2D Bayesian transdimensional inversion for b-value variations

The 2D Bayesian transdimensional inversion methodology is a data-driven methodology that allows for multiple solutions and does not need regularization. This is because Bayesian transdimensional inversion allows the retrieval of the parameters and the number of parameters needed to explain the data simultaneously. It also has intrinsic parsimony, meaning simple solutions will be chosen over complex ones. For all these reasons, it is a perfect tool to retrieve the spatial b-value variation. 
The b-value corresponds to the slope of the Gutenberg–Richter law, which relates the number of earthquakes with 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 by itself. In particular, the spatial changes in the b-value in seismicity catalogs have been associated with different stresses, 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 of the methodologies to retrieve the b-value fix the spatial window of the seismic catalog (i.e., binning) and/or use optimization methods to obtain the values, introducing methodological bias in the solutions. For this reason, we use the Bayesian transdimensional approach to objectively estimate b-value variations along two arbitrary dimensions. This implementation allows a self-defined seismic domain according to the seismic catalog information, where it is unnecessary to prescribe the location and extent of domains, as other methodologies do. 
This study focuses on obtaining 2D spatial b-values changes across the seismic region. To explore the possible changes in the b-value along the space, we use the TransTessellate2D algorithm that allows us to implement the trans-dimensional inference methodology for 2D cartesian problems with Voronoi cells. The synthetic tests were performed to analyze the spatial resolution of the methodology and the smallest b-value variation that the method can retrieve. This methodology has been successfully implemented in central-northern Chile and California, allowing us to characterize the mechanical behavior on the plate interface of subduction and cortical zones, obtaining a similar solution to previous studies, evidencing the reliability of the Bayesian transdimensional method for capturing robust b-value variations. Our future work includes extending the approach to other 2D dimensions (e.g., time, latitude, longitude, depth).