Practical techniques for 3D resistivity surveys and data inversion¹

TLDR

The study develops techniques to shorten the time required for 3D resistivity surveys and data inversion using 25–100 electrodes. By measuring along horizontal, vertical, and 45° diagonal rows through the current electrode, employing a smoothness‑constrained least‑squares inversion with an analytic Jacobian from a homogeneous half‑space and a quasi‑Newton update, the authors reduce the number of measurements to about one‑third and the computational load. The method yields satisfactory models on synthetic and field data, in roughly 20 minutes on an 80486DX2/66 microcomputer for a 7×7 grid, demonstrating that 3D resistivity surveys and inversion can be performed with commercial equipment and inexpensive computers.

Abstract

Abstract Techniques to reduce the time needed to carry out 3D resistivity surveys with a moderate number (25 to 100) of electrodes and the computing time required to interpret the data have been developed. The electrodes in a 3D survey are normally arranged in a square grid and the pole‐pole array is used to make the potential measurements. The number of measurements required can be reduced to about one‐third of the maximum possible number without seriously degrading the resolution of the resulting inversion model by making measurements along the horizontal, vertical and 45° diagonal rows of electrodes passing through the current electrode. The smoothness‐constrained least‐squares inversion method is used for the data interpretation. The computing time required by this technique can be greatly reduced by using a homogeneous half‐space as the starting model so that the Jacobian matrix of partial derivatives can be calculated analytically. A quasi‐Newton updating method is then used to estimate the partial derivatives for subsequent iterations. This inversion technique has been tested on synthetic and field data where a satisfactory model is obtained using a modest amount of computer time. On an 80486DX2/66 microcomputer, it takes about 20 minutes to invert the data from a 7 by 7 electrode survey grid. using the techniques described below, 3D resistivity surveys and data inversion can be carried out using commercially available field equipment and an inexpensive microcomputer.