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The Finite Element Method Of Two-dimensional Magnetotelluric Forward And Inversion Research Based On Double Quadratic Interpolation

Posted on:2016-11-17Degree:MasterType:Thesis
Country:ChinaCandidate:Z Q YinFull Text:PDF
GTID:2180330503454617Subject:Geophysics
Abstract/Summary:PDF Full Text Request
Magnetotelluric(MT) sounding is an effective means to study the earth electrical structure based on rock ore electrical difference and using natural alternating electromagnetic field. In terms of the forward-inversion numerical simulation problem carried out by this method, domestic and foreign scholars have already proposed many methods and achieve good results. Combining with some problems of current MT two-dimensional forward-inversion problem, this thesis carries out MT numerical simulation based on the secondary field algorithm and considers abnormal effects of the resistivity and magnetic permeability in the forward-inversion process.This essay starts from the Maxwell equations and deduces the secondary field equations of magnetotelluric method considering abnormal effects of the resistivity and magnetic permeability. In order to improve the calculation accuracy and efficiency, simplified calculation node generation, using the green’s theorem dealing with quadratic field source term, and making use of the secondary field algorithm model trial, using a triangle element meshing based on binary tree structure, derived the unit stiffness matrix expression which used the bilinear and double quadratic interpolation method, simulated the response of abnormal resistivity model and permeability model separately. During actual measurement, the secondary field algorithm is able to reduce section of subdivision and increase computational efficiency without subdividing sections on field source; it is simple in boundary treatment compared to total field algorithm; meanwhile, the consideration on both resistivity and permeability enabled forward modeling the function of multiple parameter abnormal reaction, which can solve the problem of the instability of low frequency calculation on controllable source and increase computational accuracy. The trials and analysis based on a resistivity abnormal modeling and considerations on abnormal modeling of both resistivity and permeability turned out that permeability had an obvious effect on the resistivity of controlled source and leaded to higher resistivity.Based on regularization theory proposed by Tikhonov, this essay focuses on the optimization algorithm of objective function and the identification problem of regularized factor. In addition, several widely applied optimization methods are emphatically analyzed and Quasi-Newton method is selected as the optimization method of objective function. Moreover, introducing improved L-Curve boosts the selection accuracy of regularization factor and the inversion precision and speed, which is verified in the numerical example.
Keywords/Search Tags:Magnetotelluric, The secondary field algorithm, The finite element method, Quasi-Newton method, Two-dimensional inversion
PDF Full Text Request
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