An approximate hybrid method for modeling of electromagnetic scattering from an underground target

Abstract

The main focus of this thesis is to develop and analyze a fast and accurate hybrid method, simplified integral equation (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 integral equation (IE) method to obtain the field outside that region. The hybrid method thus replaces the dense-matrix part of the rigorous IE method by sparsematrix calculations based on an approximation of Maxwell's Equations. The thesis is divided into two parts. Part I, is devoted to overview and background theory and is structured as follows: Chapter 1 provides a general introduction and presents a general framework of forward and inverse modeling. An introductory discussion of model parameters, such as porosity, saturation and electrical conductivity, is presented in Chapter 2. Emphasis has been placed on the relationship between conductivity and saturation through Archie's law. Exploration and monitoring of a petroleum reservoir are important applications of the marine controlled source electromagnetic (CSEM). These applications are presented in Chapter 3. Chapter 4 provides a review of different electromagnetic modeling approaches. In addition, detailed derivation of integral formulation of Maxwell's Equations is presented. Different solutions and approaches in the frequency domain are discussed in Chapter 5. Emphasis has been placed on IE and SIE methods. All the praises and thanks be to ALLAH for giving me the life, strength, and spirit, to complete my research in a manner that advances both my purpose in the life and the science of mathematics. Also, my beloved Prophet, Mohamed (peace be upon him), ALLAH protect you and your family. There are many people whom I would like to thank. First of all, I would like to thank my principle supervisor Trond Mannseth for his guidance, helpful discussions and continuous encouragement during the development of this work. I am also grateful for the help and support from my advisors Martha Lien and the late Magne Espedal. I would like to thank VISTA for the funding of this project. I would also like to thank friends and colleagues at CIPR for a good research environment and company for lunch. Special thanks to Mona Wolff (human resources manager) for her smile and ability to handle any social problem. I am very grateful to my beloved parents who taught me the value of education, specially for my dear father who passed away last year before seeing my success. Also, special thanks are due my wife and my three children, Radwa, Sohila and Mohamed, whose endless support and understanding have been profound throughout the difficult times of this PhD study. Without your love and support I am sure that I would not have been able to achieve so much.