Jacobian Partial Derivative Matrix Computation and Image Processing of Deep Three-dimensional High-density Resistivity Method

Abstract: Along with prospecting degree unceasingly thorough, the superficial part easy to discover and the use minerals reduces day by day, to seeks for the depth portion non-ferrous metal mineral resource the fast localization forecast technique research to constitute now one of entire geology important research subjects. The electrical prospecting explores one in geophysics main disciplines. The high density resistivity method take the ground conductive difference as the foundation, the use program control type multi-purpose electric instruments for logging oil and the program control type multi-channel electrode switches, continuously fast to section plane trundle scanning survey, gathering, memory observation data. This topic application finite difference method the three-dimensional model carries on to the direct-current field in is developing the computation, is the three-dimensional model inversion important basis, and to solves the actual problem to have the vital significance.High-density electrical method refers to the DC high-density resistivity method, but because it induced polarization method, so collectively referred to high-density electrical method. High-density resistivity method is a new method of electrical prospecting, which islow-cost, high efficiency, information-rich, easy to explain. In the field of engineering survey, it has been widely used.At present, although we can use the two-dimensional field inversion method to solve some practical problems, compared with the actual three-dimensional medium , its accuracy and holistic inversion effect still can not meet the actual needs. In the geophysical inversion theory, forward modeling is the crux of the problem. Although the ultimate purpose is geophysical inversion, the inversion largely on the basis of forward modeling. Therefore, for the inversion, three-dimensional model forward calculation is an important basis, which is about the finite difference method for three-dimensional model of the electric field in the in this subject, and it also solves practical problems in great significance.The high density data processing software is being developed now , so we need use the data from the RES3DINV which is the Swedish Geological software temporarily and convert the data into visual images by image processing. Making different colors express the electrical properties of object shape in different regions, and the coordinates of the image to the object position in the underground, so researchers can easily estimate where a certain object is the underground, and the distribution and shape of objects and other circumstances surrounding the situation of objects. This will not only be freed the staff from the data which is difficult to find and has complex rules, but also explain the results of detection more easily. It is the basis of independent research for high-density data-processing software.Designed primarily for the following two parts:Part I: the partial derivatives of the 3D model Jacobian matrix can be achieved by finite difference method in the electric field, which includes a description of the basic principles, such as the basic principles and application of the finite difference method and the Gauss quadrature formula. And programming by MATLAB software is requested. To make sure the universal of software, we must meet the following conditions: the x-axis, y-axis range and the grid spacing can be changed and so dose the position of power supply electrodes. Calculating potential partial derivatives of measurement electrode in different location, and getting the partial derivatives of the 3D model Jacobian matrix in the arrangement of the electrodes which are discretionary could be able to apply to this method.Part II: The main program modules is be completed as following: (a) data format convertion : the data will be converted into the format required, and extracted to data processing; (b) mapping interface design: several graphical interface production; (c) data preprocessing before sufer software; (d) contour map drawn for the convertion : invertion data will be changed into computer graphics.After the field testing and results analysis, the results of this design achieved the target, which could complete discretionary n * n * m-type data into three-dimensional map and operate easily…
Key words: high density resistivity method; finite difference method; Jacobian partial derivative matrix computation; image processing; contour maps

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