Exploring Temporal Variation of the b-value in Mainshock-Aftershock Sequences with the b-Bayesian Probabilistic Approach

Temporal variations of the b-value, the parameter describing the frequency distribution of earthquake magnitudes, also known as the Gutenberg-Richter law, are believed to provide critical insights into the physical processes governing earthquake sequences. Such temporal variations are often difficult to estimate because of the sudden changes in the detectability of events. The standard maximum likelihood estimate for b-value, requires truncating the seismic catalogue above a "completeness" magnitude threshold, above which all earthquakes are supposed to be detected. However, temporal variations of detectability are particularly important for mainshock-aftershock sequences, which are subject to short-term aftershock incompleteness. The b-positive approach and its recent updates are adaptations of the maximum likelihood approach to circumvent the completeness magnitude dependence for mainshock-aftershock sequences, but this method still relies on the arbitrary choice of moving-window size to capture variations in the b-value estimate. To address these challenges, we use the recent probabilistic b-Bayesian approach to jointly invert for the temporal variations in b-value and detectability. Such a probabilistic approach also provides time variations of uncertainties for these two quantities.
We will present results of the application of b-Bayesian for seismic sequences presenting short-term aftershock incompleteness, and show the potential of Bayesian methods to avoid over-interpretations of b-value temporal variations in context of large detectability changes.