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Geoinformatika 2018; 4(68) : 53-63

УДК 550.838

ORIGINAL FITTING ALGORITHM OF MAGNETIC ANOMALIES USING GRID COVERING SOURCES

P.I. Gryshchuk

International Hub of Natural resources, 28, Dubrovytska, Str., Kyiv, 04114, Ukraine, e-mail: pgryshchuk@gmail.com

Purpose. The research goal was to create a simple method of geometrical modeling that is close to the natural process. At the basis on the approach lies the principle of mass displacement, which leads to the formation of geological objects. The analysis of the method consisted in determining the average error and the percentage difference between the initial and calculated anomalies, as well as in obtaining the number of layers needed for getting the exact geometry of the theoretical model. The proposed algorithm may be used to interpret a real magnetic anomaly with the known drilling data.
Design /methodology /approach. The movement of magnetization in blocks of two-dimensional grid model is performed in four directions: left, right, up, and down. In exceptional cases, the magnetization can move at a considerable distance, for example, due to the flow of lava. The magnitude of the apparent magnetization and the direction of motion of the blocks were determined in a random manner. The theoretical model consisted from three rectangular bodies. Vertical sections from three to seven layers were considered. The selection of the model was carried out provided that the magnitude and direction of the magnetization are known. Each block had the form of a cube with the side of 1 m. Comparison of initial and calculated anomalies of the total magnetic field was performed using the average norm and error in percentage terms.
Findings. The block selection for a two-dimensional grid model is executed sequentially from right to left, and between layers – bottom-up. Upon reaching the upper starting point, the crossing between the blocks is in the opposite direction: from left to right, and between layers – from the top to the bottom. Movement of magnetization in adjacent blocks is performed for four directions: left, right, top, and bottom. Improvement of the selection was achieved by adding the possibility of moving magnetism between blocks that are abounded from each other. The value of apparent magnetization and its direction are determined by random means. Approbation of the method is performed for 2.5-dimensional objects. The theoretical model consisted of three rectangular bodies with inclined magnetization. Sections with a number of layers from three to seven were considered. The model fitting is performed when the magnitude and direction of magnetization are known. Each block had the form of a cube with the side of 1 m. The iterative process was executed by minimizing the average norm between the initial and estimated anomalies of the complete vector of the magnetic field. The conditions for completing the fitting of the anomalous field are given in percentage terms and equal 3% for getting the correct result.
Practical significance and conclusions. The results are applied for two-dimensional interpretation of the Kursk magnetic anomaly. Depth, incline, and horizontal thickness for ferruginous quartzite, which are determined by the method of moving the magnetic mass between the blocks, are consistent with the data of drilling. The developed approach permits to define the geometry of the anomalous sources by the grid distribution of apparent magnetization without using additional information.

 

Keywords: model fitting, number of model layers, magnetization, algorithm of magnetic mass movement, deviation in percent, accuracy of the fitting, Kursk magnetic anomaly.

 

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