Calculation Of Tensor Green's Functions And Research On Electromagnetic Forward Modeling By Integral Function

Electromagnetic prospecting is a branch of applied geophysics, which plays an important role in geophysical exploration in practice. With the high-precision, flexible and reliable digital field devices are emerging, explain the technology behind has become a major limiting factor in the development of electrical method. Numerical simulation and the actual electrical data processing and interpretation based primarily on forward and inversion of Two-dimensional and three-dimensional model. Numerical simulation of three-dimensional electromagnetic response is front edge research subject of geophysics, it is the base of inversion. At the same time analyzed and summarized the physical nature, apparent resistivity distribution and characteristics of the electromagnetic response of three-dimensional body by measurements is very important. This article discusses the Green function and integral equation forward problem. Integral equation numerical model is a basic algorithm which needs more complex mathematical knowledge, but this method requires only subdivision in the abnormal region, quick calculating speed, less memory. Using integral equation method to calculate the electromagnetic response of three-dimensional body of finite size is more effective. The fast and accurate calculation of tensor Green's function is a prerequisite for solving integral equations. As the need of practical application and the improving of accuracy of electromagnetic modeling, people are interested in inhomogeneous media, especially in flat layered medium of electromagnetic radiation, scattering analysis.To salve the problem with frequency domain the numerical methods based integral equations on is more convenient. The key is exactly derived the Green's function in layered medium. This article derives the tensor Green's function and integral equation kernel function in complex electromagnetic field. We calculate Green's functions in the homogeneous half-space and layered media with numerical integration method and the Hanker Transform. Compare with the result of the analytic literature and the formula. Numerical integration method get the right results. In the case of dipole in layered media stimulated and received on the ground, when calculated the Green function with the Hanker transform, dealing with the kernel function, make it constringe. Comparing with DCIM method, we found that in this case treated Hanker kernel transformation method is correct and feasible. However, in the case of stimulated at any layer and received in any layer. Even if the kernel function treated Hanker transform still can not reach the right result. The continued fraction method comparing with layer matrix method and analytical method is correct.When to solve geological problems with electromagnetic exploration, mainly on accounting the characteristics of electrical properties and induced polarization of rocks and ore, Polarization registers as the electrical resistivity properties in the stable field , while polarization registers as the complex resistivity characteristic in alternating magnetic fields. In practice, alternating electric field is more universal, therefore, the studies of forward and inverse electromagnetic field about body of complex resistivity has important practical significance. The depth analysis of the results of electromagnetic field forward is still missing. Electromagnetic response becomes more complex under the influence of anomalous bodies in the ground. This article researches forward theory of electromagnetic field about three-dimensional complex resistivity. The complex resistivity Cole-Cole model is introduced to the volume integral equation, to calculate the model which is complex resistivity 3D anomalous body in homogeneous medium. Analysis of forward result shows that: field of 3D complex resistivity body is produced by cumulative charge, electromagnetic induction and induced polarization. The real part of secondary field effected by cumulative charge and induced polarization. Cumulative charge effect: anomalous body which is low resistivity makes the field weaker, while high resistivity makes the field stronger; induced polarization effect: both high resistivity and low resistivity make the field stronger. As induced polarization effect equal to capacitance effect, with the increasing of frequency, capacitance effect is weaker, therefore, the frequency is higher induced polarization effect is weaker, while frequency is lower induced polarization effect is stronger; The imaginary part of secondary field is effected by electromagnetic induction and induced polarization. When anomalous body is low resistivity, it absorbs electromagnetic wave, the filed growing stronger, the lower the resistance, the field is stronger but high resistance is in contrast Filed becoming weaker in the case of anomalous body is high resistivity. With the electric resistivity and frequency growing up the filed is weaker. Induced polarization effect makes the field weaker whether high or low resistivity, with the polarizability becoming stronger the field is weaker. When the anomalous body is low resistivity, the direction of field produced by electromagnetic induction and induced polarization is contrary, therefore electromagnetic induction and induced polarization in tradition they interfere with each other. They must be considered in actual work, or they might draw wrong conclusions. Sum of the law of three effects of the electromagnetic response, provide a basis for accurate analysis of the abnormal, and to provide the more abundant, accurate electrical information for geological explanation.