Optimization of the Algorithm for Calculating the Electrical Resistivity of Temporal Variations Using Ves Monitoring Data to Increase the Accuracy and Reliability of the Results

Abstract

The authors are developing a method for precision monitoring of the specific apparent electrical resistivities of individual layers of the Earth’s crust. This task is extremely difficult, since the apparent resistivities are actually observed, then it is necessary to solve an entire set of complex problems for their processing: noise removal, isolating the physically determined components, and, most importantly, solving the inverse problem of reconstructing the resistivity from the measured apparent resistivity values. The aim of the work is to improve the methodological foundations of precision monitoring to increase its accuracy. The data processing algorithm is divided into a sequence of elementary operations: data aggregation, time series smoothing, noise filtering, estimation of seasonal (exogenic) effects, and solving the inverse vertical electrical sounding (VES) problem. The solution to the inverse problem is an essentially nonlinear operation, and all others become nonlinear if there are data gaps in the signal, which is virtually inevitable during long-term observations. Therefore, the final result can significantly depend not only on the settings of individual operations (width and/or type of weight function of the aggregation/smoothing window, etc.), but also on the order in which these operations are performed. The study employs a numerical experiment with real data to estimate how strongly the sequence of the above operations affects the result. The calculations used unique long-term precision monitoring data by the VES method. It is shown that the smoothing operator can be applied to both the apparent and specific resistivities, which barely affects the result. Conversely, the order of seasonal filtering and solution of the inverse problem is important. It is shown that error estimates for calculating the specific resistivity based on the internal convergence of the algorithm for solving the inverse problem are unacceptable, since they differ from the real errors by two orders of magnitude. For reliable monitoring of temporary variations in resistivity in the deep layers of the studied structure under, it is necessary to increase the stability of the selection of resistivities according to a given VES curve, as well as to take other measures for optimizing the algorithm.