THE METHOD OF DETERMINING OF DEPTHS TO BORDERS OF THE ANOMALOUS ROCK MASSIFS BY THE STABLE SOLUTION OF THE LINEAR INVERSE PROBLEMS OF THE MAGNETIC FIELD - Minenko, R.; Minenko, P.; Mechnikov, Yu. (Visnyk of Taras Shevchenko National University of Kyiv. Geology, 2025)
The aim of this work is to create a method for calculating the depths to the boundaries of magnetic anomalous bodies (MAB) for their use in solving the inverse linear magnetometry problem (LIPM) with more realistic reproduction of the magnetization intensity distribution (DM) in MAB. The inverse magnetometry problems are strongly incorrect, in particular, because in many cases equivalent magnetization distributions are obtained which, although stable,but are much different from the distribution of real DM in the rock mass and do not provide real information about the geological structure of this massif. On the other hand, it was established by theoretical examples that when choosing the exact geometry of the interpretational model (IM) and the exact values of the DM in the initial conditions, exact solutions of the LIPM are obtained immediately by iterative methods for each block. And for small deviations of these parameters, almost exact solutions of LIPM are obtained, especially when using several types of refinement iterative corrections in optimization algorithms. This gave the authors of this article hope that, at different sizes of the model, among the results of the interpretation one can see, which decision of the LIPM is true. But these intentions were not justified, since we received continuous changes in the DM when the boundary of the model jumped through the boundary of the theoretical body. For a while, we did not pay attention to the changes of other parameters of the iterative process.Eventually, it was noticed that when moving the boundary of the interpretational model across the border of the theoretical model, the graph of the curve of the root from the mean square of residuals of the magnetic field has a specific shape.This allows us to set the depths of the upper or lower boundary of the anomalous body, and in some cases, the depths of the inner boundaries of the multilayer model, which provide a more productive use of the developed method for interpreting the actual magnetic field.
Keywords: magnetometry; inverse problem; iterative method; optimization criterion; field discrepancy; depth of body boundary location