The application of an integral-equation-based automatic inversion algorithm for interpretation of vertical electrical sounding data.

This study presents the implementation of an automatic inversion algorithm designed for the analysis of direct current (DC) vertical electrical sounding (VES) data, utilizing a one-dimensional (1D) linear integral equation approach. The forward modelling problem was derived from a three-dimensional (3D) integral equation, which was elegantly simplified through numerical integration across horizontal dimensions. The inverse problem was tackled through a minimum length solution that integrated a depth-weighting function and optimized the regularization parameter based on the maximum value of the forward operator. The efficacy of this algorithm was validated by inverting synthetic datasets as well as by its application to real field data. The results highlighted the limitations inherent in 1D inversion, particularly in cases where a layered Earth is significantly violated, as evidenced by comparisons with two-dimensional inversion models. In contrast, in contexts characterized by predominantly layered subsurface structures, the algorithm successfully produced accurate representations of the subsurface models. These findings underscore the method's efficacy in various geological environments, offering a robust tool for geophysical exploration.