PROBLEM OF SUSTAINABLE SOLUTIONS OF THE INVERSE LINEAR EQUATIONS IN GRAVIMETRY - Minenko, R.; Minenko, P.; Mechnikov, Yu. (Visnyk of Taras Shevchenko National University of Kyiv. Geology, 2025)
Purpose – on the based of theoretical examples o develop the methodology for recognition of cases of constant density and its rise or decline with depth. For every example, to find the empirical coefficient functions for correcting the effect of block depths on the value of the basic iterative correction. The inverse problem of gravimetry is incorrect. Partially incorrectness of their solutions are reduced by the size of grid-block interpretation model of the geological environment, that are equal to the size of the gravity field maps. In such a way sustainable solutions are obtained. If the depth of all layers and the density of the block model are known, the inverse problem of linear gravity in the class of uniqueness of the solution migjht be to solved for the second part of the blocks. Such problem solvation are are used for structural geology, mainly in oil and gas areas, where many wellsand whole entire area of map are covered by field seismic surveys of geological structures. In the ore regions seismic investigations do not commonly carried out and therefore the morphology of the geological structures is unknown. Much wells are not drilled here. On crystalline shields wells are not always reach the boundary between the sedimentary cover and crystalline rocksor they reach a few meters or a few tens of meters below. In such a case a narrow class of uniqueness can only be a single-layer model with blocks in the form of semi-infinite vertical prisms. The results of solving the inverse problem for this model are far from the real density distribution in the geological massif. At changing for a more detailed model, which consists of a limited vertical blocks grouped in horizontal layers, we can observe a reduction in the density of deeper blocks while solving inverse problems of iterative methods for real and theoretical fields , although their actual density does not change with depth. Roman Minenko developed a two-step procedure for the preparation of sustainable and meaningful solutions of inverse linear problems of gravimetry for additional solutions with iterative clarifies amendments. But it is useful only in cases of constant density of highly anomalous bodies in the vertical direction. In this paper, for the cases of rise or decline of density with depth, the basic iterative correction coefficient functions introduced to adjust the depth of its impact on the placement of blocks. Appearence of the functions depend on the direction of changes in rock density. The final distribution of density is usually achieved by using optimization techniques with higher-order corrections.