# Collective properties of injection‐induced earthquake sequences: 2. Spatiotemporal evolution and magnitude frequency distributions - **Authors:** David Dempsey; Jenny Suckale; Yihe Huang - **Journal:** Journal of Geophysical Research: Solid Earth, vol. 121(5), pp. 3638-3665 (2016) - **Publisher:** American Geophysical Union (AGU) - **DOI (version of record):** [https://doi.org/10.1002/2015jb012551](https://doi.org/10.1002/2015jb012551) - **This page:** https://ddempsey.github.io/papers/2016-dempsey-collective-properties-injection-induced-earthquake-sequences/ - **Open PDF:** [https://ddempsey.github.io/papers/2016-dempsey-collective-properties-injection-induced-earthquake-sequences/dempsey2016-collective-properties-injection.pdf](https://ddempsey.github.io/papers/2016-dempsey-collective-properties-injection-induced-earthquake-sequences/dempsey2016-collective-properties-injection.pdf) (Accepted manuscript (peer-reviewed, author's version)) - **Full text (Markdown):** [https://ddempsey.github.io/papers/2016-dempsey-collective-properties-injection-induced-earthquake-sequences/fulltext.md](https://ddempsey.github.io/papers/2016-dempsey-collective-properties-injection-induced-earthquake-sequences/fulltext.md) - **Notice:** An edited version of this paper was published by AGU. Published 2016 American Geophysical Union. Version of record: https://doi.org/10.1002/2015jb012551 - **Also in:** UC Research Repository, https://hdl.handle.net/10092/105826 - **Explainer:** all explainers on this site are AI-generated. - **BibTeX:** https://ddempsey.github.io/papers/2016-dempsey-collective-properties-injection-induced-earthquake-sequences/citation.bib - **Topics:** Induced seismicity & faults - **Keywords:** Induced seismicity; Seismology; Geology; Magnitude (astronomy); Fault (geology); Shear (geology); Seismic hazard; Tectonics ## In brief In our model, earthquakes triggered by rising fluid pressure include a higher proportion of small events than tectonic earthquakes. Pressure lowers the static strength of a fault faster than its residual strength. Modelling the 2010–2011 Guy-Greenbrier sequence in Arkansas, we estimated a fault permeability of 5 × 10⁻¹² m². - Triggering the same modelled earthquakes by fluid pressure in place of tectonic stress raised the Gutenberg-Richter b value from 1.15 to 1.53. - As fluid pressure rose on modelled faults, the b value fell from 1.8 to 1.2. It was also higher on faults with lower initial shear stress. - Injection directly into a modelled fault produced fewer large earthquakes than a Gutenberg-Richter model predicts, because rupture was easier inside the pressurised zone than outside it. - A model of the Guy-Greenbrier sequence matched its onset and southwest migration with an aquifer permeability of 10⁻¹³ m² and a fault permeability of 5 × 10⁻¹² m². - In that model, the two disposal wells together triggered more earthquakes than the sum of each well operating alone. ## The problem Injecting fluid underground can trigger earthquakes on faults that are close to failure (Raleigh et al., 1976). Seismic hazard assessment requires an estimate of how many of these earthquakes are large compared with small ones. This is usually described by the Gutenberg-Richter model, in which the b value sets the relative number of small and large earthquakes. For b = 1, there are ten times fewer earthquakes for each step of one in magnitude. Tectonic earthquakes have b values of 0.8 to 1.2 (Schorlemmer et al., 2005). Some induced sequences have higher values, up to 2.0 during hydraulic fracturing of shales (Zhou et al., 2013). However, some wastewater disposal sequences show lower b values during injection (Lei et al., 2008; Huang and Beroza, 2015). Our goal was to determine how these differences arise from the interaction between rising fluid pressure and rupture on faults with uneven stress. ## What we did We used the earthquake sequence model developed in the first paper of this two-part series (Dempsey and Suckale, 2016). Each fault is a line, with shear stress that varies along it according to a fractal model. An earthquake starts where shear stress first reaches the static strength of the fault, as stress rises or as fluid pressure lowers the strength. Two rupture tips then spread outward and stop where the energy released is less than the energy needed to continue. A tectonic reference catalogue, loaded by a uniform increase in shear stress, gave b = 1.15. We compared it with a uniform rise in fluid pressure, with injection directly into a fault, and with injection into an aquifer above impermeable basement rock cut by a permeable fault. We then modelled the 2010–2011 earthquakes near Guy and Greenbrier, Arkansas, linked to wastewater disposal at two wells. ## What we found Triggering the same earthquakes by fluid pressure in place of tectonic stress raised the b value from 1.15 to 1.53. This is because fluid pressure lowers the static strength, which controls when slip starts, faster than the residual strength, which controls how much stress slip releases. With less stress available to drive each rupture, ruptures are shorter and the earthquakes smaller. As pressure first rose, the b value fell from 1.8 to 1.2. This is because the stress available to drive rupture is small at first and grows as pressure increases. Faults with lower initial shear stress gave higher b values. Faults poorly oriented for slip in the regional stress field experience lower shear stress. We therefore expect them to have higher b values. Injection directly into a fault with constant permeability gave b of about 2, with fewer large earthquakes than a Gutenberg-Richter model predicts. When we recomputed the same ruptures with pressure uniform along the fault, the deficit disappeared and b fell to about 1. This is because rupture is easier inside the pressurised zone than outside it. However, injection into an aquifer, the setting at Guy-Greenbrier, produced no deficit of large earthquakes. The model therefore does not explain the deficit observed there (Huang and Beroza, 2015). The Guy-Greenbrier sequence (Horton, 2012) included 1317 catalogued earthquakes. Well 1 injected 3.9 × 10⁵ m³, a cube of water about 73 m on each side, into the top of the Ozark Aquifer. Well 5 injected 0.7 × 10⁵ m³ deeper in the same aquifer. Because Well 1 also injected into an overlying aquifer, we used two scenarios, with 100% or 10% of its volume reaching the Ozark Aquifer. An aquifer permeability of 10⁻¹³ m², ten times our value for a generic disposal aquifer, matched the roughly 100-day delay before seismicity began. In the 100% scenario, a fault permeability of 5 × 10⁻¹² m², 50 times higher again, matched the southwest migration of seismicity away from Well 1. The 10% scenario matched the migration less well. However, the model did not reproduce the low b value of about 0.8 observed during injection. We matched it only by raising the average initial shear stress on the fault.
We also modelled each well alone, keeping the overall earthquake rate set to give 743 earthquakes of magnitude 1.6 or above with both wells. In the 100% scenario, Well 1 alone triggered 578 and Well 5 alone none. In the 10% scenario, Well 1 alone triggered 26 and Well 5 alone 358. Modelled pressure from the two wells is the sum of the pressure from each. However, an earthquake is triggered only once pressure exceeds a threshold, here 0.015 MPa, about the water pressure at the bottom of a 1.5 m deep pool. In our model, the seismicity from both wells together is therefore greater than the sum from each well alone. We suggest that the combined effect of neighbouring disposal wells be considered in assessing induced seismicity risk. ## Limitations Our model is one-dimensional. On a real fault, a rupture can pass around a low-stress barrier that would stop it on a line. We therefore draw qualitative conclusions only. To obtain Gutenberg-Richter scaling we needed a fractal exponent of 0.25, against estimates of 0.7 to 1.0 for real faults. A higher exponent makes stress more similar over long distances and favours large earthquakes. One possible reason for needing the low exponent is that our model holds constant the energy needed to break the fault. This energy appears to increase with rupture size (Abercrombie and Rice, 2005). Including that increase would make large ruptures harder to grow and may allow a more realistic exponent. ## Glossary An **induced earthquake** is an earthquake triggered by human activity, here by raising fluid pressure in a fault. The **Gutenberg-Richter model** states that the logarithm of the number of earthquakes above a magnitude decreases linearly with that magnitude. The **b value** is the slope of the Gutenberg-Richter model. A higher b value means a higher proportion of small earthquakes. **Shear stress** is the force per unit area acting to slide the two sides of a fault past each other. **Static strength** is the shear stress needed to start slip on a fault. **Residual strength** is the reduced strength of a fault while it slides during an earthquake. A **fractal model** describes variation that has a similar pattern at every length scale. A **catalogue** is a list of earthquakes with their properties, here modelled. **Permeability** measures how easily fluid flows through rock. An **aquifer** is a rock layer that fluid can flow through and be injected into. **Basement** is the crystalline rock beneath the aquifer, here impermeable except where it is cut by a permeable fault. The **fractal exponent** sets how similar stress is over long distances along a fault. A higher value favours large earthquakes. ## Abstract Probabilistic seismic hazard assessment for induced seismicity depends on reliable estimates of the locations, rate, and magnitude frequency properties of earthquake sequences. The purpose of this paper is to investigate how variations in these properties emerge from interactions between an evolving fluid pressure distribution and the mechanics of rupture on heterogeneous faults. We use an earthquake sequence model, developed in the first part of this two‐part series, that computes pore pressure evolution, hypocenter locations, and rupture lengths for earthquakes triggered on 1‐D faults with spatially correlated shear stress. We first consider characteristic features that emerge from a range of generic injection scenarios and then focus on the 2010–2011 sequence of earthquakes linked to wastewater disposal into two wells near the towns of Guy and Greenbrier, Arkansas. Simulations indicate that one reason for an increase of the Gutenberg‐Richter b value for induced earthquakes is the different rates of reduction of static and residual strength as fluid pressure rises. This promotes fault rupture at lower stress than equivalent tectonic events. Further, b value is shown to decrease with time (the induced seismicity analog of b value reduction toward the end of the seismic cycle) and to be higher on faults with lower initial shear stress. This suggests that faults in the same stress field that have different orientations, and therefore different levels of resolved shear stress, should exhibit seismicity with different b‐values. A deficit of large‐magnitude events is noted when injection occurs directly onto a fault and this is shown to depend on the geometry of the pressure plume. Finally, we develop models of the Guy‐Greenbrier sequence that captures approximately the onset, rise and fall, and southwest migration of seismicity on the Guy‐Greenbrier fault. Constrained by the migration rate, we estimate the permeability of a 10 m thick critically stressed basement fault to be 5 × 10−12 m2. We also consider alternative scenarios in which only one of the two disposal wells operated and suggest that, due to the wells interacting, total seismicity may be greater than that attributable to each well alone. ## Cite Dempsey, David, Suckale, Jenny, Huang, Yihe (2016). Collective properties of injection‐induced earthquake sequences: 2. Spatiotemporal evolution and magnitude frequency distributions. Journal of Geophysical Research: Solid Earth, 121(5), 3638-3665. https://doi.org/10.1002/2015jb012551 ```bibtex @article{dempsey2016collective, title = {Collective properties of injection‐induced earthquake sequences: 2. Spatiotemporal evolution and magnitude frequency distributions}, author = {Dempsey, David and Suckale, Jenny and Huang, Yihe}, journal = {Journal of Geophysical Research: Solid Earth}, year = {2016}, volume = {121}, number = {5}, pages = {3638-3665}, publisher = {American Geophysical Union (AGU)}, doi = {10.1002/2015jb012551}, url = {https://ddempsey.github.io/papers/2016-dempsey-collective-properties-injection-induced-earthquake-sequences/} } ```