DOI: https://doi.org/10.24028/gzh.0203-3100.v41i4.2019.177364

### Assembly methods of solving inverse problems as an integral element of additive technologies for interpretations of gravity anomalies

#### Abstract

In recent years, the theory of interpretation of gravitational anomalies has been replenished with fundamentally different from familiar, additive technologies for extracting information about the studied geo-density medium. The concept of «additivity» implies a summation in the results of the interpretation of information carried by each of the found admissible solutions to the inverse problem. At the same time, the results of the interpretation themselves are not expressed, as usual, in terms of one of these solutions. In the ore inverse problem of gravity exploration, an effective working tool for such technologies has become the assembly algorithms for constructing valid interpretation options. These algorithms have universal capabilities in the matter of accounting for a priori data and do not have high requirements for the formation of the initial approximation of the field source model, which is crucial from the point of view of their application in additive technologies. At the same time, all hitherto known modifications of the mounting method were designed for formulating inverse problems in which there are bodies with effective densities of the same sign. Due to the integration of the method with the procedure for separating gravitational fields, the problem of different sign densities was solved.

The separation of the observed field into two components, due to the influence of sources with positive and negative effective density, is carried out by the approximation method. To approximate the discrete values of gravity, the sets of elementary sources under each point of observation are used. The masses of sources are determined by solving a system of linear algebraic equations. The sources are successively immersed at different depths corresponding to different variants of the selection of the interpreted field components.

The article evaluates the current state and prospects for the further development of additive technologies for interpreting gravitational anomalies based on the methods that implement the concept of the mounting approach by V. N. Strakhov. Model of model examples are given illustrating the capabilities of the presented algorithms.

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Aronov, V. I. (1990). Methods for mapping geological and geophysical features and geometrization of oil and gas deposits on a computer. Moscow: Nedra, 301 p. (in Russian).

Balk, P. I. (1980). On the reliability of the results of quantitative interpretation of gravitational anomalies. Izvestia AN SSSR. Fizika Zemli, (6), 65—83 (in Russian).

Balk, P. I. (1989). Using a priori information on topological features of field sources in solving the inverse problem of gravimetry. Doklady AN SSSR, 309(5), 1082—1084 (in Russian).

Balk, P. I. (1993) The use of a priori information about the topological features of field sources when solving the inverse problem of gravimetry in the framework of the installation approach. Fizika Zemli, (5.), 59—71 (in Russian).

Balk, P. I., & Balk, S. P. (2000). On the solution of a nonlinear inverse problem of gravimetry using finite element representations of field sources. Doklady RAN, 371(2), 231—234 (in Russian).

Balk, P. I., & Balk, T. V. (1996). The combined inverse problem of gravity and magnetometry. Fizika Zemli, (2), 16—30 (in Russian).

Balk, P. I., & Balk, T. V. (1995). The structural-ore inverse problem of gravimetry. Fizika Zemli, (6), 32—41 (in Russian).

Balk, P. I., & Dolgal, A. S. (2016). Additive technologies for quantitative interpretation of gravitational anomalies. Geofizika, (1), 43—47 (in Russian).

Balk, P. I., & Dolgal, A. S. (2010). Deterministic approach to the problem of reliability of the results of interpretation of gravimetric data. Doklady RAN, 431(1), 102—106 (in Russian).

Balk, P. I., & Dolgal, A. S. (2015). Deterministic interpretation models for optimizing the location and depth of wells during the validation of gravity anomalies. Fizika Zemli, (1), 98—111 (in Russian).

Balk, P. I., & Dolgal, A. S. (2017). New possibilities of increasing the informativeness of quantitative interpretation of gravity anomalies. Doklady RAN, 476(4), 461—465 (in Russian).

Balk, P. I., & Dolgal, A. S.(2012). Inverse problems of gravimetry as the task of extracting reliable information in conditions of uncertainty. Fizika Zemli, (5), 85—101 (in Russian).

Balk, P. I., & Dolgal, A. S. (2009). Three-dimensional assembly technologies for interpreting gravimetric data. Doklady RAN, 427(3, 380—383 (in Russian).

Balk, P. I., Dolgal, A. S., & Balk, T. V. (1993). Grid models of the density medium and experience of their use in the tracing of differentiated intrusions according to gravity survey data. Geologiya i gefizika, (5), 127—134 (in Russian).

Balk, P. I., Dolgal, A. S., & Khristenko, L. A. (2011). Synthesis of linear and non-linear formulations of the inverse problem in gravity and magnetic prospecting. Geofizicheskiy zhurnal, 33(5), 51—65. https://doi.org/10.24028/gzh.0203-3100.v33i5.2011.116853 (in Russian).

Balk, T. V., & Shefer, U. (1992). Installation method for solving the combined inverse problem of gravity and magnetometry. Doklady RAN, 327(1), 79—83 (in Russian).

Balk, P. I., Shefer, U., & Balk, T. V. (1994). The structure of the minimized functional in the mounting algorithms for finding feasible solutions to the inverse problem of gravimetry. Fizika Zemli, (7), 98—106 (in Russian).

Blokh, Yu. I. (1998). Quantitative interpretation of gravitational and magnetic anomalies. Moscow: Publ. of the Moscow State Geological Survey Academy, 89 p. (in Russian).

Bloch, Yu. I. (2004). The problem of the adequacy of interpretational models in gravity and magnetic prospecting. Geofizicheskiy vestnik, (6), 10—15 (in Russian).

Bulah, E. G. (2010). Direct and inverse problems of gravimetry and magnetometry. Kiev: Naukova Dumka, 464 p. (in Russian).

Bulakh, E. G., & Korchagin, I. N. (1978). On the selection of anomalous sources of the gravitational field by the method of successive increments of the model. Doklady AN USSR. Ser. B, (12), 3—6 (in Russian).

Vasin, V. V., & Ageev, A. L. (1993). Incorrect problems with a priori information. Moscow: Nauka, 262 p. (in Russian).

Vakhromeev, G. S., & Davydenko, A. Yu. (1987). Modeling in exploration geophysics. Moscow: Nedra, 192 p. (in Russian).

Glaznev, V. N., Muravina, O. M., Voronova, T. A., & Kholin, V. M. (2014). Estimation of the thickness of the gravitational crust of the Voronezh crystalline massif. Vestnik Voronezhskogo gosudarstvennogo universiteta. Ser. Geologiya, (4), 78—84 (in Russian).

Goldshmidt, V. I. (1984). Optimization of the process of quantitative interpretation of gravity data. Moscow: Nedra, 1984, 185 p. (in Russian).

Dolgal, A. S., & Michurin, A. V. (2010). New modification of the mounting method for solving the nonlinear inverse problem of gravimetry. Uralskiy geofizicheskiy vestnik, (2), 34—40 (in Russsian).

Dolgal, A. S., & Sharkhimullin, A. F. (2011). Improving the Accuracy of the Interpretation of Monogenic Gravitational Anomalies. Geoinformatika, (4), 49—56 (in Russian).

Zhdanov, M. S. (2007). The theory of inverse problems and regularization in geophysics. Moscow: Nauchnyy Mir, 712 p. (in Russian).

Zavoysky, V. N., & Neiszhal, Yu. E. (1979). A decomposition-iterative method for solving the inverse problem of magnetic prospecting. Geofizicheskiy zhurnal, 1(12), 46—52 (in Russian).

Kobrunov, A. I. (2008). Mathematical foundations of the theory of interpretation of geophysical data: study guide. Moscow: CentrLitNefteGaz, 288 p. (in Russian).

Martyshko, P. S., Ladovskiy, I. V., Fedorova, N. V., Byzov, D. D., & Tsidaev, A. G. (2016). Theory and Methods of Complex Interpretation of Geophysical Data. Yekaterinburg: Publ. House of the Ural Branch of the Russian Academy of Sciences, 94 p. (in Russian).

Starostenko, V. I. (1978). Stable numerical methods in gravimetry problems. Kiev: Naukova Dumka, 228 p. (in Russsian).

Strakhov, V. N., & Lapina, M. I. (1976). Installation method for solving the inverse problem of gravimetry. Doklady AN SSSR, 227(2), 344—347 (in Russian).

Tikhonov, A. N. (1999). Mathematical geophysics. Moscow: Publ. House of the United Institute of Physics of the Earth of the Russian Academy of Sciences, 476 p. (in Russian).

Tikhonov, A. N., & Arsenin, V. Ya. (1979). Methods for solving ill-posed inverse problems. Moscow: Nauka, 284 p. (in Russian).

Chernousko, F. L. (1988). Estimation of the phase state of dynamic systems. The method of ellipsoids. Moscow: Nauka, 320 p. (in Russsian).

Shalaev, S. V. (1972). Geological interpretation of geophysical anomalies using linear programming. Leningrad: Nedra, 142 p. (in Russsian).

Yagola, A. G., Van Yanfei, Stepanova, I. E., & Titarenko, V. N. (2013). Inverse problems and methods for their solution. Applications to geophysics. Moscow: Laboratoriya znaniy, 216 p. (in Russian).

Schäfer, U. (1990). Die Lösung einer inversen Aufgabe für gravimetrische und magnetische Anomalien mittels der Montagmethode. Potsdam: Zentralinstitut für Physik der Erde, 137 p.

Schäfer, U., & Balk, P. (1993). The Inversion of Potential Field Anomalies by the Assembling Method. Proc. IAG. Symp. № 112. Berlin-Heidelberg, 237—241.

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