Date of Award

2014

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical Engineering

First Advisor

Kim, Jung H.

Abstract

Receiver functions are time series obtained by deconvolving vertical component seismograms from radial component seismograms. Receiver functions represent the impulse response of the earth structure beneath a seismic station. Generally, receiver functions consist of a number of seismic phases related to discontinuities in the crust and upper mantle. The relative arrival times of these phases are correlated with the locations of discontinuities as well as the media of seismic wave propagation. The Moho (Mohorovicic discontinuity) is a major interface or discontinuity that separates the crust and the mantle. In this research, automatic techniques to determine the depth of the Moho from the earth's surface (the crustal thickness H) and the ratio of crustal seismic P-wave velocity (Vp) to S-wave velocity (Vs) («= Vp/Vs) were developed. In this dissertation, an optimization problem of inverting receiver functions has been developed to determine crustal parameters and the three associated weights using evolutionary and direct optimization techniques. The first technique developed makes use of the evolutionary Genetic Algorithms (GA) optimization technique. The second technique developed combines the direct Generalized Pattern Search (GPS) and evolutionary Fitness Proportionate Niching (FPN) techniques by employing their strengths. In a previous study, Monte Carlo technique has been utilized for determining variable weights in the H- stacking of receiver functions. Compared to that previously introduced variable weights approach, the current GA and GPS-FPN techniques have tremendous advantages of saving time and these new techniques are suitable for automatic and simultaneous determination of crustal parameters and appropriate weights. The GA implementation provides optimal or near optimal weights necessary in stacking receiver functions as well as optimal H and κ values simultaneously. Generally, the objective function of the H-κ stacking problem displays multimodal surfaces with multiple local and global optima. Niching mechanism permits standard GAs to identify different subpopulations representing various peaks. In multimodal optimization, fitness sharing has been commonly used to generate stable subpopulations of individuals around multiple optimum points in the search space. In this study the newly developed FPN is implemented to identify the different local and global optima regions (niches). “Survival of the fittest” from evolutionary concepts is the basis for GA and the approximate location of the highest fitness individual (global optima) is quickly identifiable from the FPN niche masters (cluster centers). Using the approximate global optima location from the FPN as an initial point, the GPS technique provides quicker and optimal solutions for the five variables under investigation – the crustal thickness, Vp/Vs ratio and the three associated weights. Applications of GA and GPS-FPN using seismic data from seismic stations within Ethiopia and surrounding the East Africa Rift System provided results which are consistent with previously published studies. The GPS technique is among the very few provably convergent, derivativefree search methods for linearly constrained optimization problems. GPS is shown in this study to be a powerful optimization tool that provides consistent results as if it searches the parameter space exhaustively. However, GPS searches the parameter space only in a given pattern and computes objective function values at few points. Key features of GPS technique reported in this study also include repeatability of its results, unlike heuristic search approaches, repeatability of the number of iterations as well as the number of objective function evaluations as long as initial values, the lower and upper bounds, and the processing machine stay the same. GPS even produces consistently similar results irrespective of initial values. The limitation of GPS being sometimes trapped at a local optimum is solved in this study by combining it with FPN.

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