The total field magnetometric resistivity (TFMMR) method: Part I: theory and 2.5D forward modelling

Abstract

The Sub-Audio Magnetics (SAM) method is a high-resolution electrical technique that derives information on sub-surface electrical and magnetic properties by introducing an electric current into the ground and measuring the total magnetic field changes on the Earth surface at a sub-metre interval via an optically pumped magnetometer. One parameter that may be derived from any SAM survey is the total-field magnetometric resistivity (TFMMR). To date, there are few quantitative interpretational schemes for deriving resistivity from TFMMR data. This paper outlines the theory to calculate the 2.5 dimensional (2.5D) TFMMR response due to a point source of current in an otherwise two-dimensional (2D) Earth. The problem is formulated in the wavenumber domain by first solving for the electrical potential from the current source, and then deriving orthogonal horizontal and vertical components of magnetic field using the modified Biot-Savart Law. An inverse Fourier transform is then applied to yield vector magnetic field components in the spatial domain, and hence the scalar TFMMR response. A 2.5D finite-element modelling approach is developed to model TFMMR responses from various resistivity structures. For an isotropic, uniform resistivity Earth the finite-element model gives good agreement with analytical results, with an accuracy of about 4% in each of the three vector components. The greatest error is for the horizontal magnetic field component along strike. Finally, we demonstrate that the TFMMR technique is very useful for defining basement structures in areas of conductive regolith cover. The presence of a regolith (10 ?.m) has little effect on the TFMMR responses provided that its thickness is less than about one twentieth of the current-electrode separation. Thus, for a typical electrode separation of 1.2 km, the TFMMR response is sensitive to basement structures for regolith thickness of up to 60 m, and hence is an important geophysical method for exploration beneath cover.