Rapid least‐squares inversion of apparent resistivity pseudosections by a quasi‐Newton method¹

TLDR

The method employs a smoothness‑constrained least‑squares inversion that starts from a homogeneous earth model and then uses a quasi‑Newton approach to estimate partial derivatives, cutting computation time and memory usage by factors of eight and twelve relative to conventional least‑squares. Tests on synthetic and field data demonstrate that the technique is insensitive to random noise, converges rapidly, and can invert a single dataset in roughly one minute on an 80486DX microcomputer.

Abstract

Abstract A fast inversion technique for the interpretation of data from resistivity tomography surveys has been developed for operation on a microcomputer. This technique is based on the smoothness‐constrained least‐squares method and it produces a two‐dimensional subsurface model from the apparent resistivity pseudosection. In the first iteration, a homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically. For subsequent iterations, a quasi‐Newton method is used to estimate the partial derivatives which reduces the computer time and memory space required by about eight and twelve times, respectively, compared to the conventional least‐squares method. Tests with a variety of computer models and data from field surveys show that this technique is insensitive to random noise and converges rapidly. This technique takes about one minute to invert a single data set on an 80486DX microcomputer.