Izvestiya, Physics of the Solid Earth

, Volume 54, Issue 2, pp 372–387 | Cite as

Generalized Solutions of the Inverse Problem and New Technologies for the Quantitative Interpretation of Gravity Anomalies

Article
  • 6 Downloads

Abstract

The approach, fundamentally different from the known ones, to estimating the spatial location of the domain filled with the disturbing masses based on the gravity field measurement data is suggested. The main idea of the approach is, using the set of the probable variants of the interpretation, to construct the distribution of a certain parameter associated with the estimate of probability of detecting the sources of the field in any point of the studied geological medium and then to apply this distribution to each domain eligible for being the true carrier of the anomalous masses. These constructions yield the generalized admissible solutions of the inverse problem with ranking the separate fragments of the model carrier in terms of the probability of detecting anomalous masses in them.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aizerman, M.A. and Malishevskii, A.V., General theory of best variants choice: some aspects, Avtom. Telemekh., 1981, no. 2, pp. 65–83.Google Scholar
  2. Arnold, V.I., Topological problems of the theory of wave propagation, Russ. Math. Surv., 1996, vol. 51, no. 1, pp. 1–48.CrossRefGoogle Scholar
  3. Balk, P.I., On reliability of the results of quantitative interpretation of gravity anomalies, Izv. Akad. Nauk SSSR, Ser. Fiz. Zemli, 1980, no. 6, pp. 65–83.Google Scholar
  4. Balk, P.I., The use of the a priori information about the topological features of the sources of the field in the solution of the inverse problem of gravimetry, Dokl. Akad. Nauk SSSR, 1989, vol. 309, no. 5, pp. 1082–1084.Google Scholar
  5. Balk, P.I., A priori information and admissible complexity of the model of anomalous objects in the solution of inverse problems of gravity, Izv., Phys. Solid Earth, 2013, no. 2, pp. 165–176.CrossRefGoogle Scholar
  6. Balk, P.I. and Dolgal, A.S., Inverse problems of gravity prospecting as a decision-making problem under uncertainty and risk, Izv., Phys. Solid Earth, 2017, vol. 53, no. 2, pp. 214–229.CrossRefGoogle Scholar
  7. Balk, P.I., Dolgal, A.S., Balk, T.V., and Christenko, L.A., Finite-element technologies of interpretation of gravity data. Assembly method, Geofiz. Issled., 2012, vol. 13, no. 3, pp. 18–34.Google Scholar
  8. Cheremisina, E.N and Nikitin, A.A., Sistemnyi analiz v prirodopol’zovanii (Systems Analysis in Natural Resources Management), Moscow: VNIIGeosistem, 2014.Google Scholar
  9. Chernous’ko, F.L., Optimal guaranteed estimates of uncertainties with the use of ellipsoids. Part 1, Izv. Akad. Nauk SSSR, Tekh. Kiber., 1980, no. 3, pp. 3–11.Google Scholar
  10. Dolgal, A.S. and Sharkhimullin, A.F., The increase of the interpretation accuracy for monogenetic gravity anomalies, Geoinformatika, 2011, no. 4, pp. 49–56.Google Scholar
  11. Dolgal, A.S., Balk, P.I., Demenev, A.G., Michurin, A.V., Novikova, P.N., Rashidov, V.A., Khristenko, L.A., and Sharkhimullin, A.F., The finite-element method application for interpretation of gravity and magnetic data, Vestn. KRAUNTs, Nauki Zemle, 2012, vol. 1, no. 19, pp. 108–127.Google Scholar
  12. Gol’tsman, F.M., Problem questions of informational-statistical theory of interpretation of geophysical measurements, Izv. Akad. Nauk SSSR, Fiz. Zemli, 1977, no. 12, pp. 75–86.Google Scholar
  13. Gol’tsman, F.M. and Kalinina, T.B., Statisticheskaya interpretatsiya magnitnykh i gravitatsionnykh anomalii (Statistical Interpretation of Gravity and Magnetic Anomalies), Leningrad: Nedra, 1983.Google Scholar
  14. Nikitin, A.A., Determinacy and probability in processing and interpretation of geophysical data, Geofizika, 2004, no. 3, pp. 10–16.Google Scholar
  15. Raiffa, H., Decision Analysis: Introductory Lectures on Choices under Uncertainty, Reading, MA: Addison-Wesley, 1968.Google Scholar
  16. Starostenko, V.I., Ustoichivye chislennye metody v zadachakh gravimetrii (Stable Numerical Methods in the Problems of Gracvimetry), Kiev: Naukova dumka, 1978.Google Scholar
  17. Strakhov, V.N., Geophysics and mathematics, Izv. Akad Nauk, Fiz. Zemli, 1995, no. 12, pp. 4–23.Google Scholar
  18. Strakhov, V.N. and Lapina, M.I., Assembly method for solving the inverse problem of gravimetry, Dokl. Akad. Nauk SSSR, 1976, vol. 227, no. 2, pp. 344–347.Google Scholar
  19. Zienkiewicz, O., The Finite Element Method in Engineering Science, London: McGrow-Hill, 1971.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Institute of Applied GeodesyBerlinGermany
  2. 2.Mining Institute, Ural BranchRussian Academy of SciencesPermRussia

Personalised recommendations