Methods of gravitational tomography based on F-approximation

Abstract

Relevance. Currently, one of the significant directions of the theory and practice for interpreting potential fields is the development of methods aimed at studying the spatial distribution of densities from the results of processing and interpretation of gravitation prospecting data in a given volume of a geological environment with a minimum of a priori information about field sources of a given volume with a minimum a priori information about the sources of the field. The aim of the work is to develop methods of gravitational tomography based on the approximation approach to spectral analysis in gravimetry, which is called the F-approximation method. Methods. Development of spectral analysis algorithms and computer technologies, based on the approximation approach in the framework of the method of linear integral representations that was offered by B. N. Strakhov. Methods for solving systems of linear algebraic equations (SLAE) of large dimension using the solution theory of ill-posed problems. Results. Issues of the development of gravity tomography methods based on the F-approximation of the anomalous gravity field, which is characterized by complete adequacy of real geophysical practice and allowing to get rid of various idealizations (idealization of a flat field; idealization of the earth-air interface as an infinite horizontal plane; idealization of a continuous setting of a particular field element on an infinite horizontal plane or a piece of this plane; idealization of the setting another field element at the nodes of a regular geometric network, etc.) Three modifications of gravitational tomography based on the F-approximation are proposed. The first modification is based on the study of the spatial distribution of the elements of the gravitational field. In the framework of this modification, based on the F-approximation, we study the distribution of various derivatives of the anomalous gravitational field in the lower and upper half-spaces. The second modification consists in dividing the anomalous gravitational field into components due to sources lying within structural floors that differ significantly in m depth. The article considers the option of separating the anomalous field for the case of two structural floors. For this option, an algorithm and computer technologies have been developed, the method has been tested on model and real geological and gravimetric materials. The third modification is to find the spatial distribution of the Strakhov function, which is a generalization of the Berezkin function. An algorithm and computer technology for calculating the spatial distribution of this indicator and obtaining a spatial cube of data have been developed.