2.5 Dimension Boundary Element Numerical Simulation Of Resistivity Under Complex Terrains

The electrical prospecting method plays an important role in the prospecting of metal mineral and oil and gas resources as well as the detecting of coal mined-out areas and waterfilled caves.As a nation with many mountains,especially in southwestern and northwestern regions,China boasts very complex terrain landform.However,rugged terrains would cause anomalies of resistivity,which considerably increases the difficulty of the analysis and explanation of electrical prospecting data and influences the application effect of electrical prospecting in mountain areas.As a result,the key to promoting the application of electrical prospecting method in mountain areas lies in solving the problem of rugged terrains.In most cases,numerical approach is used to do forward modeling and then tackle complex geophysical problems.Besides,it is known that boundary element method is a kind of numerical simulation that boasts many advantages,such as low space dimension,less input data,high calculation precision and fast running.Thus,in this paper,boundary element method was used to simulate the 2.5-dimensional DC resistivity under complex terrains and to analyze the influence of rugged terrains on the abnormal pattern of apparent resistivity curves,so as to provide guidance for carrying out field work of electrical prospecting and offer technical support for subsequent data processing.The main work and results of this paper are summarized as follows:(1)Theoretical analysis and formulation derivation of boundary element method of 2.5-dimensional DC resistivity under complex terrains.Three-dimensional geological target body that extends to a certain direction was transformed into two-dimensional one by using Fourier transform and then complex 2.5-dimensional geoelectric model close to actual terrain was established.(2)Program design of FORTRAN90-based numerical simulation,including writing algorithm for node dissection and angle calculation,was conducted.Not only was tedious work of data input avoided,but also rugged terrain and abnormal target body models were generated by assigning values of X and Y in a coordinate system,which improves calculation efficiency and accuracy to a large extent.(3)Different complex 2.5-dimensional geoelectric models were designed to conduct forward simulation,and occurrence of the same geological target body under different rugged terrain conditions and occurrence of different geological target body under the same terrain conditions were deeply investigated and compared.Then utilized ratio method to do terrain correction and simply process as well as suppress the influence of terrain condition,in order to eliminate the effect of terrain condition on calculation results.(4)Factors that affect the calculation accuracy of boundary element method were summarized and analyzed,so as to lay the theoretical foundation for improving the calculation accuracy of boundary element method and meet the need of subsequent forward modeling in the future.