GEOPHYSICAL RESEARCH, 2016, vol.17, no.3, pp.17-31. DOI: 10.21455/gr2016.3-2
UDC 550.831
Abstract References Full text (in Russian)
MATCHING CRITERIA OF ACCEPTABLE SOLUTIONS FOR GRAVITY ORE TYPE INVERSE PROBLEM
A.S. Dolgal(1,2), P.I. Balk(3), P.N. Novikova(1,2), A.V. Michurin(1)
(1) Mining Institute, Ural Branch of the Russian Academy of Sciences, Perm, Russia
(2) Perm State University, Perm, Russia
(3) Berlin, Germany
Abstract. A new approach to the characterization of the gravity anomalies sources is presented. It is based on the construction of the representative set of acceptable solutions of the gravity inverse problem. The “best” solution is chosen using the formal criteria, i.e. the minimax criterion and the maximum a posteriori probability criterion.
The proposed definitions of hiding, lost and false information can be effectively applied to the quantitative interpretation of geophysical anomalies. The minimax criterion minimizes the loss of hidden information and provides an estimation of the proximity of the solution obtained to the true distribution of anomalous masses. An effective tool for constructing approximate solutions of the inverse problem is the fitting method that uses finite element representation of the studied density inhomogeneities.
The results of computational experiments indicate the advantages of this approach as compared to the choice of a single optimal solution of the inverse problem corresponding to the minimum residual of observational and modeling fields. The practical problem is solved using the data on the medium-scale gravity survey in the Berezovsky anomalous zone (Perm region).
The application of the approach proposed to the solution of the gravity inverse problem in prospecting and exploration of ore deposits can provide a reliable choice of the most promising gravity anomalies for future drilling operations.
Keywords: gravity prospecting, interpretation, inverse problem, solution set, criterion, information, geological object.
References
Balk P.I. O nadezhnosti rezul'tatov kolichestvennoj interpretacii gravitacionnyh anomalij (On the reliability of the quantitative interpretation results of gravity anomalies), Izv. AN SSSR. Physics of the Solid Earth, no.6, 1980, pp. 43–57.
Balk P.I. and Dolgal A.S. Three-Dimensional Assembly Technologies for the Interpretation of Gravimetric Data, Doklady Akademii nauk, vol. 427, No.3, 2009, pp. 380-383.
Balk P.I. and Dolgal A.S. Deterministic Approach to the Problem of Reliability in Interpretation Results of Gravimetric Data, DAN, vol. 431, no.1, 2010, pp. 334–338.
Balk P.I. and Dolgal A.S. Inverse Problems of Gravimetry as Retrieval of Reliable Information under Uncertainty, Izvestiya, Physics of the Solid Earth, 2012, vol. 48, no. 5, pp. 441–455
Balk P. and Dolgal A. Konechnojelementnye tehnologii modelirovanija v gravirazvedke. Montazhnyj metod i garantirovannyj podhod pri reshenii obratnyh zadach (Finite element modeling technology in gravity. The fitting method and a guaranteed approach for the inverse problems solution), LAP LAMBERT Academic Publishing, Saarbrucken, 2013.
Balk P.I. and Dolgal A.S. A Minimax Approach to the Solution of Inverse Problems of Gravity and Magnetic Prospecting, Doklady Earth Sciences, 2015, Vol. 462, Part 2, pp. 648–652.
Balk P.I. and Dolgal A.S. Deterministic Models of Interpretation for Optimizing the Locations and Depths of the Boreholes for Verifying the Anomalies in Gravity, Izvestiya, Physics of the Solid Earth, 2015, vol. 51, no. 1, pp. 95–107
P.I. Balk, A.S. Dolgal’, T.V. Balk, and L.A.Christenko. Finite-element technologies of interpretation of gravity data. Guaranteed approach, Geophysical research, vol. 13, no. 4, 2012, pp.19–33.
Bulah E.G. Prjamye i obratnye zadachi gravimetrii i magnitometrii (Direct and inverse problems of gravimetry and magnetometry), Kiev: Naukova dumka, 2010.
Dolgal A.S. and Sharhimullin A.F. Povyshenie tochnosti interpretacii monogenichnyh gravitacionnyh anomalij (Accuracy improving of the interpretation of monogenic gravity anomalies), Geoinformatika, No.4, 2011, pp. 49–56.
Gol'dshmidt V.I. Optimizacija processa kolichestvennoj interpretacii dannyh gravirazvedki (Optimization of quantitative gravity data interpretation ), Moscow: Nedra,1984.
Grausman A.L., Bakuev O.V., and Hafizov S.F. K voprosu postroenija matematicheskih modelej geologicheskih ob’ektov (The problem of constructing mathematical models of geological objects), Oil and gas geology, no.4, 2000, pp. 58–63.
Kobrunov A.I. Matematicheskie osnovy teorii interpretacii geofizicheskih dannyh: ucheb. posobie (Mathematical foundations of the interpretation theory of geophysical data: a tutorial), Moscow: CentrLitNefteGaz, 2008.
Kojfman L. I. Opyt ob’emnogo plotnostnogo modelirovanija Berezovskogo gravitacionnogo maksimuma Predural'ja (Experience of density modeling of Berezovsky gravity maximum, Preduralje), Regional'naja, razvedochnaja i promyslovaja geofizika, vol. 16, 1982, pp. 1–9.
Kosygin Ju.A. Osnovy tektoniki (Foundations tectonics), Moscow: Nedra, 1974.
Stratanovich R.L. Teorija informatsii (Information theory), Moscow: Sovetskoe. Radio,1975.
Strahov V.N. Razrushenie gospodstvujushhego stereotipa myshlenija – glavnejshaja zadacha v razvitii teorii i praktiki interpretacii potencial'nyh polej (gravitacionnyh i magnitnyh anomalij) v nachale XXI veka. (The destruction of the prevailing stereotype thinking - the main task in the development of the theory and practice of potential fields interpretation (gravity and magnetic anomalies) at the beginning of the XXI century), M.: OIFZ RAN, 2000, 44 p.
Strahov V.N. and Lapina M.I. Montazhnyj metod reshenija obratnoj zadachi gravimetrii (Fitting technique for solving the gravimetry inverse problem), Dokl. AN SSSR, vol. 227, no.2, 1976, pp. 344–347.