Modeling Of Time-domain SIP Method In Consideration Of Electromagnetic Effect

Spectrum Induced Polarization method (SIP) is also called Complex Resistivity method (CR), which is a new branch of Induced Polarization method (IP) developing all over the world during 1970s. Nowadays, Complex Resistivity method has become one of hotspots in the fields of electrical prospecting research in the world. Time-domain SIP method is developed from Complex Resistivity method in frequency-domain. Because Time-domain SIP method by measuring the time spectrum can greatly increase productivity and cut down costs,compared to Complex Resistivity method by measuring the frequency spectrum one by one,it has more broad prospects in application.The thesis is the study of the theory of Time-domain SIP method, including 1-D forward modeling and 2.5-D forward modeling by finite element method and their algorithms. We successfully solve the problem of numerical integration of the Hankel transform in 1D forward,and obtain accurate results by continued fraction algorithm. A 2.5-D forward issue is focused on in my study. Unlike Meng's and Luo's algorithms in 2000, I derive a couple of more simplified independent equations of the electric and magnetic fields from the frequency-domain Maxwell equations. In order to complete this 2.5-D forward modeling, a triangle lattice is used to simulate complex medium; those equations are discreted based on the mature finite element method and the secondary field algorithm is applied. In particular, Some explicit expressions for primary field is derived in spatial frequency domain. The results in the frequency and the spatial frequency domains are transformed into the time and spatial domains followed by the use of inverse Fourier and inverse Laplace transforms. Moreover, the Cole-Cole model is introduced to consider IP effects in both 1-D and 2.5-D forward modeling results.Based on these theories and algorithms above, I write the codes of 1-D forward on FORTRAN and the codes of 2.5-D forward by finite element method on MATLAB. The codes of 1-D forward are correct because the results of 1-D numerical simulation meet the analytic solution, and the codes of 2.5-D forward are also reliable according to the comparison of the results of 1-D and 2.5-D numerical simulation. Seven model are established to simulate geoelectric cross section. The results of model 1,2 and 5 show that the one-dimensional and 2.5-D forward modeling code are both reliable. And the results of other models show that, in consideration of the electromagnetic effect and the IP effect simultaneously, IP effect can be distinguished in late time spectrum and is regular. Therefore,the IP information of the low-resistivity polarizable body can be obtained in late time spectrum through the observation of the transient response of total field on the ground.