Abstract
A specialized class of fast algorithms for sourcewise approximation of potential fields, which is intended for mass use in the applications associated with handling large and extralarge measurement data, is developed. Pursuing the objective of the work, we included two informal requirements in the set of the criteria to be met by our algorithms: they should have a sufficiently simple mathematical structure which is transparent for the geophysicist and they should be quite easy to program. Both these requirements are dictated by the present-day practice existing in geology, when the absence of the centralized provision of program products by the geological organizations makes the interpreter create the necessary software themselves. Among the distinguishing features of the three suggested algorithms is the fact that the dimensionality of the approximating construction is not specified a priori but is determined a posteriori. Due to this, it turned out to be helpful to combine one of these algorithms with the fast wavelet transform, which enables the dimension of the future sourcewise approximation and the amount of computing resources required for the implementation of the main algorithm to be estimated a priori. The examples of the practical application of these technologies are presented. The promising paths for the future development of the algorithms for sourcewise approximation of the potential fields are outlined.
Similar content being viewed by others
References
Aronov, V.I., On reducing the gravity anomaly in a mountainous area, Geofiz. Razved., 1963, no. 14, pp. 80–91.
Aronov, V.I. and Gordin, V.M., On interpolating the derivatives of gravitational potential in a mountainous region, Izv. Vyssh. Uchebn. Zaved., Geod. Aerofotos’emka, 1965, no. 6, pp. 88–93.
Aronov, V.I., On calculating the transformation and reduction of gravity anomaly to the outer plane in a mountainous region, Izv. Akad. Nauk SSSR, Fiz. Zemli, 1967, no. 2, pp. 54–59.
Aronov, V.I. and Shirginova, A.I., A technique for calculating the potential and its derivatives in a mountainous region, Izv. Vyssh. Uchebn. Zaved., Geod. Aerofotos’emka, 1970, no. 3, pp. 91–94.
Aronov, V.I., Obrabotka na EVM znachenii anomalii sily tyazhesti polya pri proizvol’nom rel’efe poverkhnosti nablyudenii (Computer-Aided Processing of Gravity Anomaly Field with Arbitrary Topography of the Observation Surface), Noscow: Nedra, 1976.
Bulakh, E.G., Approximation constructions in uinterpretation problems of gravity and magnetic surveys: a review, Izv., Phys. Solid Earth, 2007, vol. 43, no. 7, pp. 610–620.
Dolgal, A.S., Pugin, A.V., Simanov, A.A., and Batyreva, P.N., Application of analytical approximations to geopotential fields modeling and interpretation, Ros. Geofiz. Zh., 2011, no. 49-50, pp. 42–51.
Golizdra, G.Ya., The history of the theory and methods for analytical continuation of potential fields, in Razvitie gravimetrii i magnitometrii v XX veke. Trudy konferentsii (Proc. Conf. “Development of Gravimetry and Magnetometry in XXCentury), Moscow: OIFZ RAN, pp. 149–168.
Novikova, P.N., Dolgal, A.S., and Simanov, A.A., Threedimensional interpolation and suppression of near-surface heterogeneiry influence in the gravimetric processing, Vestn. Permskogo Univ., Ser. Geol., 2013, no. 1, pp. 50–56.
Pashko, V.F. and Starostenko, V.I., Metody resheniya pryamykh i obratnykh zadach gravimetrii i magnitometrii na EVM (po materialam zarubezhnykh issledovanii) (Methods for Computerized Solution of Direct and Inverse Problems in Gravimetry and Magnetometry (Based on the Results of International Studies)), Moscow: Obzor VIEMS, 1992.
Strakhov, V.N., On constructing the best computational schemes for transformations of potential fields, Izv. Akad. Nauk SSSR, Ser. Geofiz., 1963, no. 12, pp. 1780–1797.
Strakhov, V.N. and Lapina, M.I., The assembly method for solving the inverse problem of gravimetry, Dokl. Akad Nauk SSSR, 1976, vol. 227, no. 2, pp. 334–337.
Strakhov, V.N., Kerimov, I.A., and Stepanova, I.E., Razrabotka teorii i komp’yuternoi tekhnologii postroeniya lineinykh analiticheskikh approksimatsii gravitatsionnykh i magnitnykh polei (Development of the Theory and Computer-Aided Technology for Constructing Linear Analytical Approximations of Gravitational and Magnetic Fields), Moscow: OIFZ RAN, 2009.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © P.I. Balk, A.S. Dolgal, A.V. Pugin, A.V. Michurin, A.A. Simanov, A.F. Sharkhimullin, 2016, published in Fizika Zemli, 2016, No. 6, pp. 122–138.
Rights and permissions
About this article
Cite this article
Balk, P.I., Dolgal, A.S., Pugin, A.V. et al. Effective algorithms for sourcewise approximation of geopotential fields. Izv., Phys. Solid Earth 52, 896–911 (2016). https://doi.org/10.1134/S1069351316050025
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1069351316050025