The Diffusion Equation Method for Global Optimization and Its Application to Magnetotelluric Geoprospecting

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Hartman-Baker, Rebecca Jean

Contributors dc:contributor

• Heath, Michael T.

• Computer Science

Language dc:language

eng

Identifier

(MiAaPQ)AAI3199014

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/81683