Обернені лінійні задачі гравіметрії та магнітометрії з уточнюючими ітераційними поправками вищого порядку

Abstract

The purpose of the paper is to develop iterative methods of solving inverse problems concerning gravity and magnetic fields with high-order corrections to obtain an accurate geological data interpretation of physical fields. The iterative method has been previously used to solve linear inverse problems for gravity and magnetic fields on the basis of combining several types of parameter corrections. However, gravity and magnetometry inverse problems give inaccurate geological data, with different optimization criteria yielding various solutions. Quite often they show essential differences in some of the areas of the geometrical model. There have been developed methods for solving gravity and magnetometry linear inverse problems under Gaussian error distribution, which is connected with structural problems of detecting ore and hydrocarbon deposits. Other methods have been developed for obtaining the solution of gravity and magnetometry linear inverse problems, using iterative corrections which contain a complete set of divergences between the measured physical data and the theoretical calculations. However, the non-Gaussian errors, together with the shortcomings of the existing methods, show a low level of convergence of the iterative process and the true solution of the inverse problem. Moreover, they cause difficulties in reaching an ultimate solution, thus reducing the geological value of the inverse problem solution. New methods are suggested to raise the geological value of the inverse problem solutions with the help of high-order corrections to enhance the well-known iterative formulae and the formulae of optimization criteria. We differentiate between two types of corrections: field misfit ones and those concerning the geological medium density models. Each correction to a field misfit generates one order higher clarifying correction as to the density correction, and vice versa. Either of these corrections, though, can be used either independently in any iterative formula or together with other corrections of the same type. The most accurate field modeling is ensured by using an iterative formula with three corrections (of the same type) of the first, second and third order and a formula with three separate corrections of the other type. Each optimization criterion for such a formula has a complete set of two orders higher corrections.