Minimization risk technique for solving gravity inverse problems in weak assumptions about geological noise properties


  • P. I. Balk Berlin, Germany
  • A. S. Dolgal Mining Institute of the Ural Branch of the Russian Academy of Sciences, Perm, Russian Federation



gravitational exploration, interpretation, inverse problem, field source, noise, anomalous error, empirical risk minimization


The concept of the hidden information on the gravity anomaly sources as joint fragment of the true and model disturbing objects was introduced. In the presence of uncertainty inherent to inverse problems, limit possibilities of algorithms for constructing the best estimates of the parameters of source models is to maximize the secure amount of the extracted reliable information. Justified application to “ore” type gravity nonlinear inverse problems known to minimization risk concept in solving the choice problem under conditions or a priori information shortage. According to this concept as the best of the feasible solutions of the inverse problem is chosen at which the minimum of the expectation value error of interpretation results is achieved. It is assumed zero median noise in the observed gravity field, i.e. the presence of positive and negative noise with equal probability, but it is not excluded that the absolute value of the interference of some of the same sign may prevail. Constructing a sufficiently representative set of feasible interpretation options of which the best one will be chosen, has been performed by fitting algorithm in the finite element class models of geological bodies. An important advantage of the method, which is based on the idea of minimizing the risk is the possibility of an approximate estimate of the proximity of the proposed mathematical model to the true anomaly sources. Produced the results of computational experiments confirming the effectiveness of such assessments, as well as higher quality of the inverse problem solution using the proposed method in comparison with the traditional approach.


Ayzerman M. A., Malishewskiy A. V., 1981. Some aspects of the general theory of best option choice. Avtomatika i telemekhanika (2), 65—83 (in Russian).

Balk P. I., 1980. On a stable method of localization of homogeneous geological objects by gravitational anomalies. Geologiya i geofizika (10), 89—98 (in Russian).

Balk P. I., 2004. About fundamental shortcomings of conventional forms of presentation of the results of mathematical interpretation of potential fields. Geofizicheskiy zhurnal 26(5), 124—132 (in Russian).

Balk P. I., 2011. Parameter Estimation of functional dependence at zero median value of noise in the measurements. Avtomatika i telemekhanika (5), 69—81 (in Russian).

Balk P. I., Dolgal A. S., 2015a. Deterministic models of interpretation for optimizing the locations and depths of the boreholes for verifying the anomalies in gravity. Fizika Zemli (1), 98—111 (in Russian).

Balk P. I., Dolgal A. S., 2015b. The minimax approach to solving inverse problems of gravity and magnetic data. Doklady RAN 462(6), 706—710 (in Russian).

Balk P. I., Dolgal A. S., Balk T. V., 1993. Grid methods for solving inverse problems and experience of their use in tracking intrusions differentiated according to the gravity prospecting. Geologiya i geofizika (5), 127—134 (in Russian).

Balk P. I., Dolgal A. S., Balk T. V., Khristenko L. A., 2015. Coordination of comppetitive variants of gravity data interpretation by empirical risk minimization method. Geoinformatika (4), 24—35 (in Russian).

Dolgal A. S., Sharkhimullin A. F., 2011. The increase of the interpretation accuracy for monogenetic gravity anomalies. Geoinformatika (4), 49—56 (in Russian).

Nikitin A. A., 2004. Determinancy and probability in the processing and interpretation of geophysical data. Geofizika (3), 10—16 (in Russian).

Stratonovich R. L., 1975. Information Theory. Moscow: Sovetskoye radio, 424 p. (in Russian).

Strakhov V. N., 1995. Geophysics and Mathematics. Fizika Zemli (12), 4—23 (in Russian).

Strakhov V. N., Lapina M. I., 1976. Mounting method for solving the inverse problem of gravimetry. Doklady AN SSSR 227(2), 344—347 (in Russian).



How to Cite

Balk, P. I., & Dolgal, A. S. (2016). Minimization risk technique for solving gravity inverse problems in weak assumptions about geological noise properties. Geofizicheskiy Zhurnal, 38(5), 108–118.