| Objectively,the conductivity anisotropic medium of earth media does exist.Along with the development of high precision instruments and equipment of controlled-source electromagnetic method and the requirements on data processing elaboration,the ignorance of the influence of conductivity anisotropic medium may lead to greater deviation of interpretation on controlled-source electromagnetic data,and even worse,the wrong underground geological information would be obtained.Forward modeling is the basis of inverse modeling and data interpretation.However,the existing forward modeling calculation of frequency domain electromagnetic method,mostly,is based on the theory of conductivity isotropic medium,which cannot simulate the real situation of conductivitr anisotropic medium of earth media.Therefore,in the paper,the conductivity anisotropic model is regarded as the precondition for systematically studying on one-dimensional forward modeling method,2.5-dimensional finite element numerical modeling method and three-dimensional vector finite element numerical modeling method on the basis of previous studies,wherein the above-mentioned methods are applicable both to the marine controlled-source electromagnetic methods and to the ground controlled-source audio frequency magnetotelluric methods.Meanwhile,different geoelectric models of the conductivity anisotropic medium are calculated.As well,the influence of conductivity anisotropic medium on controlled-source electromagnetic methods data is analyzed.The electric dipole source CSEM total space electromagnetic response modeling method of conductivity vertical anisotropic medium horizontal stratum frequency domain is realized.According to Maxwell's equations,Magnetic vector potential and scalar potential are introduced,thereby obtaining the electric dipole source CSEM magnetic vector potential boundary value of conductivity vertical anisotropic medium horizontal stratum frequency domain.Then,the magnetic vector potential in the spatial domain undergoes Fourier transform,which is transformed into wave-number domain.And boundary condition recursion is utilized for obtaining wave-number domain electromagnetic field values of all strata in the wave-number domain.Furthermore,Inverse-Fourier transform operation is implemented for obtaining electromagnetic field value of arbitrary position in the spatial domain.This method provides a mathematical instrument for the arbitrary position in the spatial domain background electric field based on three-dimensional controlled source electromagnetic finite element simulation using the secondary field.At last,the influence of conductivity anisotropic medium in the covering layer and middle stratum on controlled-source electromagnetic data is analyzed.The paper makes a study of the 2.5-dimensional numerical simulation of the CSEM based on isoparametric finite element method for the conductivity orthogonal anisotropic medium,which is carried out by taking the influence of the undulating terrain into consideration.With the utilization of fourier transform,electromagnetic coupled equations in wave-number domain of conductivity orthogonal anisotropic medium is therefore deduced.By the adoption of Galerkin weighted residual method,corresponding finite element equations gets deduced.By employing the arbitrary quadrilateral element,the research area is subdivided.Together with the implementation of the biquadratic interpolation in the unit,the finite element equations is converted into linear algebra equations;and solving the linear equations and the Inverse-Fourier transform,the electromagnetic field value in spatial domain is consequently obtained.Finally,it renders the analysis on the influence of different anisotropic medium coefficients on MCSEM electromagnetic response as well as the influence of conductivity anisotropic medium on MCSEM electromagnetic data under the condition of rugged topography is analyzed.Considering the continuous variation of actual resistivity,the realization of the three-dimensional CSEM node finite element simulation using the secondary field for continuous variation of electrical conductivity within each block is therefor achieved.The extended variational principle is introduced for deducing variation of electric dipole source three-dimensional CSEM secondary electric field boundary value according to secondary electric field boundary value.Arbitrary hexahedral element is adopted for subdividing the research area.In addition,trilinear interpolation is implemented on conductivity and secondary electric field in unit analysis.Controlled-source electromagnetic three-dimensional finite element numerical modeling based on secondary field under the condition of continuous variation of conductivity within each block is realized.The precision of the algorithm is checked through comparing the calculation results of the paper with analytical solution results of stratified models.Effectively,the abnormal form is also reflected through finite element calculation results of a combination model on three-dimensional anomalous body,inclined anomalous body as well as other complex models.The three-dimensional controlled-source electromagnetic modeling using vector finite element method for arbitrary anisotropic medium is realized.The cuboid unit is adopted for subdividing the study area according to the boundary value of conductivity anisotropic medium three-dimensional medium grounded source CSEM secondary electric field and corresponding variation.Field components are defined on the boundary of subdivision elements.Vector finite element method is utilized for solving variation,thereby realizing controlled-source electromagnetic three-dimensional vector finite element numerical modeling of conductivity arbitrary anisotropic medium.The electromagnetic field numerical solution and analytical solution of the one-dimensional conductivity anisotropic medium model are fitted auite well.Regardless of the distance is near or far away from the source,the error is less than 1%.The calculation results of the conductivity anisotropic medium two-dimensional model are fitted extremely well with the non-structural finite element modeling results adopted in existing literature.Accordingly,the numerical results on three-dimensional geoelectric model show that conductivity anisotropic medium tensor conductivity spindle components and Euler angles exert prominent influence on ocean controlled-source electromagnetic response of various devices. |
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