A statistical framework for detection of b-value anomalies in Italy

Abstract

This study presents a new robust statistical framework, in which to measure relative differences, or deviations from a hypothetical reference value, of Gutenberg-Richter b-value. Moreover, it applies this method to recent seismicity in Italy, to find possible changes of earthquake magnitude distribution in time and space. The method uses bootstrap techniques, which have no prior assumptions about the distribution of data, keeping their basic features. Excluding Central Italy, no significative b-value variation is found, revealing that the frequency-magnitude distribution exponent is substantially stable or that data are not able to reveal hidden variations. Considering the small size of examined magnitude samples, we cannot definitively decide if the higher b-values in Central Italy, consistently founded by all applied tests, have a physical origin or result from a statistical bias. In any case, they indicate short-lived excursions which have a temporary nature and, therefore, cannot be associated solely to spatial variations in tectonic framework. Both the methodological issues and the results of the application to seismicity in Italy show that a correct assessing of b-value changes requests appropriate statistics, that accurately quantify the low accuracy and precision of b-value estimation for small magnitude samples.