Abstract
An inverse gravity problem is solved for a geological model consisting of bodies of Sretenskii’s class. The position of the middle plane is fixed for each body. It is required to determine the upper and lower boundaries of a body, which are described by analytical functions and are parameterized. The solution of the problem is illustrated by an example.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. G. Bulakh, “Gravity Inversion for Several Perturbing Bodies,”; Geofiz. Sb. AN USSR, No. 22, 91–97 (1967).
E. G. Bulakh, An Automated System for the Interpretation of Gravity Anomalies (Minimization Method) (Naukova Dumka, Kiev, 1973) [in Russian].
E. G. Bulakh, “Gravity Inversion for Geological Models of Sretenskii’s Class,” Dokl. NAN Ukrainy, No. 1, 117–119 (2002).
E. G. Bulakh, “On an Alternative Approximation of a Geological Model of Sretenskii’s Class for Gravity Inversion,” Dokl. NAN Ukrainy, No. 5, 128–132 (2002).
E. G. Bulakh, “On the Use of the Fitting Method in Solving Inverse Problems of Gravimetry and Magnetometry,” Fiz. Zemli, No. 2, 72–77 (2006) [Izvestiya, Phys. Solid Earth 42, 156–160 (2006)].
E. G. Bulakh, V. A. Rzhanitsyn, and M. N. Markova, Application of the Minimization Method to Problems of Structural Geology Using Gravity Data (Naukova Dumka, Kiev, 1976) [in Russian].
E. G. Bulakh and I. V. Shinshin, “Algorithmic and Numerical Construction of an Analytical Model of the Gravity Field,” Geofiz. Zh. 28(2), 107–114 (2000).
I. M. Gel’fand, E. B. Vul, S. L. Ginzburg, and Yu. G. Fedorov, Method of Ravines in Problems of X-ray Analysis (Nedra, Moscow, 1966) [in Russian].
L. V. Kantorovich, “An Efficient Method for Solving Extreme Problems with Quadratic Functionals,” Dokl. Akad. Nauk SSSR 48(7), 483–487 (1945).
L. V. Kantorovich, “On the Steepest Descent Method,” Dokl. Akad. Nauk SSSR 56(3), 233–236 (1947).
L. V. Kantorovich, “Functional Analysis and Applied Mathematics,” Usp. Mat. Nauk 3(6), 89–185 (1948).
A. I. Kobrunov, Theoretical Foundations of Data Inversion in Geophysics (Ukht. Politekh. Inst., Ukhta, 1995).
L. N. Sretenskii, “Uniqueness of the Shape Determination for an Attracting Body from Its External Potential Values,” Dokl. Akad. Nauk SSSR 99(1), 21–22 (1954).
V. I. Starostenko, Robust Numerical Methods in Gravity Problems (Naukova Dumka, Kiev, 1978) [in Russian].
V. I. Starostenko and S. M. Oganesyan, “Ill-Posed Problems in the Hadamard Sense and Their Approximate Solution by Tikhonov’s Regularization Method,” Geofiz. Zh. 23(6), 3–20 (2001).
V. N. Strakhov, “On the Theory of the Fitting Method,” Izv. Akad. Nauk SSSR, Ser. Geofiz., No. 4, 494–509 (1964).
V. N. Strakhov, “On Gravity and Magnetic Data Inversion,” Dokl. Akad. Nauk SSSR 212(6), 1339–1342 (1973).
V. N. Strakhov, “Parameterization of Gravitational Inverse Problems,” Izv. Akad. Nauk SSSR, Ser. Fiz. Zemli, No. 6, 39–49 (1978).
V. N. Strakhov, “A New Technology for 2-D Interpretation of Local Gravity Anomalies,” Geoinformatika, No. 1, 27–31 (2005).
Author information
Authors and Affiliations
Additional information
Original Russian Text © E.G. Bulakh, M.N. Markova, 2008, published in Fizika Zemli, 2008, No. 7, pp. 21–27.
Rights and permissions
About this article
Cite this article
Bulakh, E.G., Markova, M.N. Inverse gravity problems for models composed of bodies of Sretenskii’s class. Izv., Phys. Solid Earth 44, 537–542 (2008). https://doi.org/10.1134/S1069351308070033
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1069351308070033