Data-driven spatial b value estimation with applications to California seismicity: To b or not to b

In this paper we present a penalized likelihood-based method for spatial estimation of Gutenberg-Richter's b value. Our method incorporates a nonarbitrary partitioning scheme based on Voronoi tessellation, which allows for the optimal partitioning of space using a minimum number of free parameters. By random placement of an increasing number of Voronoi nodes, we are able to explore the whole solution space in terms of model complexity. We obtain an overall likelihood for each model by estimating the b values in all Voronoi regions and calculating its joint likelihood using Aki's formula. Accounting for the number of free parameters, we then calculate the Bayesian Information Criterion for all random realizations. We investigate the ensemble of the best performing models and demonstrate the robustness and validity of our method through extensive synthetic tests. We apply our method to the seismicity of California using two different time spans of the Advanced National Seismic System catalog (1984-2014 and 2004-2014). The results show that for the last decade, the b value variation in the well-instrumented parts of mainland California is limited to the range of (0.940.04-1.150.06). Apart from the Geysers region, the observed variation can be explained by network-related discrepancies in the magnitude estimations. Our results suggest that previously reported spatial b value variations obtained using classical fixed radius or nearest neighbor methods are likely to have been overestimated, mainly due to subjective parameter choices. We envision that the likelihood-based model selection criteria used in this study can be a useful tool for generating improved earthquake forecasting models.