Three-Dimensional Magnetotelluric Forward Modeling By The Method Of Thin Layer Approximation

This paper deals with the application of the thin layer approximation in3-D MTforward modeling.Thin-layer approximation method was first put forward in theresearch of natural electromagnetic field in heterogeneous media by A.T.Price(U.S1949).T.R.Madden with his students R.P.Ranganayaki and S.K.Park given a furtherstudy on this basis. The key of thin layer approximation method is establishingequations by using FDM(Finite difference method) in wave number (kx,ky,z)domain.In the horizontal level,the x and y variable,in the spatial domain(x, y, z),isconverted to the wavenumber domain(kx and ky) by fourier transform to simulate theelectromagnetic field in the horizontal symmetric anisotropic media. And then,useingthe mean of vertical field value variation to approximation instead of the vertical fieldvalue derivative, use the horizontal derivative of field value in the bottow of layer tosimilar alternative the horizontal derivative of field value about the level of thehorizontal layer. The field value of the top layer is equal to the bottom layer whichadjacent to the surface, by the continue boundary condition of tangential componentof electromagnetic fields in the interface. So that we can use the finite differencemethod (FDM) to establish the recurrence relations of the layers from the bottom.Combined with the source and boundary conditions at th earth surface, we can obtainthe model electromagnetic field response in wave number domain. After a inverseFourier transform, we can get electromagnetic fields in spatial domain. Theoretically,the thin layer approximation method can calculate electromagnetic fields at randomposition.This article refer to S.K.Park’s field value method, arrangement and improverelevant programs, and establish a model that contains only a relatively low resistivitymedium, to simulate the electromagnetic fields or the apparent resistivity response indifferent conductivity tensor and the initial value of K. Include the following twoparts:①XY and YX mode apparent resistivity curves are parted in the apparentresistivity value axes,λ=1curve is the symmetrical line, associated with the increaseof conductivity tensor anisotropy parameters λ; With anisotropic electrical spindle and the measurement axis angle increase from0degrees to90degrees, the apparentresistivity response curve confined to the area consisting of XY and YX apparentresistivity curve in θ=0and the apparent resistivity axis. The XY and YX apparentresistivity curve exchange the distribution range after the45degrees.②By differentcombinations of initial Kx and Ky parameters,we can get a set of XY and YX modes’field response to analysis its effect about the simulation. The results show that theinitial Kx and Ky parameters can be considered as the physical property distributionin the measurement layer interface. When measured at the earth surface, the air layer’sbottom boundary is the top of the measurement surface.So that the initial Kx and Kyparameter is taken as0.The initial wave number of parameters should be calculatedaccording to actual situation when measurement position is located in the layerIn order to verify the correctness of the method, give some forward modelingabout four typical three-layer horizontally layered homogeneous medium model. Bothfit very well when compared the simulation results of the thin layer approximationwith the one-dimensional magnetotelluric forward analytical solution results. Theresults indicate that the thin layer approximation method with hjgh accuracy iscredible and effective.Then, we establishment a L-shaped low resistivity model simulation, andanalysis the response informations of model electromagnetic fields,apparentresistivity,phase,and skewness at different frequencies. Using a single high or lowresistivity model and a hybrid model to simulate the response information for furtherverification.In the hybrid model simulation, giving different values of basal parameters toanalysis the effect of different substrate parameters about the simulation by combinedwith the apparent resistivity and phase response information in the XY and YXmode.The results show that the resistance of high-resistivity base is more conduciveto the discovery of the abnormal body.At last,simulation of a complex models.Theresults reveal the good prospect of applying the thin layer approximation in MTmeasurements in the condition of complex structrure.