Sensitivity distributions in 2D cross-hole MMR - a numerical study

Abstract

Towards the adaptation of magnetometric resistivity (MMR) to cross-hole imaging, sensitivities were calculated for a 2D cross-hole scenario using finite-element forward modeling and a perturbation approach. The 2D setup considers borehole measurements of the magnetic field as a response to borehole current injection; in this case the magnetic field has only one non-zero component (perpendicular to the considered plane). Spatial distributions of sensitivity are presented for single-pole and dipole injection arrangements, homogenous and inhomogeneous 2D conductivity distributions, and multiple-offset source-receiver configurations. For the homogenous case, distinct regions of negative and positive sensitivities are found for all electrode configurations. These regions are evenly distributed for the single-pole injection and show higher resolution towards the considered boreholes for both vertical and horizontal dipole current injection. Furthermore, our numerical study reveals that measurements with a source-receiver offset exceeding the distance between the boreholes have almost no sensitivity. For the considered three-layer case, sensitivity patterns are significantly disturbed for both conductive and resistive middle layers depending on the given conductivity contrast. By comparison with DC sensitivity patterns for corresponding measurement configurations it is found that both methods, DC and MMR, in fact provide complementary information with respect to current flow.