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Studying On1D Parameterized Inversion And3D Finite Volume Simulation Of Controlled-source Electromagnetic Method In Anisotropic Formation

Posted on:2015-02-25Degree:DoctorType:Dissertation
Country:ChinaCandidate:J M ZhouFull Text:PDF
GTID:1260330428482994Subject:Theoretical Physics
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Controlled source audio magnetotelluric (CSAMT) is a ground source frequencydomain sounding artificial methods developed on the basis of magnetotelluric (MT)and audio magnetotelluric (AMT). Because the execution ground source is randomand the signal is weak, observation for MT is very difficult. CSAMT workshop usecontrolled sources. CSAMT is an important geophysical exploration methods, whichwidely used in a variety of geological survey, exploration of oil, natural gas,geothermal, metallic minerals, hydrology, engineering, environmental protection andother complex exploration ground structure.Modeling and inversion of CSAMT in1D isotropic horizontally layeredformations is very important, because1D model is simple and its analytical solutionexists, it helps to understand the basic physical properties of the electromagnetic fieldas a basic geoelectric model, it is also the basis of preliminary interpretation andanalysis of data, selected initial model of the multi-dimensional inversion. Electricalanisotropy is always present on some scale, for example, alternating layers of thinsand shale is a typical anisotropic configuration. Data interpretation without consideranisotropy for the anisotropic formations will be difficult to get effective inversionresults. Therefore, the study of anisotropic formation CSAMT inversion theory is avery important issue.In this thesis, we study the modeling and inversion of CSAMT in1D anisotropichorizontally layered formations, discuss the impact of anisotropy for the CSAMTresponse, and provide a theoretical basis and practical guidance for the interpretationof the data. Like other geophysical inverse problems, inversion of CSAMT in1Danisotropic horizontally layered formations includes forward calculation, choosemodel space, Fréchet derivatives,and iterative correction to get effectively inversionresults.In chapter two, Using the two-dimensional Fourier transform and matrix decomposition techniques, Maxwell equations decompose into two transmission lineequation of TM and TE waves. Appling the transmission line theory and superpositionprinciple, according to the characteristics of CSAMT only using electric dipolesource, we improve the transmission line algorithm by only introducing the currentsource transmission line Green function to solve TM and TE waves. Then weestablish a new algorithm for electric and magnetic current source dyadic Green’sfunctions in frequency-wavenumber domain. Compared to conventionaltransmission line theory, the new algorithm can improve the efficiency of forward ofCSAMT. On this basis, using the fundamental solution of transmission lines Greenfunction and boundary conditions, and appling the generalized reflection coefficientand amplitude recursive formula, we obtain the analytical solutions of transmissionline Green’s function for each stratum; then using the inverse Fourier transform andBessel formula, CSAMT response can be expressed as the Sommerfeld integral form.According to the characteristics of the layered model, this paper presents a cubicspline interpolation technique combined Lommel integral formula to calculate theSommerfeld integral. Compared to digital filtering algorithm commonly used ingeo-electromagnetic community, our method is faster with the same accuracy.In chapter three, we select the parametric model space which can obtain thequantitatively inversion model parameter. Aiming at the characterisation of the1-Danistropic media that is piecewise constant, we first introduce a model vectorcomposed of not only the horizontal and vertical conductivities but also the depths ofhorizontal interfaces. We give the expressions of the spatial distribution ofconductivity in the anistropic media described by the model vector and theperturbation in the conductivity determined by change in the model vector. Then thedyadic Green’s functions given by Michalski and Mosig are applied to model theCSAMT responses in the media and to compute the Fréchet derivatives of theCSAMT response with respect to model vector. In order to enhance the computationalefficiency, we derive the analytic expressions of the Fréchet derivatives in the form ofSommerfeld integral and apply semi-analytical algorithm by the combination of cubicspline interpolation and Lommel integral formula to determine the synthetic CSAMT data and all components of Fréchet derivatives. Furthermore, we establish anadaptively regularized inversion of CSAMT data to simultaneously reconstruct allmodel parameters. Finally, we present numerical results to validate the algorithm.Numerical results showed that CSAMT data is much less sensitive to the verticalconductivity than to other model parameters. The inversion of CSAMT data in1-Danisotropic media recovers the main features of the model despite large initial errorsexist. Choice of initial interfaces is very important to improve inversion results.Whole parameter inversion improves the inversion results much better than theinversion with fixed interfaces but with wrong values. The inversion is also effectivefor the case that the layer number of the initial model being different from that of thetrue model.Marine controlled source electromagnetic (MCSEM) is the frequency domainelectromagnetic method used for subsea oil and gas exploration. Since its ability toprovide spatial distribution of resistivity of subsea formation, MCSEM is becomingan important tool for both offshore hydrocarbon exploration and gas-hydrateidentification.The seabed may have complex structure including bathymetryvariations, near-surface variations of resistivity, anisotropy, and targets close toresistive basements. Survey design and data processing and interpretation of MCSEMneed a lot of numerical simulations.3D forward method for MCSEM becomes aresearch topic since1D and2D forward technology for MCSEM is becoming mature.The method for3D forward of MCSEM include finite element, finite difference, finitevolume and integral equation method. Based on Yee ’s staggered grid, finite volumemethod for Maxwell’s equations on each unit’s integral discrete treatment, it caneffectively reduce the order of the differential equation, and also can reduce theimpact on the formation of discontinuous discrete conductivity results. In this thesis,we develop a finite volume method to simulate the response of MCSEM in3Danisotropic formation.In order to effectively simulate three-dimensional marine controlled sourceelectromagnetic (CSEM) response in anisotropic formation, a coupled potential finitevolume method is established. As Electric field decompose by vector potential and scalar potential, the Maxwell’s equation is reformulated into Helmholtz equations interms of coupled scalar-vector potentials with Coulomb gauge. As the results, itovercome the low induction numbers problems. Then Yee’s staggered girds, finitevolume averaging and interpolation technique are used to discrete the Helmholtzequations. After that, a large, sparse and complex linear system with a blockdiagonally dominant structure is obtained. A direct solver PARDISO is applied tostalely and accurately solve the system of large-scale models. In order to improve theaccuracy of the near field without significantly reduce the computational efficiency, amethod using difference fields is proposed to reduce the source singularity effect ofanisotropic formation. The anisotropic modeling examples show that marine CSEMresponse is predominantly sensitive to reservoir vertical resistivity and not to reservoirhorizontal resistivity, provided that the reservoir are thin and high-resistivity; but themarine CSEM response is sensitive to both horizontal and vertical resistivity of theoverburden on top of the reservoir.
Keywords/Search Tags:controlled-source electromagnetic method, anisotropic, parameterized inversion, finite volume method, direct method
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