A globally convergent algorithm for the frequency sounding and Slichter-Langer-Tikhonov problem of electrical prospecting

TL;DR

This paper introduces a globally convergent algorithm designed to improve the accuracy and efficiency of solving coefficient inverse problems in electrical prospecting and frequency sounding, with enhanced spatial and contrast resolution.

Contribution

It develops a new iterative refinement method based on a previous globally convergent approach, significantly improving resolution and computational effectiveness in inverse problems.

Findings

Enhanced spatial and contrast resolution demonstrated

Algorithm effective in electromagnetic and acoustic frequency sounding

Numerical experiments confirm improved accuracy

Abstract

The paper presents a globally convergent algorithm for solving coefficient inverse problems. Being rooted in the globally convergent numerical method (SIAM J. Sci. Comput., 31, No.1 (2008), pp. 478-509) for solving multidimensional coefficient inverse problems, it has two distinctive features: the new iterative and refinement procedures. These novelties enhance, sometimes significantly, both the spatial and contrast resolutions. The computational effectiveness of the proposed technique is demonstrated in numerical experiments with two applied coefficient inverse problems: electromagnetic or acoustic frequency sounding and electrical prospecting of layered media. The Slichter-Langer-Tikhonov formulation is exploited as a mathematical model of the latter.