Geological faults may produce earthquakes under induced stresses associated with hydrocarbon extraction, geothermal extraction, or CO₂ storage. The associated risks depend on the frequency and magnitude of these earthquakes. Within seismic risk analysis, the exceedance probability of seismic moments, , is treated as a pure power law distribution, , where the power law exponent, β, may vary in time or space or with stress. Insights from statistical mechanics theories of brittle failure, statistical seismology, and acoustic emissions experiments all indicate this pure power law may contain an exponential taper, , where the taper strength, ζ, decreases with increasing stress. The role of this taper is to significantly reduce the probability of earthquakes larger than ζ⁻¹ relative to the pure power law. We review the existing theoretical and observational evidence for a stress‐dependent exponential taper to motivate a range of magnitude models suitable for induced seismicity risk analysis. These include stress‐invariant models with and without a taper, stress‐dependent β models without a taper, and stress‐dependent ζ models. For each of these models, we evaluated their forecast performance within the Groningen gas field in the Netherlands using a combination of Bayesian inference, and simulations. Our results show that the stress‐dependent ζ model with constant β likely offers (75–85%) higher performance forecasts than the stress‐dependent β models with . This model also lowers the magnitudes with a 10% and 1% chance of exceedance over the next 5 years of gas production from 4.3 to 3.7 and from 5.5 to 4.3, respectively.

中文翻译：

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格罗宁根气田诱发地震的应力大小

地质断层可能在与碳氢化合物提取，地热提取或CO ₂储存相关的诱发应力下产生地震。相关的风险取决于这些地震的频率和强度。在地震风险分析中，地震矩的超出概率被视为纯幂律分布，其中幂律指数β会随时间，空间或应力而变化。统计力学理论对脆性破坏，统计地震学和声发射实验的见解都表明，这种纯幂律可能包含指数锥度，其中锥度强度ζ随应力增加而减小。相对于纯幂律，此锥度的作用是显着降低大于ζ ^-1的地震的可能性。我们回顾了应力依赖指数锥度的现有理论和观察证据，以激发一系列适用于诱发地震活动风险分析的幅值模型。这些模型包括带或不带锥度的应力不变模型，不带锥度的应力相关β模型以及与应力相关的ζ模型。对于这些模型中的每一个，我们结合贝叶斯推断和模拟评估了它们在荷兰格罗宁根气田中的预测性能。我们的结果表明，应力依赖性ζ具有恒定β的模型比具有应力的β模型具有更高的性能预测（75–85％）。该模型还将在未来5年内将天然气产量分别从4.3降低到3.7和从5.5降低到4.3的幅度降低到10％和1％。