The Diffusion Equation Method for Global Optimization and Its Application to Magnetotelluric Geoprospecting
Hartman-Baker, Rebecca Jean
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https://hdl.handle.net/2142/81683
Description
Title
The Diffusion Equation Method for Global Optimization and Its Application to Magnetotelluric Geoprospecting
Author(s)
Hartman-Baker, Rebecca Jean
Issue Date
2005
Doctoral Committee Chair(s)
Heath, Michael T.
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
In geoprospecting, the conductivity of rock is determined from its effect on electromagnetic waves. From the conductivity, we can deduce the type of rock (or oil or water) and the nature of the geological formation. Unfortunately, electromagnetic inverse problems of this kind are ill-posed. We investigate the use of the Diffusion Equation Method (DEM) for global optimization in implementing an approximate quasisolution method for determining the size, shape, and orientation of an underground deposit. We examine the theoretical underpinnings of the DEM, first discussing the concepts of smoothing and continuation and then establishing the effects of diffusion upon sinusoids and polynomials. From these foundations, we explain the effect of diffusion upon coercive functions and its implications for solving global optimization problems. We examine the robustness of the DEM and its limitations in finding the global optimizer, introduce a discrete DEM using finite differencing, and compare its cost to other global optimization methods. The main computational expense for this application is in repeatedly evaluating the objective function, which fortunately can be done in a highly parallel manner. We discuss our parallel implementation of the magnetotelluric geoprospecting objective function and discrete DEM, and analyze the performance and scalability of our approach.
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