Analysis of the spatial distribution and temporal variation of the Completeness Magnitude and b-value in the Gutenberg-Richter law

This Ph.D. thesis presents a detailed study the spatial distribution and temporal variationof the Magnitude of Completeness (Mc) and b-value parameters, fundamental to theGutenberg-Richter Distribution (GR) within a seismically active region. The main objectiveis to provide a nuanced understanding of local seismicity through statistical analysis ofrecorded earthquake data. The research begins with a rigorous construction and validationof seismic catalogues, ensuring a robust foundation for further analysis. Mc, which definesthe minimum magnitude at which events are reliably recorded, is a critical parameterfor catalogue accuracy and is studied here with advanced estimation techniques, such asMaximum Curvature and other tests. These methods allow for a precise delineation of Mcacross temporal and spatial domains, identifying completeness thresholds critical for seismicmodelling. The second focus, the b-value, reflects the relative frequency of smaller tolarger earthquakes and is essential for assessing regional tectonic stress and seismic hazardpotential. Through advanced statistical analysis techniques and computational methods,including Maximum Likelihood Estimation (MLE) and b-positive, this study evaluatesb-value variations across different geodynamic settings. A comprehensive comparativeanalysis examines the Mc and b-value across Italy, Taiwan, and Iceland, each characterizedby unique tectonic activities. Italy’s complex plate interactions, Taiwan’s convergentboundary dynamics, and Iceland’s mid-ocean ridge environment highlight how localgeodynamic conditions shape seismic patterns. The study further applies the EpidemicType Aftershock Sequence (ETAS) model to distinguish mainshocks from aftershocks,enhancing the understanding of clustering patterns within the seismic data of Sicily. Thisapplication supports the exploration of spatiotemporal seismic behaviour and correlateswith regional geodynamic factors. Furthermore, this thesis introduces the Tremors softwaretool developed to streamline the calculation and visualization of the Mc and b-value,particularly addressing the challenges posed by short-term aftershock incompleteness. Thisinnovative tool not only aids in effective data processing, but also adapts to varied seismicconditions, contributing a valuable resource for both academic and applied seismology.This research provides a comprehensive framework for applied seismology, advancing theunderstanding of seismicity in complex tectonic regions. Its findings have implications forseismic risk assessment and offer foundational insights for future seismological research.