evaluates the X, Y and Z components of the magnetic field in the full three dimensions of the model space. TFMMR measurements may then be computed as a linear combination of these components. The modelling procedures developed are shown to be extensible to modelling Total Field Magnetometric Induced Polarisation (TFMMIP) responses resulting from electrically polarisable structures. Comparison of TFMMR computer models generated by analytical and the derived numerical means shows good agreement for a hemispherical sink and two dyke models. An underestimate of the response for a dipping interface model was observed because of the inability of the scheme to accurately model boundary conditions when conductivity in homogeneities extend to artificial model boundaries. An analysis of strike length on MMR response is made using conductive, rectangular prism models of varying lengths. This analysis showed a dependence of the MMR response approximately proportional to strike length of the prism. Investigation of the effect of conductive overburden on MMR response showed consequences of the layer were negligible compared to masking that occurs in conventional resistivity methods.