Electronic Theses and Dissertations

Identifier

5983

Date

2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Earth Sciences

Concentration

Geophysics

Committee Chair

Chris H. Cramer

Committee Member

Oliver Boyd

Committee Member

Eric Daub

Committee Member

Arleen A. Hill

Abstract

The rate at which earthquakes occur is dependent on their magnitudes, a distribution quantified by the Gutenberg-Richter relation. This relation is characterized by a parameter, b, that is a measure of the dependence of the rate on the magnitude. Here, we develop a method to measure b and its associated uncertainty accurately. The maximum likelihood function of Aki (1965) generally used to estimate the b parameter is shown to apply only to a minimum span of magnitudes. Formulas are derived that are accurate for any magnitude span. These formulas also detect the regions of the Frequency-Magnitude Distribution (FMD) that minimize bias in the b-value estimate. A sampling method improves the accuracy of the estimates markedly and provides immediate means to assess uncertainties to the estimates of b. The sources of uncertainties in estimating b are analyzed and bootstrap methods are used to determine the final uncertainty. A comparison to published results using the Aki formula shows that these methods give significantly lower estimates of b for the magnitude spans involved.

Comments

Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.

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