Study On 2.5D Complex Resistivity Electromagnetic Forward And Inversion

At present among data interpretation of electromagnetic method, the computation quantity of 3D forward problem and inversion is enormous. So it has no practicality before the speed and precision of 3D problem is solved well. The 2D forward problem and inversion has small computation quantity and achieve many achievements of research. But because of the source is 3d or finite, so the 2D forward problem and inversion is only approximate simulation. Our country is a country with a lot of mountains area. Compared with 2d profile survey, the applied effect of 3D electromagnetic survey can not be improved but the cost has to be increased greatly. So 2.5D model(3D or finite source over an earth whose conductivity varies in only 2D ) simulation have particular predominance. Compared with 3D model , the 2.5D model reduces the computation quantity, which can be fulfilled easily on common computers. Compared with 2D model, it is easier for 2.5D model to approach field geologic setting. so the research on electromagnetic forward and inversion of 2.5D model has important theoretical and practical significance. The characteristic of complex resistivity on rock and ore has been cognized by people for a long time. It has been proved that the electrical anomaly of geologic body can be quantitative estimated by complex resistivity model parameters(direct resistivity, chargeability, time constant and frequency dependence ).In order to study the characteristic of complex resistivity on rock, people develop various DC and AC induced polarization method .In order to study the characteristic of resistivity on rock and ore, people develop all kinds of dc electric methods, frequency domain and time domain electric methods. The electromagnetic coupling will become the interference factor on induced polarization method, while the induced polarization will become the interference factor on frequency domain and time domain electric methods. In practical, electromagnetic effect and induced polarization exist together and influence each other, so it is hard to separate them. Considering all these problems, we develop the research on electromagnetic forward and inversion of 2.5D complex resistivity.In the past, the finite element arithmetic of computing 2.5D electromagnetic response is based on coupling electromagnetic differential equation. In this paper, we divide target area into many small parts according to the finite element method, then we deduce the independent functional of electric field component and magnetic field component according to Maxwell equation for this block homogeneous medium. As a result, the calculation speed of 2.5D forward problem is improved quickly. A 2D finite element method is adopted to subdivide a rectangular lattice by adding two diagonal lines in the rectangular lattice, furthermore the grid are small and denser in the middle area ,while the grid are big and sparser at the edge of area. The grid grow bigger gradually from the center to the edge. As a result, not only is there enough space for dividing area, but also complex parts of the geoelectric cross section gather in the center of dividing area. At the same time, we use the Gauss elimination to eliminate unknown variables to be calculated at the central node of the rectangular lattice, thus the computation quantity is reduced. In order to make sure of computation accuracy, the third boundary conditions are adopted. Introducing Cole-Cole model into the 2.5D electromagnetic model,we realize the algorithm of 2.5 D complex resistivity forward problem. By Comparing with the result of 1D digital filter, the accuracy of the algorithm in this paper is proved. Then we calculate the spectrum curve of electric field on horizontal component for homogeneous polarized field and layered polarized field. Finial we summarizes the laws about complex resistivity parameters effect on spectrum curve.The inversion of induced polarization parameter usually base on the hypothesis about apparent resistivity and true parameters. The hypothesis of electromagnetic coupling effect can bring error for the result of inversion, and the traditional methods can't inverse the geometry parameters. This paper develops the partial derivative matrix that reflects the rate of real measurement field to the Cole-Cole model parameters. Then we realize the 2.5d complex resistivity inversion of dipole source by using classical damped least square method. In order to improve the speed of inversion, we just invert the parameter of target area. The inversion result of theoretical model show that it needn't any hypothesis about apparent resistivity and true parameters we can to directly inverse the true Cole-Cole model parameters according to electromagnetic field of the earth's surface. So the apply range of inversion is more wide. Due to strong correlativity between time constant and chargeability, the time constant can't be accurate inversed when all the complex resistivity parameters take part in the inversion. For this problem, considering the chargeability can be measured or estimated before the inversion calculation. So we fixed the values of the chargeability in the inversion, and then inversed other resistivity parameters. Through the method we can obtain accurate result of inversion.A negative response may appear in the transient electromagnetic measure. The appearance of negative response lie on relatively magnitude of induction current and polarization current in different time. In forepart,the electromagnetic effect dominate,then diminishes rapidly. In late time stage,the gradually dominate. Using this difference in time ,It is possible to respectively extract electromagnetic effect or induced polarization. The induced polarization effects on transient electromagnetic responses can be researched by calculating the response of some polarized model. This paper change frequency domain electromagnetic responses into transient electromagnetic responses by cosine transform and calculate the transient electromagnetic responses of homogeneous polarized half-space, polarized layered earth model and 3D polarized body in homogeneous half-space, then discuss the laws of the induced polarization effects on transient electromagnetic responses. The calculation of theoretical model show that the induced polarization effects on transient electromagnetic responses are influenced by geometric,electrical and induced polarization parameters. the shorter of the distance between transmitter and receiver , the stronger of induced polarization ;the bigger of complex resistivity parameters of polarized body or adjacent bed resistivity,the stronger of induced polarization;the shallower of the depth of polarized body,the stronger of induced polarization. When using different array (dipole electrode array or equatorial array),the transient responses have bigger difference. When the second layer is polarized on layered earth model,the transient responses curve of bigger distance between transmitter and receiver become complex. Cognition and summarizing these laws can help to better interpret the data of transient electromagnetic.The production of study further promotes the development of 2.5D complex resistivity forward and inversion. This paper realizes 2.5D complex resistivity forward and inversion of the electric dipole source and summarizes the induced polarization effects on transient electromagnetic response. It has important theoretical and practical significance.