Do spatial and/or temporal b-value variations exist within the Groningen induced earthquake catalogue?
Authors: Muntendam-Bos Annemarie , Güdük Nilgün 
Published: March 2021

&lt;p&gt;We present a data-driven analysis to derive whether statistically significant spatial and/or temporal Gutenberg-Richter b-value variations exist within the induced earthquake catalogue of the Groningen gas field. We utilize the method developed by Kamer and Hiemer (2015; J. Geophys. Res. Solid Earth, 120, doi:10.1002/2014JB011510 ) which is based on optimal partitioning using Voronoi tessellation, penalized likelihood, and wisdom of the crowd philosophy. Our implementation derives both the magnitude of completeness and the b-values simultaneously. The magnitude of completeness is computed with the maximum curvature method with a correction applied to avoid bias due to catalogue incompleteness. Finally, following Marzocchi et al. (2020; Geophys. J. Int. 220, doi: 10.1093/gji/ggz541) the b-values computed are corrected for bin size and small sample sizes.&lt;/p&gt;&lt;p&gt;In a first step we have limited the analysis to spatial variations in the b-values. A significant advantage of the approach taken is that it is feasible to also derive b-values in regions of very low data density. We will show that a statistically significant variation in b-values is obtained. Very low b-values (b&lt;0.8) are observed in the central-northern part of the gas field. However, in the west near the production cluster Eemskanaal (EKL) and in the east near the city of Delfzijl significantly higher b-values (b&gt;1.1) are observed. A Kolmogorov-Smirnov test of frequency-magnitude distributions for the two areas obtains a p-value of 1.5 10-13 and 2.3 10-12 for the EKL region and Delfzijl regions, respectively, rendering the difference more than statistically significant at the 99% confidence level.&lt;/p&gt;&lt;p&gt;In a second step we extended the spatial analysis to a spatial-temporal analysis. The results of the analysis show that the Groningen earthquake database is too small to derive meaningful spatial results for the full Groningen gas field based on multiple random temporal nodes.&amp;#160; We divided the dataset in two almost equal datasets: both containing roughly 50% of the data and of comparable spatial resolution. Spatial analysis of these two subsets of the catalogue shows a significant decrease of the b-values in the central and southern regions. Particularly in the western EKL region the b-value decreases from 1.2 to 0.92. The decrease is close to significant at the 90% confidence level. The northern region exhibits comparable low b-values in both periods. As the data in the first decade is primarily concentrated in the northern region, we have attempted to assess the spatial b-value here in the period prior to 2005. We find the high b-value area is significantly smaller and the minimum value is higher (b = 0.96 pre-2005 versus b = 0.88 post-2012). The difference is significant only at the interquartile level, but the model resolution is low.&lt;/p&gt;&lt;p&gt;Based on our results, we could conclude a spatial and temporal variation in b-value is observed. However, despite our efforts to limit bias in the derivation, variations could still result from the presence of a truncation. Hence, we will extend the current analysis by a comparable analysis assuming a constant b-value and estimating the corner magnitude of a taper truncation.&lt;/p&gt;