## Finite-element technologies of interpretation of gravity data. Guaranteed approach

Category: 13-4

*UDC 550.831*

P.I. Balk^{(1)}, A.S. Dolgal’^{(2)}, T.V. Balk^{(1)}, L.A.Christenko^{(2)}

^{(1) }Berlin*, Germany*

^{(2)}* Mining Institute Ural Branch Russian Academy of Sciences, Perm, Russia*

**Abstract**

The main disadvantages of traditional forms for the representation of results of interpretation of gravity anomalies in terms of single allowable (optimal) solution of inverse problem are emphasized. Authors suggest that the most total extraction of reliable information from observed gravity data is impossible without the construction and purposeful analysis of some representational subset of possible variants of interpretation. We entrust to guaranteed approach the solution of this problem. Guaranteed approach was very useful in different areas of applied mathematics but it hasn’t high profile in geophysical research.

The most general description of the guaranteed approach of inverse problem solution as compared with already published specifications is given here. Authors also give the method of structuring of geological medium as the development this conception. Assembly algorithms are offered as main tools for realization of guaranteed approach. The efficacy of complex “guaranteed approach – assembly method” is illustrated on practical examples.

**Keywords: **gravitational exploration, guaranteed approach, assembly method, modeling, algorithm, geological objects.

**References**

Aizerman, M.A. and Malishevsky, A.V., Some aspects of the general rational choice theory, *Avtomatika i telemekhanika*, 1981, no. 2, pp. 65–83.

Balk, P.I. and Dolgal, A.S., Deterministic approach to the problem of reliability in interpretation results of gravimetric data, *Dokl. Earth Sci*., 2010, vol. 431, no. 1, pp. 334–338.

Balk, P.I., Dolgal, A.S., Fusing the advantages of the functional-analytical and probabilistic-statistical approach for combined algorithms of solving inverse problems of gravimetry and magnetometry, *Geoinformatika*, 2011, no. 1, pp. 33–42.

Balk, P.I., Dolgal’, A.S., Balk, T.V., and Christenko, L.A., Finite-element technologies of interpretation of gravity data. Assembly method, *Geophysical Research Journal*, 2012, no. 3, pp. 18–34.

Balk, P.I., Mathematical formalism and unclaimed ideas in the theory of interpretation of potential fields, *Geofizika*, 2002, no. 2, pp. 41–46.

Balk, P.I., On fundamental shortcomings inherent in conventional representation of the mathematical interpretation results for the potential fields, *Geofiz. Zh*., 2004, vol. 26, no. 5, pp. 124–132.

Balk, P.I., On Reliability of the Results of Quantitative Interpretation of Gravity Anomalies, Izv. Akad. Nauk SSSR, *Fiz. Zemli*, 1980, no. 6, pp. 65–83.

Balk, P.I., The conflict of geophysical and mathematical interests as a main source of contradictions in the modern theory of interpretation of potential fields, *Geofiz. Zh*., 2000, vol. 22, no. 4, pp. 3–20.

Balk, P.I., The Use of A Priori Information on the Topology of the Field Sources in the Solution of the Inverse Problem of Gravimetry, *Dokl. Akad. Nauk*, 1989, vol 309, no. 5, pp. 1082–1084.

Dolgal, A.S. and Sharhimullin, A.F., Determining parameters for individual geo-density inhomogeneities using the localization function, *Geodinamika, Glubinnoye striyeniye, Teplovoe pole Zemli, Interpretatsiya geofizicheskih poley* (Geodynamics, Deep structure, Earth’s thermal field, Interpretation of geophysical fields), 6th Yu.P. Bulashevich scientific readings, 2011, pp. 121–124.

Dolgal, A.S., Solving the inverse problem of gravity survey for cupronickel ore prospecting, *Geofizicheskiy zhurnal*, 1993, no. 6, pp. 83–88.

Kaufman, A. A. and Hansen, R., *Principles of the gravitational method*, Russian transl., Tver: AIS, 2011, 376 p.

Rokityanskiy, I.I., Modeling in geo-electrics, 1. Ambiguity, *Geofizicheskiy zhurnal*, 1985, vol. 7, no. 1, pp. 15–24.

Tsypkin, Ya.Z., Optimality in problems and approaches of the modern control theory, *Vestnik AN SSSR*, 1982, no. 9, pp. 116–121.

Vasin, V.V. and Ageev, A.L., *Nekorrektnye zadachi s apriornoy informatsiey (Ill-defined problems with a priori information)*, Ekaterinburg, 1993, 262 p.

Vasin, V.V., Perestoronina, G.Ya., Prutkin, I.L., and Timerkhanova, L.Yu., Solving 3-dimensional inverse problems of gravimetry and magnetometry for a 3-layer medium, *Matematicheskoye modelirovaniye*, 2003, vol. 15, no. 2, pp. 69–76.