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The earthquake Magnitude‐Frequency‐Distribution is usually modeled with the Gutenberg‐Richter law, where the b‐value controls the relative rate of small and large earthquakes. b‐value shows an inverse dependence on differential stress, it increases with fault roughness and in areas with fluid involvement in faulting. b‐value analyses have been also applied to infer temporal evolution of the stress state along active faults or to discriminate between foreshocks and aftershocks. For the Mw 6.5 2016–2017 Central Italy seismic sequence, we show that: (a) away from the major earthquake faults, b‐values are controlled by lithology and style of deformation; (b) the absolute number of the b‐values depends on the adopted magnitude scale and catalog, but differences induced by lithology are preserved; (c) the selection of the fault source volume can strongly influence b‐value changes in time, highlighting some complexities on the applicability of the b‐value as fault stress meter. Plain Language Summary The exact proportion of large and small earthquakes in a particular time or place is defined by the b‐value of the earthquake Magnitude‐Frequency‐Distribution, or the Gutenberg‐Richter law. In this work we document that, away from the fault that hosted the mainshock, the b‐value is influenced by lithology and style of deformation of the involved rocks. For some seismic sequences the evolution of the b‐value with time has been used as a proxy to infer changes of the fault stress state. Our work shows that for this type of analysis the dimension of the fault source volume strongly influences the results, because by enlarging the fault volume it is possible to include deformation/seismicity influenced by lithology that is not connected to the earthquake fault. Key Points Lithology and associated style of deformation control the b‐value The absolute numbers of the b‐values depend on the adopted magnitude scale and earthquake catalog The selection of earthquake fault volume influences b‐value changes in time and its physical interpretation

During an Enhanced Geothermal System (EGS) experiment, fluid is injected at high pressure into crystalline rock, to enhance its permeability and thus create a reservoir from which geothermal heat can be extracted. The fracturing of the basement caused by these high pore‐pressures is associated with microseismicity. However, the relationship between the magnitudes of these induced seismic events and the applied fluid injection rates, and thus pore‐pressure, is unknown. Here we show how pore‐pressure can be linked to the seismic frequency–magnitude distribution, described by its slope, theb‐value. We evaluate the dataset of an EGS in Basel, Switzerland and compare the observed event‐size distribution with the outcome of a minimalistic model of pore‐pressure evolution that relates event‐sizes to the differential stressσD. We observe that the decrease of b‐values with increasing distance of the injection point is likely caused by a decrease in pore‐pressure. This leads to an increase of the probability of a large magnitude event with distance and time. Key Points The b‐values of induced earthquakes decrease with distance from the injection point We propose a pressure‐driven geomechanical model to explain our observation We estimate the probability of induced large magnitude events in space and time

Earthquake magnitude‐frequency distributions exhibit significant space‐time variations, which can provide critical insights into the physical processes driving seismicity. Understanding these variations is crucial for assessing seismic hazards and uncovering the physical processes driving earthquakes. One key parameter, the b‐value, describes the relative proportion of small to large earthquakes and is thought to reflect factors such as stress conditions and fault properties. However, empirical evidence linking b‐value variations to physical processes in real tectonic settings is still limited. Here, we show that b‐value is systematically higher in regions with elevated heat flow, consistently across different tectonic settings and faulting style. This suggests that thermal conditions play a fundamental role in controlling earthquake size distributions, controlling the likelihood of large earthquakes in the different areas.

For the 2016/2017 central Italy earthquake sequence, various studies reported spatiotemporal variations in the Gutenberg–Richter b‐value, including its unexpected increase before the Mw6.5 Norcia mainshock. Here, we investigate this specific observation with a combination of machine learning techniques. Before the mainshock, we identify two seismicity volumes with asynchronous activity, disparate fault orientations, and distinct b‐values. Throughout the sequence, both structures maintain their distinct b‐values; only when combined, the b‐value apparently increases before the mainshock (and drops afterward). Our observation suggests that a temporal b‐value variation in a large volume, or the entire extent of this sequence, originates from individual structures with distinct b‐values being active at different times. More generally, temporal b‐value variations may also reflect changes in the spatial distribution of seismicity besides other underlying processes. Our findings highlight that b‐value interpretation must acknowledge the structural heterogeneity, such as associated fault segments and their orientations.

Gas extraction from the Groningen gas field resulted in significant induced seismicity. We analyze the magnitude‐frequency distribution of these earthquakes in space, time and in view of stress changes calculated based on gas production and reservoir properties. Previous studies suggested variations related to reservoir geometry and stress. While we confirm the spatial variations, we do not detect a clear sensitivity of b‐value to Coulomb stress changes. However, we find that b‐value correlates positively with the rate of Coulomb stress changes. This correlation is statistically significant and robust to uncertainties related to stress change calculation. This study thus points to a possible influence of stress change rate on the probability of the magnitude of induced earthquakes. Plain Language Summary Gas extraction from an underground reservoir in the Netherlands has induced significant seismicity. We analyze how stress changes and the rate of stress changes influence the magnitude of these earthquakes. We find that more smaller earthquakes tend to occur at higher stress change rates. Earthquakes triggered at a lower stress change rate may thus grow to larger magnitudes than those triggered at high stress change rate. This observation is statistically significant and independent of the method used to calculate stress change. Key Points We report a positive correlation between the b‐value and the rate of Coulomb stress change of induced earthquakes in Groningen This trend is statistically significant and robust to changes in the mechanical model used to calculate the stress changes We interpret earthquake growth inhibition through a decrease of nucleation lengths at high stress change rates

Noninvasive diffusion magnetic resonance imaging (dMRI) has been widely employed in both clinical and research settings to investigate brain tissue microstructure. Despite the evidence that dMRI‐derived fractional anisotropy (FA) correlates with white matter properties, the metric is not specific. Recent studies have reported that FA is dependent on the b‐value, and its origin has primarily been attributed to either the influence of microstructure or the noise‐floor effect. A systematic investigation into the inter‐relationship of these two effects is however still lacking. This study aims to quantify contributions of the reported differences in intra‐ and extra‐neurite diffusivity to the observed changes in FA, in addition to the noise in measurements. We used in‐vivo and post‐mortem human brain imaging, as well as numerical simulations and histological validation, for this purpose. Our investigations reveal that the percentage difference of FA between b‐values (pdFA) has significant positive associations with neurite density index (NDI), which is derived from in‐vivo neurite orientation dispersion and density imaging (NODDI), or Bielschowsky's silver impregnation (BIEL) staining sections of fixed post‐mortem human brain samples. Furthermore, such an association is found to be varied with Signal‐to‐Noise Ratio (SNR) level, indicating a nonlinear interaction effect between tissue microstructure and noise. Finally, a multicompartment model simulation revealed that these findings can be driven by differing diffusivities of intra‐ and extra‐neurite compartments in tissue, with the noise‐floor further amplifying the effect. In conclusion, both the differences in intra‐ and extra‐neurite diffusivity and noise‐floor effects significantly contribute to the FA difference associated with the b‐value. The current study conducted both in‐vivo and ex‐vivo human brain imaging to investigate the signal mechanism of the FA dependence on the b‐value. We found that both the differences in intra‐ and extra‐neurite diffusivity and noise‐floor effects significantly contribute to the FA difference associated with the b‐value.

Abstract In the Calabrian Arc subduction zone, the notable lack of seismicity at depths near 100 km strongly suggests the presence of slab detachment. Contrary to typical patterns, where b‐values decrease with depth, our b‐value mapping reveals unexpectedly high b‐values at these depths. Within the 100–150 km depth interval, the gradient of the b‐value reaches its peak, indicating a significant reduction in stress. We propose four potential interpretations for these observations: (a) fluid‐induced weakening due to dehydration processes, (b) heterogeneity at the slab tip reducing rupture propagation, (c) creeping zone behavior at the detachment tip, and (d) post‐detachment damage to the rocks, leaving them unable to support stress. These hypotheses remain beyond experimental verification at present. This study underscores the complex interplay of geological processes at depth and their implications for seismic hazard assessment in subduction zones.

Large earthquakes can activate complex aftershock fault networks. In such systems, what controls the spatiotemporal evolution of early aftershocks remains a critical yet unresolved problem. Here, using the 2019 M 7.1 Ridgecrest earthquake as an example, we partition the first 10 days of aftershocks onto 15 branching faults activated by the mainshock. For each branching fault, we assess the spatial and temporal influence of mainshock‐induced Coulomb failure stress change (ΔCFS) on aftershock patterns and b values. We find that positive ΔCFS may promote aftershock occurrence across multiple faults during the initial 3 days following the mainshock, but this effect diminishes afterward. Moreover, on most branching faults, higher aftershock b values tend to be associated with areas experiencing negative ΔCFS and reduced differential stress. These findings indicate that mainshock‐induced stress plays an important role in controlling initial aftershock generation and size‐frequency characteristics, providing constraints on aftershock forecasting in complex fault systems.

We explore the hypothesis that the relative size distribution of earthquakes, or b‐value, systematically depends on the style‐of‐faulting of seismotectonic zones. Because the b‐value has been shown to be inversely proportional to stress, we expect to find b(thrust) < b(strike‐slip) < b(normal). We test this expectation for the case of Italy. We first of all build a seismotectonic zonation model, consisting of 10 distinct tectonic zones. The faulting style of each zone is then characterized by the summed moment tensor of first‐motion and full‐waveform based focal mechanism. We calculate the b‐value for each zone: the lowest values are obtained for reverse zones (0.75–0.81), highest for the normal (1.09), followed by the strike‐slips (0.9–0.92). Our results suggest that b‐values, which are a critical parameter in all seismic hazard assessments, should be set according to the local faulting regimes. In addition, seismotectonic zonation models should take b‐value variations as one input.

The b‐value from the Gutenberg‐Richter law is a crucial parameter in the assessment of seismic hazard. Its temporal variations may also bring useful insights on the processes driving seismicity at depth, even if not yet fully understood. In this paper, we focus on the temporal evolution of the b‐value in the Ubaye Region (French Western Alps) which was hit by seismic swarms (2003–2004) and complex sequences with several mainshocks (2012–2015). The swarm‐like sequences show a common temporal behavior of b‐value characterized by an increase and then a return to the initial level. The temporal b‐value pattern for the mainshock‐aftershock‐like sequences is quite different. After a drop in the b‐value that may follow the mainshock, the b‐value increases above the background level before going back to it. Moreover, no precursory pattern can be identified before the mainshock. Fluid processes are recognized to play a crucial role in the driving mechanisms of these seismic sequences. Drawing parallel between swarms and aftershock sequences suggests that the b‐value depicts fluid‐processes in the Ubaye Region seismicity. We propose that b‐value shows a complex behavior, with variations due to Coulomb stress‐transfer from the mainshock and fluid‐pressure processes. Therefore, even with a catalog made at the French national scale, the b‐value variations may help to monitor the on‐going processes at depth. Key Points We study b‐value evolution in the Ubaye Region (France), an area with a prolific and complex seismicity involving fluid‐driven processes Seismic swarms show a similar increase of b‐value b‐value evolution during mainshock‐aftershocks sequences is consistent with an interplay of fluid migration and stress transfer