R. Minenko1, MSc, E-mail: maestozo.1_pavel@mail.ru;

P. Minenko1, Dr. Sci. (Phys.-Math.), Prof.;

Yu. Mechnikov2, Engineer-Geologist


THE PROBLEM OF FINDING MEANINGFUL SOLUTIONS TO LINEAR INVERSE PROBLEMS

OF MAGNETOMETRY BY INTEGRATION OF INTERPRETIVE MODELS


1 Krivorozhsky National University, 54, Gagarina Avenue, Krivoy Rog, 50086 Ukraine,

2 Krivoy Rog Geophysical Department, 2 Geologichna Str., Krivoy Rog, 50001 Ukraine


The aim of this work is the creation of methods for solving the inverse problem of magnetometry in the conditions of uncertainty in the spatial distribution of the magnetization of rocks. As a rule, the solution of the inverse problem of magnetometry is ambiguous because of the inaccuracy of the model chosen, its displacement relative to the real masses, the degree of discrepancy between the real physical parameter of rock with specified initial conditions. Unlike gravity, the complexity of solving the inverse problem of magnetometry due to the fact that the magnetic properties of rocks are so heterogeneous that they simply cannot be reliably determined on samples from outcrops or boreholes nor according to well logging data, i.e. the micro level is not acceptable to the magnetic survey. The only method to determine the magnetic properties at the macro level is the solution of the inverse problem. However, comparing of the interpretation results does not seem possible in a material sense. One can only solve the inverse problem by different methods. It is desirable that these methods were varied and were based on a grid-block interpretation models with different linearity. For example, when using multi-layer models of the geological environment with finite-height and semi-infinite blocks, we get totally different results of solving the inverse problem. Since direct methods for solving the inverse problem are developed very poorly, the decision has to be done by optimized iterative methods which are much better designed. With the help of multi-layer theoretical models it was found that for semi-infinite prisms the definable intensity of magnetization decreases to a prism with increasing of the depth, though in fact, it is constant in a geological massif. For multilayer models with finite-height prisms the deeper is the prism in the model, the greater is the intensity of magnetization, although, more accurately, this is true only to a certain depth and even height of the prism. Such a set of rules might result in deadlock the interpretation of magnetic anomalies by mesh methods. In nature, however, vertical bodies can have falling or increasing intensity of magnetization with depth, which further complicates the definition of the geological situation. This article describes the methods we have developed that speed up or slow down the processes of change of magnetization with depth in the solution of the inverse problem. A formula has been developed concerning iterative corrections to the physical parameter. It takes account of the depth of the block location in the interpretation model and adjusts the distribution of the residuals of the field into blocks of different depths to recalculate them in a correction to the intensity of magnetization of the block. By use of several interpretative models with various clarifying corrections, stable and meaningful solution of the inverse problem can be achieved.

Keywords: gravimetry, inverse problem, iterative method, iterative correction, optimization criterion, the correction for depth.


References:

1. Kobrunov A.I., (1989). Teorija interpretacii dannyh gravimetrii dlja slozhnopostroennyh sred: uchebnoe posobie. K.: MVSSO USSR UMZh VO, 100 p. (In Russian).

2. Minenko P.A., (2006). Isledovanie kristalicheskogo fundamenta lineynonelineynymi metodami magnitometrii i gravimetrii. Geoinformatika, 4, 41-45. (In Russian).

3. Minenko P.A., Minenko R.V., (2012). Uproshhennye algoritmy reshenija obratnyh zadach gravimetrii filtracionnymi metodami. Geoinformatika, 2(42), 27-29. (In Russian).

4. Minenko R., M│nenko P., (2014). Obernen│ l│n│jn│ zadach│ grav│metr│┐ ta magn│tometr│┐ z utochnjujuchimi │terac│jnimi popravkami vishhogo porjadku // Visnyk of Taras Shevchenko National University of Kyiv: Geology, 1(64), 78-82. (In Ukrainian).

5. Petrovskij A.P., (2006). Matematicheskie modeli i informacionnye tehnologii integralnoj interpretacii kompleksa geologo-geofizicheskih dannyh: dis. … doktora fiz.-mat. nauk: 04.00.22. Kyiv, 364 p. (In Russian).

6. Starostenko V.I., Kozlenko V.G., Kostjukevich A.S., (1986). Sejsmogravitacionnyj metod: principy, algoritmy, rezultaty. V│snik AN URSR, 12, 28-42. (In Russian).

7. Strahov V.N., (1990). Ob ustojchivyh metodah reshenija linejnyh zadach geofiziki. II. Osnovnye algoritmy. Izv. AN SSSR. Fizika Zemli, 8, 37-64. (In Russian).