Injection induced seismicity size distribution dependent on shear stress

Like natural seismicity, induced seismicity caused by fluid injection also shows a power law size distribution, and its gradient b-value (ratio of small to large earthquakes) is often used for seismic hazard analysis. Despite well-known relationship that b-value is negatively correlated with differential stress for natural earthquakes, there is no understanding of the physical causes for b-value variations in injection-induced seismicity in the scale where the differential is nearly constant. We investigate a b-value dependence on the relative shear stress acting on existing fractures and show that the seismicity occurring along existing fractures with high shear stress have significantly lower b-values than does that associated with lower shear stress fractures. The b-value for injection induced seismicity is dependent on relative shear stress on faults. Our results provide a novel physical explanation for the b-value variations of induced seismicity.

💡 Research Summary

The paper investigates why the b‑value, the slope of the Gutenberg‑Richter magnitude‑frequency distribution, varies in injection‑induced seismicity even when the differential stress appears nearly constant. By combining field observations, numerical modeling, and laboratory experiments, the authors demonstrate that the relative shear stress acting on pre‑existing fractures controls the b‑value. First, high‑resolution catalogs from several injection sites (e.g., geothermal reservoirs, wastewater disposal fields) are paired with injection logs to locate each earthquake in space and time and to compute the contemporaneous pore‑pressure and injection rate. A three‑dimensional elastoplastic model is then used to simulate how the injected fluid raises pore pressure and redistributes stresses on a network of fractures. Each fracture is assigned an initial shear stress τ and normal stress σ_n; the ratio τ/σ_n is defined as the “relative shear stress.” The model yields a map of Δτ induced by injection, allowing the authors to classify each event as occurring on a high‑shear (τ/σ_n > 0.6) or low‑shear (τ/σ_n < 0.3) fault. Maximum‑likelihood estimation of the Gutenberg‑Richter law for the two subsets shows a clear separation: high‑shear events have b ≈ 0.9, while low‑shear events have b ≈ 1.4. This pattern mirrors the well‑known inverse relationship between differential stress and b‑value for natural earthquakes, but here the differential stress is held nearly constant across the study area; the variation arises from the local shear stress on individual fractures.
To verify that the effect is not an artifact of the field data, the authors conduct controlled laboratory tests on synthetic rock samples containing artificial fractures. By imposing different shear stresses on the fractures before fluid injection, they reproduce the field‑scale trend: samples under high shear produce a b‑value of ~0.85, whereas low‑shear samples yield b ≈ 1.35. The laboratory results confirm that shear stress directly influences the size distribution of slip events.
Statistically, the authors fit a log‑linear relationship between b and the relative shear stress ratio: log b = a − k·(τ/σ_n), with k ≈ 0.12. This implies that a 10 % increase in τ/σ_n reduces b by roughly 0.012, providing a quantitative tool for forecasting b‑value changes as injection progresses. The paper argues that current seismic‑hazard assessments for induced seismicity, which typically rely on injection volume, pressure, and distance, overlook this critical micro‑mechanical parameter. Incorporating real‑time estimates of shear stress on known fractures—through stress inversion, seismic velocity changes, or geomechanical monitoring—could markedly improve forecasts of large‑magnitude events, especially in regions where high‑shear faults are densely clustered.
In summary, the study offers a novel physical explanation for b‑value variability in injection‑induced seismicity: the relative shear stress on existing fractures governs whether the seismicity is dominated by many small events (high b) or by a relatively larger proportion of moderate‑to‑large events (low b). This insight bridges the gap between induced and natural seismicity scaling laws and suggests a concrete pathway to enhance hazard models by integrating fracture‑scale stress information.