In the absence of a priori information about the geological structure of study area the structural nonlinear inverse problem (IP) is incorrect and its solution is ambiguous and even physically nonsense or difficult to interpretation. Therefore it is possible to use a space-fixed multilayered model of linear IP with horizontal strata which are composed of quite a large number of blocks in the boxes form (400 to 2500) and to solve the linear IP relative to anomalous density (AD) or the intensity of magnetization (IM) of each block. The positive experience of solving of linear IP for models of 4 layers with 400–1200 boxes in each layer is available due to the high stability of the solutions which are obtained by iterative filtration methods. Attributing the center of each block the AD or IM value which is obtained by solving of IP and holding isolines between them in the space we obtain the maps and sections of AD or IM which are geologically informative, inclusive and easily interpretable. They have areas of rather smooth isolines and zones of intense anomalies with a complicated configuration of isolines. In the paper the various methods of optimization of solutions of IP and methodological techniques is describes. Its alternation in solving of structural linear IP of gravimetry and magnetometry allows using the model of 8 horizontal layers with 400 boxes in each. That is enough to build a simple but yet quite detailed vertical AD and IM sections.

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