An approximate hybrid method for modeling of electromagnetic scattering from an underground target
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The detection of a potential petroleum reservoir is achieved through inversion of electromagnetic data acquired in sea floor receivers. Inversion of electromagnetic data requires a number of repeated solves of the mathematical/numerical model in an iteration process. The computational efficiency of the solver will therefore have great impact of the computational efficiency of the inversion. Various types of solvers, like finite difference, finite element, integral equation (IE), and hybrid methods, have been applied. The different types of methods have different computational advantages and disadvantages. With rigorous IE, a dense-matrix problem must be solved. For problems involving many grid cells in the target region, a huge computational effort is then needed. The main focus of this thesis is to develop and analyze a fast and accurate hybrid method, simplified IE (SIE) modeling, for modeling of electromagnetic scattering from an underground target. The method consists of solving a finite volume problem in a localized region containing the target, and using the IE method to obtain the field outside that region. The hybrid method thus replaces the dense-matrix part of the rigorous IE method by sparse matrix calculations based on an approximation of Maxwell’s Equations. The thesis shows that both theoretical and practical computational performance of SIE is orders of magnitude better than that of rigorous IE on large-scale problems. Also, SIE produced excellent accuracy for typical CSEM frequencies. The thesis presents a novel order-of-magnitude analysis for Maxwell’s equations and a proper assessment of the range of validity of a novel approximate method for CSEM.
Paper A: Geophysics, Volume 74( 5) A P. F107-F117, Shaaban A. Bakr and Trond Mannseth, Feasibility of Simplified Integral Equation Modeling of Low frequency Marine CSEM with a Resistive Target, Published version. Copyright 2009 Society of Exploration Geophysicists. All rights reserved. Reproduced with permission. The published version is also available at: http://dx.doi.org/10.1190/1.3192910Paper B: Shaaban A. Bakr and Trond Mannseth, Numerical Investigation of the Range of Validity of a Low-Frequency Approximation for CSEM. Published in 72nd EAGE Conference and Exhibition, Barcelona, Expanded Abstracts, P.D34–D38. 2010. Published version.Paper C: Shaaban A. Bakr and Trond Mannseth An Approximate Hybrid Method for Electromagnetic Scattering from an Underground Target: Part 1 – Accuracy and Range of Validity D Fast 3D Modeling of the Low-Frequency CSEM Response of a Petroleum Reservoir. Submitted to IEEE Transactions on Geoscience and Remote Sensing. Full text not available in BORA.Paper D: Shaaban A. Bakr and Trond Mannseth, Fast 3D Modeling of the Low-Frequency CSEM Response of a Petroleum Reservoir. Published in 79th Annual International Meeting, SEG, Expanded Abstracts, P. 669-673. Published version. Copyright 2009 Society of Exploration Geophysicists. All rights reserved. Reproduced with permission.Paper E: Shaaban A. Bakr and Trond Mannseth An Approximate Hybrid Method for Electromagnetic Scattering from an Underground Target: Part 2 – Computational Complexity and Cost. Submitted to IEEE Transactions on Geoscience and Remote Sensing, 2010. Full text not available in BORA.