Parallel Algorithm Research Of Two-Dimensional Complex Resistivity Forward Modeling And Inversion Based On MPI

Complex resistivity(CR) method is one of the most important methods in the electrical exploration methods. It is a very promising method and has been applied to solid mineral resource, hydrogeology, environmental monitoring, engineering geology, oil and gas resources and et al. Compared with other electrical exploration methods, CR method inverts mutli-parameter simultaneously, and thus it can proviod more underground geoelectrical information. Currently, the research about CR method which considers both electromagnetic effects and induced polarization effects is a hot topic around the world. Here, with the introduction of Message Passing Interface(MPI), this paper finished parallel algorithm research of two-dimensional complex resistivity forward modeling and inversion.In terms of forward modeling, according to second field algorithm, deduce the differential equations from Maxwell equations. With the introduction of Cole-Cole model, we employ finite element method(FEM) to accomplish 2D SIP forward modeling which considers electromagnetic effects and induced polarization effects simultaneous, and obtain the forward modeling equations. It needs a great memory to store the coefficient matrix of the forward modeling equations entirely, and we adopt the strategy of row compression storage to reduce the memory needs. As for the solution of equations, we use two different methods to calculate. After a comparative analysis, under the condition that the precision meets the requirements, we choose the symmetric successive over relaxation bi-conjugate gradient method. After the calculation of several synthetic models by the forward modeling codes, we get the results and compare them with the results calculated by the open codes from Kerry key. And the results show that the forward modeling codes describled in this paper is correct.For inversion, we adopt data space OCCAM method in which different constraint of both model smoothness and parametric boundaries are applied to recover the four parameters of Cole-Cole model simultaneously using multi-array electrical data. This approach not only improves the stability of inversion but also reduces ambiguity of the inversion significantly.With the consideration of calculation speed, we introduce MPI parallel computing. For the forward modeling which contains multiple transmitting sources and multiple frequencies, we complete the forward parallel programs based on transmitting source in parallel. And for the forward modeling which contains multiple frequencies, we complete the forward parallel programs based on frequency in parallel. Then we verify the accuracy of the forward modeling parallel programs by a synthetic model, and analyze the parallel efficiency with statistical time data. In terms of the inversion problem which contains multiple transmitting sources and multiple frequencies, we complete the inversion parallel program based on transmitting source in parallel. Then we verify the accuracy of the inversion parallel programs by synthetic models, and analyze the parallel effiency by statistical time data. The experients indicate that the calculation speed is greatly improved with the application of MPI parallel, and with the number of process which participates in parallel computing increases, the speed-up ratio increases, but the parallel efficiency decreases.