Precision Solution of the VES Inverse Problem for Experimental Data of Long-Term Monitoring of the Earth’s Crust

Abstract

Earlier, the authors carried out a unique experiment on long-term continuous precision monitoring of crustal resistivity variations in a highly seismic region. The result of this experiment can be considered a special type of VES profile, in which, instead of a linear coordinate, the sounding date changes from picket to picket. When processing precision monitoring data, it is necessary to solve the inverse VES problem with the highest possible accuracy. Standard programs for inversion of VES curves do not allow this, and even with very small fitting residuals, the actual error in reconstructing the resistivity can be huge due to equivalence effects. The authors have previously developed a special method for regularizing the residual functional, which multiply increases the accuracy in solving the inverse problem for the considered type of resistivity section, and a method for obtaining realistic, rather than underestimated estimates of the solution error. To do this, a package of synthetic resistivity profiles is formed that imitates a real section, the VES direct problem is solved, and time series of apparent resistivity are constructed, on which noise similar to real noise is superimposed. After that, the VES inverse problem is solved and the errors in reconstructing the model resistivity curves are analyzed. Such calculations were carried out both for the total signals and their components, obtained as a result of decomposition of the apparent resistivity series into physically determined components. The developed approach makes it possible to solve the inverse VES problem with heretofore unattainable accuracy. We emphasize that a reliable estimate of the solution errors is provided not by the convergence criteria of the inversion algorithm (they are almost always overly optimistic), but by direct calculations of the direct and inverse problems for synthetic profiles similar to real signals. In the present article, the profile of the experimental VES curves obtained in the course of this experiment is inverted. Series of resistivity variations are calculated in four layers of a geoelectric section with a duration of more than 12 years. It has been established that the upper layer of the section is characterized by trend and seasonal changes in resistivity with a large amplitude. Significant anomalous seasonal effects were found in the second layer of the section. For the third layer, the presence of small-amplitude seasonal effects was established, while there are no significant resistivity trends. Variations in the resistivity of the fourth layer are less reliably estimated; to detect the effects of external factors on electrical resistivity, it is necessary to use signal stacking methods.