b-transD: Spatial and temporal variation of b-value and their uncertainty using Bayesian trans-dimensional inference

The b-value corresponds to the slope of the Gutenberg–Richter law, which relates the number of earthquakes to their magnitude. Several authors agree that the changepoints of the b-value (i.e., the places where the b-value varies) show more valuable information than the value itself. Spatial and temporal changes in the b-value have been linked to stress variation, fluid processes, geological structures, and earthquake hazard estimation. Given this parameter's importance, robustly retrieving and characterizing b-values and their changepoints is essential.  

In general, most b-value retrieval methodologies fix the spatial or temporal window of the seismic catalog (i.e., binning) and/or use optimization methods to estimate b-values, thereby introducing methodological bias into the solutions.  

In this work, we focus on determining the spatial and temporal variations in b-value to characterize seismic evolution across different regions. On one hand, to explore possible changes in the b-value across space, we use the TransTessellate2D algorithm for 2D Cartesian problems with Voronoi cells, on the other hand, for b-value variation in time, we use the reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm, which allows us to model changes in a single dimension, both algortithm are implemented with a Bayesian trans-dimensional inference methodology.  

The Bayesian transdimensional inversion enables the simultaneous retrieval of both the b-value and the number of b-values necessary to explain the data. It allows for a self-defined seismic domain based on seismic catalog information, eliminating the need to prescribe domain locations and extents. This methodology furthermore has intrinsic parsimony, meaning simple solutions will be chosen over complex ones. As a Bayesian inference method, it also allows for obtaining all the statistical analyses of the solution, including uncertainty and confidence intervals. For all these reasons, it is a perfect tool for retrieving spatial and temporal b-value variation.  

This methodology has been successfully implemented in central-northern Chile and California, helping us characterize the mechanical behavior at the plate interface of subduction and cortical zones. We also apply the methodology to areas with large-magnitude earthquakes and their precursor events (e.g., the 2011 Tohoku, 2015 Illapel, and 2025 Kamchatka earthquakes). Finally, we use both methodologies to obtain results in three dimensions.

Our results show the method's capability to retrieve b-value changes both spatially and temporally. We observe a strong dependence on the number of earthquakes, their distribution, and proximity to obtain a solution with low uncertainty. However, the solutions are consistent with previous studies, further strengthening the reliability of the Bayesian transdimensional method for robustly capturing b-value variations.