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Balk P.I.,Institute of Applied Geodesy
Izvestiya, Physics of the Solid Earth | Year: 2013

We study the problem of selecting an admissible complexity of the model of gravity sources, which largely governs the quality of the inverse problem solution and has been poorly explored to date. The reasons why the interpretation theory of anomalous gravity has not yet suggested clear guidelines on this subject are analyzed. Among these reasons is the inadequacy of the prerequisites that are used in the theory of inverse problems to the real conditions of a geophysical experiment. The standard scheme of constructing the algorithms for quantitative interpretation of gravity data is expanded by the missing elements that are necessary for the solution of the problem. The most important role in the improved scheme is played by the algorithmic approaches that allow the interpreter to assess the size of the set of admissible solutions of the inverse problem, the corrections for the inadequacy of the used model of gravity sources to the actual physical distribution of the anomalous masses, and the new forms of representation of the results, which provide monotonic dependence of the solution's quality on the amount of the a priori information. © 2013 Pleiades Publishing, Ltd. Source

Balk P.I.,Institute of Applied Geodesy | Dolgal A.S.,Russian Academy of Sciences
Izvestiya, Physics of the Solid Earth | Year: 2012

The guaranteed approach to the solution of inverse problems of gravimetry, which is fundamentally different from the common solution, is presented. Instead of providing single (optimum) estimates of the model parameters, whose quality is, generally, random, the interpretation in the suggested approach yields that volume of reliable information on disturbing objects, which is contained in the field measurements, together with the a priori constraints. The method of solving the inverse problem of gravimetry is developed within this approach, where, in contrast to the conventional approach, both the geometrical parameters of the geological bodies and the densities of their composing rocks are treated as unknowns. The generalized assembly algorithm suggested by V. N. Strakhov is proposed as a basic working tool to implement this approach. The results of testing this algorithm and the guaranteed approach itself on the model and practical examples are discussed. © 2012 Pleiades Publishing, Ltd. Source

Balk P.I.,Institute of Applied Geodesy
Automation and Remote Control | Year: 2011

In the paper, we study a problem of estimating functional dependency parameters by empirical data with random noises. A specific feature of the formulation is a replacement of a traditional assumption of zero mathematical expectation of a noise by the condition of equality to zero of a median value of the noise. We represent an algorithm for constructing estimates of parameters minimizing a mathematical expectation of losses including the variant of spline approximation. We interpret such estimates. The results of the experiments are given. © 2011 Pleiades Publishing, Ltd. Source

Balk P.I.,Institute of Applied Geodesy
Izvestiya, Physics of the Solid Earth | Year: 2014

The fact that most of the basic points in the methodology of interpretation theory of gravity anomalies are inadequate to the targeted intention-to extract the maximal volume of reliable information about the sources of the field-has barely been noticed so far. It is established that objectivation of the real possibilities of gravimetry in the particular conditions of interpretation is mainly blocked by the contradiction between the objective existence of a variety of a priori equivalent variants of the interpretation, on one hand, and the desire to describe its structure by a single element, the "optimal" solution of the inverse problem, on the other hand. A complete, to any extent, solution of the problem of reliability of the information retrieved from the gravimetry data can only be obtained in the case if the results of the interpretation contain the information about the properties of the studied object that is consistent with all the admissible solutions of the inverse problem. The informativity of conventional representations of the results of interpretation is assessed in comparison to the informativity of the alternative representations. © 2014 Pleiades Publishing, Ltd. Source

Balk P.I.,Institute of Applied Geodesy | Dolgal A.S.,Russian Academy of Sciences
Izvestiya, Physics of the Solid Earth | Year: 2015

We present the algorithm and results of the first experience in synthesizing the updated deterministic models of interpretation and simplest statistical techniques for determining the coordinates and depths of the verification boreholes based on the results of gravity prospecting. The suggested algorithm implements the ideas of guaranteed approach and construction of generalized assembly algorithms for finding the separate variants of interpretation if the a priori information is available for the sources of the field. In this paper, we present the first results of joint application of the deterministic techniques for constructing the representative subset of the admissible solutions of the inverse problem of gravity prospecting and describe the simplest statistical methods for their processing for elaborating the substantiated recommendations on determining the surface coordinates and depths of the verification boreholes. The suggested algorithms rely on the concept of a guaranteed approach to the inverse problems of geophysics and on the methodological idea of reconciling the different admissible interpretations of gravity data intended aimed at increasing the reliability of the conclusions. For finding the individual admissible variants of solution of the inverse problem, we use the finite-element descriptions of density heterogeneities and modern modifications of the assembly method suggested by V.V. Strakhov, which are flexible for the formalizations and allowance for heterogeneous a priori information. © 2015, Pleiades Publishing, Ltd. Source

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