Inversion of capacitively coupled resistivity (line-antenna) measurements

Abstract

The capacitively coupled resistivity method using line antennas (or electrodes) has been widely applied for various kinds of applications. To solve the associated inversion problem, the general practice (i.e., the indirect inversion method) for 2D surface resistivity surveys is to approximate the line-electrode array by an equivalent point-electrode array, so that the existing direct current resistivity inversion programs can still be used. Based on the experimental evidence from this study that two resistivity arrays with a similar sensitivity (1D) curve offers comparable measurement, we optimized the equivalent point-electrode array by minimizing the sensitivity (1D) difference between the line- and point-electrode arrays in terms of the depth of investigation difference (DID). The dipole length of the optimal equivalent point-electrode array can be determined by considering only the array with the shortest dipole distance. For the line-electrode arrays with the dipole lengths of 2.5, 5, and 10 m, the suggested optimal dipole lengths are 74%, 73%, and 73% of the respective dipole lengths. The numerical examples carried out in this study prove the effectiveness of the indirect inversion method for 2D surface resistivity surveys when the appropriate equivalent point-electrode array with a low DID value is chosen, and vice versa. The direct inversion of the line electrode resistivity measurements from 3D resistivity surveys is achieved with a MATLAB-based, open-source resistivity inversion package called RESINVM3D incorporating line electrodes. The usefulness of this modified code was demonstrated with a numerical example that considered cross-borehole resistivity tomography using line electrode measurements. The location of the assigned resistivity anomaly and the boundary between two soil layers were well captured by the direction inversion.