GEOPHYSICAL RESEARCH, 2018, vol. 19, no. 4, pp. 16-30. https://doi.org/10.21455/gr2018.4-2
UDC 550.83.016
Abstract References Full text (in Russian)
SOURCEWISE APPROXIMATION OF GEOPOTENTIAL FIELDS. FROM THEORY TO PRACTICE
A.V. Pugin
Mining Institute, Ural Branch of Russian Academy of Sciences, Perm, Russia
Abstract. Theoretical definitions contain idealizations and by that differ from practical ones. Various algorithms of sourcewise approximation produce different distributions of equivalent sources. They all are theoretically equivalent but practically result to odds in mathematical transformations of geopotential fields. The article shows a practical definition has finite bounds of an integration domain whilst a theoretical one has no limits. This leads to the fact: different approximations have diverse complete surface integrals of field which is not possible the same as for real anomalous sources. The problem has no general solution but cannot be ignored. Interpreter could choose most useful algorithm to solve the geological problem if he has a number of them. The approximation algorithm has distinct advantages if it is able to analyze the structure of input data. This increases its chance to be selected for applying.
Keywords: sourcewise approximation, geopotential field, problem definition, algorithm, equivalent source, transformation.
References
Aleksidze M.A. Priblizhyonnye metody resheniya pryamyh i obratnyh zadach gravimetrii (Approximate Methods for Solving of Direct and Inverse Problems of Gravimetry). Moscow: Nauka, 1987. 336 p.
Aronov V.I. Metody postroeniya kart geologo-geofizicheskih priznakov i geometrizaciya zalezhei nefti i gaza na EVM (Methods of Mapping Geological-Geophysical Attributes and Geometrization of Oil-and-Gas Deposits Using ECM). Moscow: Nedra, 1990. 301 p.
Aronov V.I. O vychislenii transformant i redukcii anomalii sily tyazhesti na vneshnyuyu ploskost v gornom raione (About Calculation of Transformants and Reductions of Gravity Anomalies onto Exterior Plane in Mountains Area). Izv. Phys. Solid Earth, 1967, no. 2, pp. 54-59.
Balk P.I., Dolgal A.S., Pugin A.V., Michurin A.V., Simanov A.A., Sharkhimullin A.F. Effective algorithms for sourcewise approximation of geopotential fields. Izv. Phys. Solid Earth, 2016, vol. 52, no. 6, pp. 896-911.
Bjerhammar, A. On Gravity. Royal Inst. Of Techn., Division of Geodesy, Stockholm, 1968, 129 p.
Bulakh E.G., Lapina E.P. K voprosu o postroenii analiticheskoi modeli vneshnego magnitnogo polya (To the Problem of Plotting Analytical Model of External Magnetic Field). Geophysical Journal, 2008, vol. 30, no. 2, pp. 42-50.
Gordin V.M., Mikhailov B.O., Mikhailov V.O. Fizicheskie aspekty approksimacii i filtracii anomalnyh polei (Physical Aspects of Approximation and Filtration of Anomalous Fields). Izv. Phys. Solid Earth, 1980, no. 1, pp. 78-93.
Instrukciya po gravirazvedke. (Instructions for Gravimetrical Prospecting). Moscow: Nedra, 1980. 80 p.
Mikov D.S. Integralnye metody interpretacii gravitacionnyh i magnitnyh anomalii (Integral Methods of Interpretation of Gravity and Magnetic Anomalies). Tomsk State University: Tomsk, 1975. 94 p.
Molodensky M.S. Osnovnye voprosy geodezicheskoi gravimetrii (Main Issues of Geodetic Gravimetry), in Trudy Centralnogo nauchno-issledovatelskogo instituta geodezii, aehrosemki i kartografii (Proceedings of Central Scientific and Research Institute of Geodesy, Aerosurvey and Cartography). Iss. 42. 1945. 110 p.
Shvank O.A., Lustickh E.N. Interpretaciya gravitacionnyh nablyudenii (Interpretation of Gravity Measurements). Moscow: State Sci.-Tech. Publisher of Oil and Mining-Energy Literature, 1947, 400 p.
Tikhotsky S.A., Shur D.U. Primenenie mnogourovnevyh istokoobraznyh approksimacii k zadacham magnitnoi kartografii i analiza magnitnogo polya (Applying of Multilevel Soursewise Approximation to Problems of Magnetic Cartography and Magnetic Data Analyses), in Materialy 28-i sessii Mezhdunarodnogo seminara im. D.G.Uspenskogo (Proceedings of 28 session of International Uspensky Conference), Moskow: The Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences, 2001, pp. 130-131.