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PACIFIC GEOSCIENCE CENTRE EARTH PHYSICS BRANCH DEPARTMENT OF ENERGY, MINES AND RESOURCES, SIDNEY BC Canada , V8L 4B2
Abstract
Maximum likelihood estimation of the earthquake parameters No and ß in the relation N = No exp (–ßm) is extended to the case of events grouped in magnitude with each group observed over individual time periods. Asymptotic forms of the equation for ß reduce to the estimators given for different special cases by Aki (1965), Utsu (1965, 1966), and Page (1968). The estimates of ß are only approximately chi-square distributed. For sufficiently large numbers of events, they can be estimated from the curvature of the log-likelihood function.
Sample calculations for three earthquake source zones in western Canada indicate that for well-constrained data sets, the often-used, least-squares estimation procedures lead to compatible results, but for less well-defined data sets, the effect of subjective plotting and weighting methods used for least-squares fitting leads to appreciably different parameters.
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