Estimating the Error in Solving the Inverse VES Problem for Precision Investigations of Time Variations in a Geoelectric Section with a Strong Seasonal Effect

Abstract

As part of studies on the search for earthquake precursors, the authors have conducted an experiment on long-term precision monitoring of variations in the resistivity of the Earth’s crust in a highly seismic region of Tajikistan. The primary data 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. VES curve inversion programs commonly used in electric exploration do not allow this. The authors have previously developed a special method for regularizing the residual functional, which suppresses the effect of resistivity buildup, due to which the error in reconstructing the resistivity of rocks for profiles with a strong seasonal variation in resistivity is reduced by an order of magnitude. However, in some cases, the regularized algorithm strongly biases estimation of the amplitude of the seasonal resistivity variation in the lower layers of the section. In this paper, the operation of the proposed algorithm is tested in detail for nine model profiles simulating a real geoelectric section. The considered profiles differed in the characteristics of the seasonal variability of resistivity in the lower layers of the section (the phase and amplitude of seasonal effects varied). It is shown that resistivity buildup is effectively suppressed in all cases. For each model profile, the error in solving the inverse problem is estimated. The effect of a biased estimate of the amplitude of seasonal variation is studied. It is shown that in most cases, analysis of the solution makes it possible to reveal the presence of such distortions and qualitatively assess their character. It is also shown that for profile options supposedly closest to the experimental profile, the estimates have minimal bias. For all profiles, the ratio of the average and maximum errors in calculating the resistivity in different layers to the residual in the solution to the inverse problem was evaluated. This makes it possible to evaluate the actual error of the reconstructed resistivity values knowing only the fitting residual. The paper also studied the possible effect of increasing the accuracy in solving the inverse problem in the case of preliminary decomposition of the apparent resistivity curves into seasonal and flicker noise components. It is shown that for small fitting residuals, the results change insignificantly. According to the results obtained, the error in reconstructing the aperiodic (flicker noise) component of resistivity variations in the lower layers of the considered section can be decreased to 0.4%. The accuracy in reconstructing the seasonal component of resistivity variations depends on the amplitude and phase of seasonal effects in the model profile. For the considered profiles, the error varies from 1 to 2%.