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%.
REFERENCES
Avtomatizirovannaya obrabotka dannykh na Garmskom geofizicheskom poligone (Automated Data Processing at Garm Geophysical Research Area), Sidorin A.Ya., Ed., Moscow: Nauka, 1991.
Bobachev, A., Complex IPI-1D: One-dimensional profile interpretation of VES and VES-IP data. http://geoelectric.ru/ipi2win.htm. Cited June 26, 2020.
Bobachev, A.A., Deshcherevskii, A.V., and Sidorin, A.Ya., Regularization algorithms for increasing the stability of the solution to the inverse problem in precision monitoring of electrical resistivity using the VES method, Seism. Instrum., 2021а, vol. 57, no. 4, pp. 409–423. https://doi.org/10.3103/S0747923921040022
Bobachev, A.A., Deshcherevskii, A.V., and Sidorin, A.Ya., Features of instability in solving the inverse problem of vertical electrical sounding for precision monitoring, Seism. Instrum., 2021b, vol. 57, no. 3, pp. 302–320. https://doi.org/10.3103/S0747923921030038
Bobachev, A.A., Deshcherevskii, A.V., and Sidorin, A.Ya., Regularization of the solution of the inverse VES problem by the contrast stabilization method: Testing the algorithm on model data, Seism. Instrum., 2022, vol. 58, no. 5, pp. 581–600. https://doi.org/10.3103/S074792392205005X
Deshcherevskii, A.V., Filtering seasonal components of variations in geoelectric parameters at the Garm test area, Cand. Sci. (Phys.–Math.) Dissertation, Moscow: Inst. of Geosphere Dynamics, 1996.
Deshcherevskii, A.V., Fraktal’naya razmernost’, pokazatel’ Khersta i ugol naklona spektra vremennogo ryada (Fractal Dimension, Hurst Indicator, and Angle of Inclination of the Spectrum of Time Seires), Moscow: Ob”edinennyi Inst. Fiz. Zemli Ross. Akad. Nauk, 1997.
Deshcherevskii, A.V. and Sidorin, A.Ya., Experimental studies of seasonal variations in apparent resistivity with respect to the problems of seismology, Seism. Prib., 1999a, no. 32, pp. 62–75.
Deshcherevskii, A.V. and Sidorin, A.Ya., Nekotorye voprosy metodiki otsenki srednesezonnykh funktsii dlya geofizicheskikh dannykh (Some Issues of the Methodology of Assessing the Average-Seasonal Functions for Geophysical Data), Moscow: Ob”edinennyi Inst. Fiz. Zemli Ross. Akad. Nauk, 1999b.
Deshcherevskii, A.V. and Sidorin, A.Ya., Hidden periodic components and flicker noise in electrotelluric field, Izv., Phys. Solid Earth, 1999c, vol. 35, no. 4, pp. 306–316.
Deshcherevskii, A.V. and Sidorin, A.Ya., A two component model of geophysical processes: Seasonal variations and flicker noise, Dokl. Earth Sci., 2001, vol. 376, pp. 65–70.
Deshcherevskii, A.V. and Sidorin, A.Ya., Anomalous dependence of the seasonal variation amplitude of apparent electric resistivity on the spacing, Dokl. Earth Sci., 2003a, vol. 388, no. 1, pp. 110–113.
Deshcherevskii, A.V. and Sidorin, A.Ya., A flicker-noise problem in the study of cause-and-effect relationships between natural processes, Dokl. Earth Sci., 2003b, vol. 392, pp. 1030–1034.
Deshcherevskii, A.V. and Sidorin, A.Ya., Seasonal variations of the apparent resistivity as a function of the sounding depth, Izv., Phys. Solid Earth, 2004, vol. 40, no. 3, pp. 177–193.
Desherevskii, A.V. and Sidorin, A.Ya., 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, Seism. Instrum., 2020, vol. 56, no. 5, pp. 540–554. https://doi.org/10.3103/S0747923920050072
Deshcherevskii, A.V. and Zhuravlev, V.I., Testirovanie metodiki otsenki parametrov flikker-shuma (Testing of the Methodology for Estimating the Flicker-Noise Parameters), Moscow: Ob’’edinennyi Inst. Fiz. Zemli Ross. Akad. Nauk, 1996.
Deshcherevskii, A.V., Zhuravlev, V.I., Lukk, A.A., and Sidorin, A.Ya., Attributes of flicker-noise structure by temporal realizations of electrometric parameters, Izuchenie prirody variatsii geofizicheskikh polei (Studying the Nature of Variation of Geophysical Fields), Sadovskii, M.A. and Sidorin, A.Ya., Eds., Moscow: Ob’’edinennyi Inst. Fiz. Zemli Ross. Akad. Nauk, 1994, pp. 5–17.
Deshcherevskii, A.V., Zhuravlev, V.I., and Sidorin, A.Ya., The spectrum linearity features of non-annual components of the geophysical fields temporal series, Dokl. Akad. Nauk, 1996, vol. 346, no. 6, pp. 815–818.
Deshcherevskii, A.V., Zhuravlev, V.I., and Sidorin, A.Ya., Spectral-temporal features of seasonal variations in apparent resistivity, Izv., Phys. Solid Earth, 1997a, vol. 33, no. 3, pp. 217–226.
Deshcherevskii, A.V., Lukk, A.A., and Sidorin, A.Ya., Flicker noise structure in the time realizations of geophysical fields, Izv., Phys. Solid Earth, 1997b, vol. 33, no. 7, pp. 515–529.
Desherevskii, A.V., Zhuravlev, V.I., Nikolsky, A.N., and Sidorin, A.Ya., Technologies for analyzing geophysical time Series: Part 1. Software requirements, Seism. Instrum., 2017a, vol. 53, no. 1, pp. 46–59. https://doi.org/10.3103/S0747923917010030
Desherevskii, A.V., Zhuravlev, V.I., Nikolsky, A.N., Sidorin, A.Ya., Technology for analyzing geophysical time series: Part 2. WinABD—A software package for maintaining and analyzing geophysical monitoring data, Seism. In-strum., 2017b, vol. 53, no. 3, pp. 203–223. https://doi.org/10.3103/S0747923917030021
Desherevskii, A.V., Zhuravlev, V.I., Nikolsky, A.N., and Sidorin, A.Ya., Problems in analyzing time series with gaps and their solution with the WinABD software package, Izv., Atmos. Ocean. Phys., 2017c, vol. 53, no. 7, pp. 659–678. https://doi.org/10.1134/S0001433817070027
Desherevskii, A.V., Modin, I.N., and Sidorin, A.Ya., Method for constructing a model of a geoelectric section taking into account seasonal variations based on data from long-term vertical electric sounding monitoring in search of earthquake precursors, Seism. Instrum., 2018a, vol. 54, no. 4, pp. 424–436. https://doi.org/10.3103/S0747923918040023
Deshcherevskii, A.V., Modin, I.N., and Sidorin, A.Ya., Constructing the optimal model of the geoelectric section using vertical electrical sounding data: Case study of the central part of the Garm research area, Izv., Atmos. Ocean. Phys., 2018b, vol. 54, no. 10, pp. 1490–1511. https://doi.org/10.1134/S0001433818100031
Deshcherevskii, A.V., Modin, I.N., and Sidorin, A.Ya., Seasonal variations in specific resistivity in the upper layers of the Earth crust, Seism. Instrum., 2019, vol. 55, no. 3, pp. 300–312. https://doi.org/10.3103/S0747923919030058
Elektricheskoe zondirovanie geologicheskoi sredy. Chast’ 1 (Electric Sounding of Geological Medium. Part 1), Khmelevskoi, V.K. and Shevnin, V.A., Eds., 1988.
Elektricheskoe zondirovanie geologicheskoi sredy. Chast’ 2 (Electric Sounding of Geological Medium. Part 2), Khmelevskoi, V.K. and Shevnin, V.A., Eds., 1992.
Elektrorazvedka metodom soprotivlenii (Electric Sounding by Resistance Method, Khmelevskoi, V.K. and Shevnin, V.A., Eds., Moscow: Moscow Gos. Univ., 1994.
Garmskii geofizicheskii poligon (Garm Geophysical Research Area), Sidorin A.Ya., Eds., Moscow: Nauka, 1990.
Koefoed, O., Geosounding Principles: Resistivity Sounding Measurements, Amsterdam: Elsevier, 1979.
Lukk, A.A., Deshcherevskii, A.V., Sidorin, A.Ya., and Sidorin, I.A., Variatsii geofizicheskikh polei kak proyavlenie determinirovannogo khaosa vo fraktal’noi srede (Variations of Geophysical Fields as Appearance of Deterministic Chaos in Fractal Medium), Moscow: Ob”edinennyi Inst. Fiz. Zemli Ross. Akad. Nauk, 1996.
Ostashevskii, M.G. and Sidorin, A.Ya., Apparatura dlya dinamicheskoi geoelektriki (Equipment for Dynamical Geoelectrics), Moscow: Nauka, 1990.
Ostashevskii, M.G. and Sidorin, A.Ya., Multifunctional station of electric sounding and results of its use, Kompleksnye issledovaniya po prognozu zemletryasenii (Complex Studies on Forecasting of Earthquakes), Moscow: Nauka, 1991, pp. 182–199.
Sidorin, A.Ya., Variations in the electrical resistance of the upper layer of the Earth’s crust, Dokl. Akad. Nauk SSSR, 1984, vol. 278, no. 2, pp. 330–334.
Sidorin, A.Ya., Results of precision observations of apparent resistivity in Garm area, Trans. (Dokl.) USSR Acad. Sci. Earth Sci. Sect., 1986, vol. 290, no. 1, pp. 81–84.
Sidorin, A.Ya., Predvestniki zemletryasenii (Forerunners of Earthquakes), Moscow: Nauka, 1992.
Sidorin, A.Ya. and Ostashevskii, M.G., The method of precision electric sounding for earthquake precursors detection, Seism. Prib., 1996, nos. 25–26, pp. 189–211.
Yakubovskii, Yu.V., Elektrorazvedka. Uchebnik dlya vuzov (Electric Sounding: Textbook for Universities), Moscow: Nedra, 1980, 2nd ed.
Zaborovskii, A.I., Elektrorazvedka: Uchebnik dlya vuzov (Electric Sounding: Textbook for Universities), Moscow: Gostoptekhizdat, 1963.
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The study was carried out according to project FMWU-2022-0010 of the state task of the Schmidt Institute of Physics of the Earth, Russian Academy of Sciences.
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Bobachev, A.A., Deshcherevskii, A.V. & Sidorin, A.Y. Estimating the Error in Solving the Inverse VES Problem for Precision Investigations of Time Variations in a Geoelectric Section with a Strong Seasonal Effect. Seism. Instr. 58 (Suppl 2), S219–S233 (2022). https://doi.org/10.3103/S0747923922080059
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DOI: https://doi.org/10.3103/S0747923922080059