Gutenberg-Richter b -value maximum likelihood estimation and sample size

摘要: The Aki-Utsu maximum likelihood method is widely used for estimation of the Gutenberg-Richter b-value, but not all authors are conscious method’s limitations and implicit requirements. Aki/Utsu requires a representative estimate population mean magnitude; requirement seldom satisfied in b-value studies, particularly those that use data from small geographic and/or time windows, such as b-mapping b-vs-time studies. Monte Carlo simulation methods to determine how large sample necessary achieve representativity, rounded magnitudes. size weakly depends on actual b-value. It shown that, commonly precisions, samples give meaningless estimations b. Our results estimates probabilities getting correct b given desired precision different sizes. We submit published studies reporting should include information about used.