Efficient computational methods for electromagnetic imaging with applications to 3D magnetotellurics

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Publication Type dissertation
School or College College of Science
Department Mathematics
Author Kordy, Michal Adam
Title Efficient computational methods for electromagnetic imaging with applications to 3D magnetotellurics
Date 2014-12
Description The motivation for this work is the forward and inverse problem for magnetotellurics, a frequency domain electromagnetic remote-sensing geophysical method used in mineral, geothermal, and groundwater exploration. The dissertation consists of four papers. In the first paper, we prove the existence and uniqueness of a representation of any vector field in H(curl) by a vector lying in H(curl) and H(div). It allows us to represent electric or magnetic fields by another vector field, for which nodal finite element approximation may be used in the case of non-constant electromagnetic properties. With this approach, the system matrix does not become ill-posed for lowfrequency In the second paper, we consider hexahedral finite element approximation of an electric field for the magnetotelluric forward problem. The near-null space of the system matrix for low frequencies makes the numerical solution unstable in the air. We show that the proper solution may obtained by applying a correction on the null space of the curl. It is done by solving a Poisson equation using discrete Helmholtz decomposition. We parallelize the forward code on multicore workstation with large RAM. In the next paper, we use the forward code in the inversion. Regularization of the inversion is done by using the second norm of the logarithm of conductivity. The data space Gauss-Newton approach allows for significant savings in memory and computational time. We show the efficiency of the method by considering a number of synthetic inversions and we apply it to real data collected in Cascade Mountains. The last paper considers a cross-frequency interpolation of the forward response as well as the Jacobian. We consider Pade approximation through model order reduction and rational Krylov subspace. The interpolating frequencies are chosen adaptively in order to minimize the maximum error of interpolation. Two error indicator functions are compared. We prove a theorem of almost always lucky failure in the case of the right hand analytically dependent on frequency. The operator's null space is treated by decomposing the solution into the part in the null space and orthogonal to it.
Type Text
Publisher University of Utah
Subject Finite element method; Inverse problem; Magnetotellurics; Maxwell's equations; Model order reduction; Rational krylov subspaces
Dissertation Institution University of Utah
Dissertation Name Doctor of Philosophy
Language eng
Rights Management Copyright © Michal Adam Kordy 2014
Format Medium application/pdf
Format Extent 3,119,013 bytes
Identifier etd3/id/3313
ARK ark:/87278/s6nw2sgx
Setname ir_etd
Date Created 2015-02-19
Date Modified 2017-10-02
ID 196878
Reference URL https://collections.lib.utah.edu/ark:/87278/s6nw2sgx