Based On The Dc Resistivity Method Of Three-dimensional Finite Difference Forward Modeling Research

The direct current (DC) electrical resistivity method is one of the most importantelectrical methods. It has been widely used in many domains. The precision and speed arerequired higher for3D resistivity inversion, while the inversion is based on the forwardmodeling, so the3D direct current resistivity forward modeling is still one of the currentfocused researches.This paper is based on the3D finite difference forward modeling algorithm, which isabout the3D forward modeling of the earth electric field for the point pole. It is startedfrom the basic equation, which is discretized by finite difference combined the mixedboundary and grid continuation skill, which make the infinite problem into the finiteproblem, and then we get the linear equation system. The formula about the node of thegrid is detailed derived, and then the program is compiled. The research for solving theequation contain the coefficient matrix symmetrization and scaling, the storage of thematrix, and using the SSOR-PCG to solve the equation，as a result the memory and thecomputation efficient are highly improved.The abnormal potential method can avoid the influence of the singularity of thecurrent source and improve the precision and decrease the memory requirementsremarkably. The chosen of the relaxation factor for being the higher efficient to solve theequation by using the SSOR-PCG method is studied here. And the design of the3D directcurrent resistivity forward modeling based on MPI is detailed discussed.Finally, the result of the modeling of one simple models shows that the numericalsolution of this scheme is almost in agreement with its analytical solution and the3D DCresistivity modeling can improve the precision and decrease the memory requirementsremarkably. The response characteristic of the complex anomalous body is analyzed,which is got by the3D E-SCAN resistivity measurement. The response shows that3D DCresistivity modeling combined the3D E-SCAN resistivity measurement is highly efficient,and the response of the low resistivity is very well. So the more abundance informationwhich is used to fix the range of the anomaly body can be got by the3D E-SCANresistivity measurement.