Date of Award
Doctor of Philosophy
Chris H. Cramer
Arleen A. Hill
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.
dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.
Kutliroff, Jerome Robert, "Estimating the Proportions of Large to Small Earthquakes in Seismic Regions with a Short Span of Earthquake Magnitudes" (2017). Electronic Theses and Dissertations. 1679.