A Robust Statistical Framework to Properly Test the Spatiotemporal Variations of the b-Value: An Application to the Geothermal and Volcanic Zones of the Nevado del Ruiz Volcano

Abstract Estimating and testing b-value changes spatially and temporally is challenging due to the lack of constraints in the methodology. Commonly, only the direct information of earthquake catalogs is used to test the b-value variation hypotheses, and the same dataset is used both to define anomalous spatiotemporal areas and to perform the test. Here we propose a rigorous statistical framework to estimate and test b-value spatial and temporal differences. This framework is then applied to earthquake magnitude data from the Nevado del Ruiz Volcano (NRV) in Colombia acquired between 2000 and 2018. Our b-value spatial analysis is constrained by geological and geophysical data of the study area, and the timing of volcanic eruption periods is used for temporal variations of b-values. High b-values with a low level of uncertainty occur within a geothermal zone at the NRV and over a zone of magmatic activity. The b-value spatial test is validated using a novel weighted likelihood method that clearly defines these high b-value anomalies. In terms of temporal variations, contrary to observations at other volcanoes, high b-values are obtained outside eruption time windows, whereas during eruption periods the b-value decreases. Our framework sets a foundation for distinguishing spatial and temporal b-value behavior in other active seismic zones.