| With the extent of exploitation higher and higher, it becomes a important issue at present to study how to find deep ore because the shallow beds were less and less. As one of the effective geophysical exploration methods, DC resistivity is widely used in mineral resources exploration, hydrological and environmental survey. The field using this method is in continuous evolution, the survey space is expanded to under-ground and under-water, it is developed into high-density and high-precision in recent years. With the rapid development of the technique of electronics and computer, and the springing up of intelligent resistivity equipment, the quality of the field data acquisition has been raised, and more advanced techniques for the interpretation of resistivity data are needed correspondingly. Although we can use 2-D forward and inversion to solve problem in work, but the method is not adapted with 3-D geoelectric section. At present, it is hard to make use of 3-D resistivity modeling and inversion method in practical because some crucial problem, such as precision and speed of calculation, had not been solved.The boundary value and variational equation of total and anormalous potential on point-source electrical field of three-dimensional geoelectric section were introduced beginning with the differential equation of potential. Then, the method dividing full area into cubic cells and inserting value in a cell used in the finite element method to solve 3-D electric field were introduced. The result of calculation using total potential and anormalous potential were compared and analysed. The quantic-boundary condition method for resistivity modeling on 3-D geoelectric section is presented in this paper, that is, simplified boundary condition of 3-D point-source electrical field to increase the speed of forward, the time of numerical modeling was shorten from more then twenty hours to 15 minutes. In order to get high precision, the appropriate distance of boundary were determined compared result of FEM with exact solution and calculated large number of examples. Thequantic-boundary condition method made the 3-D resistivity modeling using FEM applied in practical.Using the finite element method under the quantic-boundary condition, forward the apparent resistivity in complex condition, such as tunnel and below water. The anomalous form and characteristic of each set of DC resistivity were presented. The analysis of kinds of influences and corrections method in tunnel and under water will offer direction for resistivity in special conditions.Based on Seigel's theory, using the relation between apparent induced polarization responses and the partial derivatives to get the result of numerical modeling IP values on 3-D section, compared with equivalent resistivity method, it takes more little time.The calculation of the partial derivatives is important in modeling IP and inversion resistivity. We can get the partial derivatives using difference in 1-D inversion. We must take much time to gei it if using same way in 2-D and 3-D inversion. The way using in this paper is get from anormalous potential formula of the finite element method, which speed and precision is appropriate.Finally, the inversional technique of resistivity and induced polarization were presented particularly. Compare with total potential, the method modeling 3-D geoelectric section using anormalous potential in FEM, because of less error on nods near point-source, the precision is higher, so is the result of inversion. The addition of prior information made with volume gene in the least-squares can resolve effectively ill-posed problem in 3-D inversion and improve the resolving capability of deeper units. Aiming at the restrict of inversion based on FEM, getting the logarithm of actual resistivity and theoretic resistivity, can improve the stability of inversion. Using exponential form to correct value of the model can fetch up the bug which get minus resistivity and reduce iterations in inversion. Changing full inversion...
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