Modeling of a geoelectric section based on a set of feasible solutions of the inverse problem of vertical electrical sounding

Abstract

Introduction: the article presents the theoretical foundations for constructing geoelectric models of subhorizontally layered media based on vertical electrical sounding (VES) data using serial solutions of the inverse problem. For this purpose, additive inversion technologies are used, based on the guaranteed approach of L. V. Kantorovich, which were previously proposed for solving inverse problems of gravity and magnetic exploration. Their distinctive feature is fundamentally new mathematical forms of presenting the results of quantitative interpretation in the form of a certain set of geologically meaningful invariants on a set of admissible solutions of the inverse problem.

Methodology: for a set of solutions of the inverse problem with a power of at least 100, the discrete values ​​of a function dependent on spatial coordinates are calculated, characterizing the probability of belonging of individual fragments of the geological space to one of the studied geoelectric boundaries. An algorithm has been developed and implemented in the Python programming language, which sequentially performs the following operations: formation of a set of admissible solutions of the inverse VES problem using a genetic algorithm («DEAP» library); division of the geological space into a number of sub-regions consisting of elementary rectangular cells, with an assessment of the probability of intersection of each of them by the sought boundary of the layer with a given value of specific electrical resistance; construction of the most statistically reliable boundaries of the modeled geoelectric horizons; visualization of the obtained interpretation results (Matplotlib library). It has been established that smoothing of the assumed boundaries leads to improvement of interpretation constructions and can have a certain physical and geological justification.

Results and discussion: the algorithm capabilities were assessed using a synthetic example and practical materials on the VES profile located near the village of Oktyabrsky in the Perm region, which includes 28 sounding points with a power line AB spacing of up to 320 m. In general, the geoelectric boundaries obtained using the developed algorithm are consistent with the specified model and the inversion results with the ZOND program. However, the probabilistic representation of the location of the geoelectric boundaries allows for a comparative assessment of the resolution of the VES method vertically and laterally.

Conclusion: the presentation of the VES inversion results as a set of admissible solutions to the inverse problem and its spatial-statistical analysis and visualization of the results increases the reliability of the geological results of electrical exploration.