2.5D Modeling And Inversion Of The Surface To Hole Resistivity Imaging Research And Application

Compared to resistivity image on the surface, the surface to hole resistivity technique has a better resolution, because of the surface to hole resistivity technique will place the current electrodes to the hole, and close to the research target, It can inspire more abnormal, generate greater potential difference in the receiving electrode surface. Well it is because of surface to hole resistivity imaging method these characteristics, therefore, the surface to hole resistivity technique has a large potential for development and application prospects, to the city engineering geophysical prospecting and deep geophysical prospecting concealed ore deposits、analyze the distribution of the residual oil in high water cut oil field. This paper summarized in detail about the concept of the surface to hole resistivity technique, research history and application status and research achievements. Based on these, the paper through finite element numerical simulation and the regularization inversion, it established a variety of numerical simulation of theoretical models of 2D modeling and inversion, and good results have been achieved.This paper is divided into six chapters. The first section is preface, the section introduced the research background and significance of the paper, and forward invers algorithm research status of the surface to hole resistivity technique, and the main research content of the paper. The second section is forward theory of the surface to hole resistivity technique, the section introduced the differential equation and the boundary value of 2D geoelectric section point current source. And the apparent resistivity formula of different devices. The main content of this paper is introduce and deduct finite element method of the surface to hole resistivity technique in the third section. 2D forward calculation problem of the surface to hole resistivity technique is to solve the boundary value, and the differential equation and the boundary value of 2D geoelectric section point current source equivalent to variational problem. Variational problem is functional extremum problems, and can resolve multiple source function extremum, it be well known. It is basic thought of finite element method. The specific approach: 2D geoelectric section point current source is 3D geoelectric field(electric potential), but the electric potential in the geologic body stretching direction is symmetry. Therefore, we can use cosine transform make differential equation of 3D electric potential transform 2D differential equation. After mesh dissection, the bounding value reduction to the linear equation of mesh points, compute Fourier electric potential, compute electric potential with arc cosine transform. The fourth section is regularization inversion of the surface to hole resistivity technique, the section introduced the regularization inverse theory, discuss the design of regularization factor and stabilizing factor. The fifth section introduce application examples of application effects of the surface to hole resistivity technique. In the last section is conclusion section, summarize results of the work and some unsolved defects.In the paper, wrote forward and inverse calculate program of the surface to hole resistivity technique with C programming language. In forward calculate, the arc cosine transform calculate filter coefficients of high accuracy with optimization method. In inverse calculate, detailed analysis the regularization factor and stabilizing factor contributing to the inversion result. The author illuminated the creditability of forward and inverse theory mode and mathematic physics model, clarified the feasibility of the calculate program. The application of the surface to hole resistivity technique in the urban engineering survey, in the work area of karst cave, karst fissure fracture zone and rich hose has achieved good results in geological hazard survey. The inverse results can precisely divide the spatial position and the border of target body of geoelectric cross section, design effort and late for safe construction have got the necessary technical support.