The proximity of wastewater disposal to the Precambrian basement is a critical factor influencing induced earthquake rates in the Central United States, but the impact of reducing injection depths has not been widely demonstrated. Beginning in 2015, state regulatory efforts in Oklahoma and Kansas mandated that wells injecting into the lower Arbuckle Group, a basal sedimentary unit, be backfilled with cement (i.e., “plugged back”) so that they inject into shallower formations. This plug back activity gives us a unique opportunity to investigate the relationship between injection depth and induced seismicity rate. To evaluate the impact that decreased injection rates and plug backs had on the seismicity rates, we created a suite of rate–state earthquake models. Observed seismicity rates are best fit when only lower Arbuckle volumes are considered, suggesting the lower Arbuckle injectors were primarily responsible for the seismicity and that plug backs were effective at isolating the injected volumes to shallower formations. Our models demonstrate that if these wells had not been plugged back, seismicity rates would be multiple times larger than they are today. We find that the combination of well plug backs and injection volume decreases can be an effective strategy for reducing induced seismicity rates.

Between 1973 and 2007, seven M ≥ 3 earthquakes in northern Oklahoma and southern Kansas are reported in the Advanced National Seismic System (ANSS) Comprehensive Catalog (ComCat; U.S. Geological Survey Earthquake Hazards Program, 2017; Fig. 1). Following 2007, earthquake rates began to increase in this region with a dramatic rise starting in 2011. The earthquake rate peaked at 940 M ≥ 3 earthquakes in 2015, making Oklahoma the most seismically active state of the conterminous United States at the time. Since this seismicity increase began, five earthquakes with Mw≥5 have occurred in Oklahoma: the 2011 Mw 5.7 Prague, 2016 Mw 5.1 Fairview, 2016 Mw 5.8 Pawnee, 2016 Mw 5.0 Cushing, and 2024 Mw 5.1 Prague earthquakes. Seismicity rates in northern Oklahoma and southern Kansas have declined since 2016, but the ongoing seismicity is still well above the background rate. Between 2019 and 2023, there was an average of 21 M ≥ 3 earthquakes per year in the area.

The vast majority of these recent earthquakes were induced by wastewater disposal into the Arbuckle Group (e.g., Walsh and Zoback, 2015), a group of Cambrian–Ordovician formations composed principally of dolomitized carbonates that extend across most of Oklahoma and neighboring states (Merriam, 1963). Either this Arbuckle Group or a comparatively thin strata of the Reagan Sandstone and Honey Creek Limestone overlay the Precambrian basement (Merriam, 1963), where most of the induced earthquakes have occurred. Much of the fluid disposed in these units originated from hydrocarbon production in the Mississippi Limestone Play, which has a high (∼10:1) volumetric ratio of water to hydrocarbons (e.g., Mitchell and Simpson, 2015). The transportation and disposal of such large amounts of fluid could be an economic burden in some basins, but the Arbuckle Group, located several hundred meters beneath the Mississippi Limestone Play, was viewed as a cost‐effective site for disposing of this produced water because of its relatively high permeability and sub‐hydrostatic pore fluid pressure. With hydrocarbon production activities in this limestone play increasing around 2010, the disposal rates into the Arbuckle increased and the earthquake rates followed suit. The Arbuckle injection rate peaked in 2015, and a corresponding declining seismicity rate was observed as the injection rate decreased (e.g., Langenbruch et al., 2018).

Most of the earthquakes induced by Arbuckle disposal primarily occurred in the central/northern portion of Oklahoma and southern Kansas. Earthquakes within the bordering Woodford and Woodford–Caney Plays, located to the southwest and southeast of this area, respectively (Fig. 1), are primarily induced by hydraulic fracturing rather than wastewater disposal (e.g., Skoumal, Ries, et al., 2018) and are not a focus of the study. Here, we investigate the factors responsible for the decline of wastewater disposal‐induced seismicity, using suites of rate–state friction earthquake rate models to test the implications of various scenarios of the effect of plug backs and decreasing injection.

Multiple agencies regulate wastewater disposal operations within our study area. Wastewater disposal volumes into the Arbuckle Group from 1995 to 2010 come from Norbeck and Rubinstein (2018). We obtain a comprehensive wastewater disposal volume dataset from 2011 to 2023 through a combination of the Oklahoma Corporation Commission (OCC), the Kansas Geological Survey, and the U.S. Environmental Protection Agency (EPA). The disposal wells in Osage County, Oklahoma, are regulated by the EPA, and they only provided injection volumes for wells that injected either more than a cumulative fluid volume of ∼160,​000  m3 or at a rate that exceeded ∼16,​000  m3/month⁠. In addition, some incomplete well data from Osage County are in the form of the maximum monthly injection rate at a well for periods of up to 15 months. For these incomplete periods, we assume the wells injected at a constant rate set at its maximum reported volume. Given that the volumes for the Osage County wells with incomplete data correspond to <3% of the monthly total Arbuckle injection in our area of interest, this assumption does not significantly affect our regional analysis. All injection data are also corrected for suspected reporting errors, which are identified by searching for wells with a reported monthly volume that was at least an order of magnitude more than the surrounding time period. With this assumption, 100 monthly volume corrections from 95 wells were made, for a total reduction of ∼8  million  m3 of fluid, representing <1% of the total disposal volume. We assume all other industry reporting is complete and accurate for this study.

Monthly injection into the Arbuckle Group in Oklahoma and southern Kansas steadily increased from 1995 to 2011 (Fig. 2b). Arbuckle injection rates dramatically increased in 2012 and peaked in March 2015 with ∼16  million m3 of fluid injected, whereas non‐Arbuckle injection remained relatively constant through the period for which we have data (2011–2023), averaging ∼3  million m3/month⁠. As seismicity rates continued to climb, state regulators attempted to mitigate future earthquakes by ordering wells to be shut in, capping injection volumes, and reducing the permitting of new Arbuckle wells (Oklahoma Corporation Commission [OCC], 2022). Starting in 2015, the OCC issued 33 directives related to mitigating wastewater disposal‐induced seismicity. These directives ranged from regional orders to reduce volumes across Oklahoma to orders focused in response to individual earthquake sequences. For example, following the 2022 January Mw 4.5 earthquake near Clyde, Oklahoma, seven wells within ∼10 km were shut‐in and 15 other wells within ∼16 km had their maximum permitted rates reduced by 50%. Following the 2016 Mw 5.8 Pawnee earthquake, the OCC and EPA shut in 32 wells and reduced rates at 35 other wells injecting into the Arbuckle that were in Pawnee and Osage Counties (Murray et al., 2023). Similar to Oklahoma, the Kansas Corporation Commission (KCC) took regulatory actions beginning in 2015 to reduce the volume of wastewater injected at Arbuckle wells in southern Kansas. The KCC imposed daily injection limits of ∼1300  m3 of fluid for wells in five ellipsoidal areas of southern Kansas in 2015. In 2016, injection limits of ∼2500  m3 of fluid were imposed for an expanded region encompassing most of Harper and Sumner Counties (Buchanan et al., 2023).

Both regulatory and economic forces are likely responsible for the decrease in wastewater volumes in the Arbuckle Group beginning in 2015 (Roach, 2018). In late 2014, prior to these regulatory efforts, unrelated economic factors led to oil prices decreasing by more than 50% within months (Fig. 2a). As a result, oil production in the Mississippi Limestone Play declined, followed by a shift in production to the adjacent Anadarko and Arkoma basins that were deemed more economical. This reduced the amount of fluid needed to be disposed of in the study area (Fig. 2b). There were 198 Arbuckle disposal wells that operated in 2013–2017 but did not report any disposal volumes in 2018–2023, including 63 wells that were plugged back.

The proximity of an injection well to the Precambrian basement is a crucial factor in controlling the likelihood of well‐inducing earthquakes throughout the Central and Eastern United States (Skoumal, Brudzinski, and Currie, 2018; Scanlon et al., 2019). In Oklahoma, it was estimated that the seismic moment could be reduced by half if injection depths were restricted to several hundred meters above the basement (Hincks et al., 2018). The role of mitigating seismicity by increasing the injection distance to the Precambrian basement was also observed at the Decatur, Illinois, CO2 sequestration site (Kaven et al., 2015). There, the injection was shifted from the lower to upper Mount Simon Sandstone, and the seismicity rate was reduced despite an increase in the injected volume.

One explanation for this depth sensitivity in seismic activity is naturally occurring barriers to vertical flow. The Arbuckle Group contains numerous subtidal, intertidal, and supratidal faces with evidence for a variety of diagenetic changes (e.g., Fritz et al., 2012). These depositional and diagenetic differences may serve to inhibit vertical flow through the Arbuckle Group. If these baffles are present, reducing the depth of an Arbuckle well could be an effective means of isolating the seismogenic faults in the Precambrian basement from injection effects.

In 2015, the OCC required 229 wells injecting into the lowermost 30 m of the Arbuckle to plug back their wells so that injection was at least 30 m above the Precambrian basement. Seven wells within our study area (Fig. 3) that are regulated by the EPA were also plugged back, but only four of these wells had any reported volume. The plug back dates for EPA wells are unknown, so we assume a plug back date of September 2016 for plug backs in Osage County, equivalent to an immediate response to the Mw 5.8 Pawnee earthquake. The KCC required wells within their response areas that had drilled lower than the Arbuckle to plug back to a depth “approved by Commission Staff” (Kansas Corporation Commission [KCC], 2015). Nine wells were mandated to plug back, and six additional wells outside of the response area were also plugged back.

Following these regulatory actions, a total of 251 wells (OCC: 229, EPA: 7, and KCC: 15) in our study area that were originally drilled into the lowermost 30 m of the Arbuckle or deeper were plugged back an average of ∼120 m (Fig. 3). Of the 244 OCC and KCC plug backs, 219 (∼90%) were plugged back during March 2015 to June 2016 as earthquake rates peaked. Prior to plug backs, these wells had injected ∼340  million m3 of fluid into the Arbuckle since 1995. More than 240  million m3 of fluid have been injected at these wells following plug back through 2023, and these plugged‐back wells account for ∼30%–40% of the volume injected into the Arbuckle each month.

The timing of these Arbuckle well plug backs is coincident with the decrease in disposal volume (Fig. 2b), and it is therefore challenging to observationally determine the relative importance each action had on decreasing the seismicity rates. Here, we use a rate–state friction earthquake nucleation model (Dieterich, 1994) to evaluate the role the decreased injection rates and well plug backs had on the seismicity rate decline. Specifically, the time‐varying change in seismicity rate within a representative volume R is modeled by a first‐order ordinary differential equation driven by changes in Coulomb failure stressing rate (⁠τ˙⁠). Following Segall and Lu (2015), Dieterich’s original formulation can be recast as a single equation:
in which τ˙0 is the background stressing rate, and tc=Aσ/τ˙0⁠, a decay‐time constant which is a function of the direct effect parameter: tc=Aσ/τ˙0⁠. The rate R is the ratio of induced seismicity to the background seismicity rate. To convert the injection rate to the Coulomb stressing rate, we follow the methodology of Norbeck and Rubinstein (2018), which treats the Arbuckle like a single‐injection disposal reservoir with uniform thickness and uniform poromechanical properties. Further, in their approach, τ˙ is approximated as the pressurization rate p˙⁠, which scales directly with the aggregate injection rate q˙ as
in which V is the volume being injected into with porosity ϕ and total compressibility β⁠. This formulation assumes that the Arbuckle is confined on its top and bottom surfaces and that stress changes in the basement are induced instantaneously and associated with elastic volume changes in the Arbuckle. In other words, with this approach, there is no time‐lag introduced between injection and stress change in the basement that might be caused by explicitly considering poroelastic effects with vertical fluid diffusion. Although this is a simplified representation of the physical controls on induced seismicity rates, numerous studies from various settings indicate that it captures first‐order variations in the rate of induced earthquakes over large regions (e.g., Zhai et al., 2020; Skoumal et al., 2021). This model allows us to forecast the earthquake response to varying injection scenarios using a set of physically justifiable parameters such that we can attempt to match the observed behavior.

Unlike the statistical seismicity modeling approaches that can be calibrated to a given region without the requirement of physically justifiable parameters, modeling earthquake rates with a physics‐based approach like this requires selecting accurate and physically realistic parameters that can only come from a limited range. Although the values for all parameters used in Norbeck and Rubinstein (2018) are reasonable estimates for the Arbuckle Group, these parameters have relatively high uncertainties owing to natural variability, and some values could be expected to differ by an order of magnitude. We take a modified approach by considering a range of values for the background seismicity rate (⁠r0=0.1–1.0 earthquakes/yr), background stressing rate (⁠τ˙0=0.7×10−4 to 0.7×10−2  MPa/yr⁠), direct effect parameter (⁠A=1.3×10−3 to 3.3×10−2⁠), effective normal stress (⁠σ=40–60  MPa⁠), and porosity (⁠ϕ=0.1–0.2⁠) that encompass the reasonable estimates selected by Norbeck and Rubinstein (2018) and tested by Kroll and Brudzinski (2024). We use the same reservoir compressibility (⁠β=3.2×10−10  Pa−1⁠) and reservoir thickness (225 m) values from Norbeck and Rubinstein (2018) as they are better constrained. Similar to Norbeck and Rubinstein (2018), we attempt to match a Reasenberg (1985) declustered catalog for the M ≥ 3 earthquakes in the ANSS ComCat catalog during 1995–2023. We use a declustered catalog because the rate–state formulation that we use forecasts the effect of injection, whereas the aftershocks are driven by the static and dynamic stresses of mainshocks and would require separate forecasts.

We consider four wastewater injection rate scenarios. In scenario 1, all Arbuckle injection is used to calculate the pressurization rate (equation 2). For scenarios 2–4, we consider three new ways to treat the injection histories in which shallow Arbuckle injection does not affect the seismicity. Effectively, we are assuming that wells that inject >30 m from the Arbuckle‐basement contact do not have downward vertical fluid migration due to the aforementioned diagenetic changes in the Arbuckle, and we consider only volumes injected within 30 m of the basement. Using these lower Arbuckle volumes, we evaluate three scenarios in which plug backs were (1) completely effective, (2) 50% effective, and (3) completely ineffective in reducing seismicity rates. We implement these scenarios by treating the volumes following plug back as if they were still being injected into the lower Arbuckle at 0%, 50%, and 100% of their actual rate, respectively (Fig. 4a).

Considering our model parameters, there are ∼100,000 unique parameter set combinations. We evaluate each parameter set and determine the mean squared error (MSE):
in which Y is the observed earthquake rate, Y^ is the modeled earthquake rate, and n is the number of predicted values. We find that the best‐matched model is produced when only lower Arbuckle volumes are considered and where the plug backs are fully effective at reducing earthquake rates (Fig. 4b). This best model is produced considering a background seismicity rate of 0.6 earthquakes/yr, background stressing rate of 1.25×10−3  MPa/yr⁠, direct effect parameter of 2.17×10−2⁠, effective normal stress of 47 MPa, and porosity of 0.14. When compared to this best‐fit result, residuals for the best models from the other scenarios are larger. The plug back 50% effective, plug back ineffective, and total Arbuckle scenarios are ∼1.5, ∼2.6, and ∼3.7 times larger, respectively, than the plug back effective scenario (Fig. 4b). These poorer fitting models underpredicted the peak seismicity rate and overpredicted more recent seismicity rates.

We then sought to quantify the impact that plugging back lower Arbuckle wells had on seismicity rates. Using model results considering the lower Arbuckle volumes, we select the 100 parameter combinations that produced the lowest misfits. We then evaluate scenarios in which (1) only half of the volume had been plugged back and (2) no plug backs occurred. If only half of the lower Arbuckle volumes had been plugged back, the seismicity rate in 2024 would be ∼2.5 times larger than the real plug back scenario; if no plug backs had occurred, the seismicity rate would be ∼4.4 times larger (Fig. 4c).

The decrease in the total disposal volume was largely driven by a change in production in the Mississippi Limestone Play to more economical hydrocarbon plays, namely the South Central Oklahoma Oil Province (SCOOP) and Sooner Trend, Anadarko, Canadian and Kingfisher (STACK) plays to the southwest. Crude oil production in Oklahoma increased following this transition, peaking at ∼3  million m3 of fluid in December 2019 (Fig. 2a); the current production of ∼2  million m3/month is equivalent to the production at the time earthquakes peaked in 2015 (U.S. Energy Information Administration [USEIA], 2024). Significant hydrocarbon production has continued in Oklahoma, albeit with an emphasis on other plays that have lower ratios of produced water to hydrocarbons, whereas maintaining an earthquake rate much lower than in 2015.

Although economic forces caused a decline in seismicity in Oklahoma, regulatory actions were also critical in reducing the earthquake rate. For example, the rapid intervention of regulators limiting injection near large seismic events had localized influences on reducing aftershock productivity (e.g., Goebel et al., 2019) and likely reduced the likelihood of further sequences along those seismogenic, critically stressed faults. Because both pore pressure and poroelastic responses to fluid disposal are generally highest near the injection site, the local directives from the OCC to shut in and reduce volumes at wells in proximity (∼15 km) to notable seismicity could be viewed as a practical, yet reactive, method of mitigating future earthquakes. However, these local directives alone would likely not be sufficient for mitigating seismic hazards within a larger area of interest, such as in this study. Owing to the high permeability of the Arbuckle and far‐field poroelastic effects, some earthquakes in Oklahoma and Kansas have been induced > 40 km from Arbuckle injection wells (Goebel et al., 2017; Peterie et al., 2018). The role of regional directives that sought to reduce injected volumes on larger spatial scales, like volume caps for all Arbuckle wells across the region, therefore serves as an effective component of seismic mitigation for Oklahoma and southern Kansas.

Reducing injection rates into the lower Arbuckle through the combination of volume reductions and well plug backs was likely an effective strategy for reducing induced earthquake hazards in Oklahoma and Kansas. Our earthquake forecasts suggest that the plug back requirements for lower Arbuckle wells reduced earthquake rates by a factor of ∼4. Although a reduction in injection rate into basal formations since 2015 has likely had an effective role in reducing the earthquake risk for the region, the recent February 2024 Mw 5.1 Prague earthquake serves as a reminder that these actions have not eliminated the potential of future M > 5 induced earthquakes.

With 74 M ≥ 3 earthquakes during 2020–2023, earthquake rates in Oklahoma and southern Kansas are still elevated above the historical average of fewer than one M ≥ 3 earthquakes per year. If hydrocarbon production from formations with high ratios of water to hydrocarbons like the Mississippi Limestone Play increases in the future, then disposal into the upper Arbuckle and shallower formations may increase as well. This would serve as a test of the ability of these shallower formations to insulate the ubiquitous seismogenic faults in the Precambrian basement from the pore pressure and poroelastic effects.

The Advanced National Seismic System (ANSS) Comprehensive Catalog (ComCat) is available from the U.S. Geological Survey (USGS; https://earthquake.usgs.gov/data/comcat). Wastewater disposal volumes in Oklahoma (excluding Osage County) were obtained from the Oklahoma Corporation Commission (OCC; https://oklahoma.gov/occ) and plug back records were provided by Colin Brooks. Wastewater disposal volumes for large‐rate injectors and Arbuckle well plug backs in Osage County were provided by Jeanne Eckhart from the Environmental Protection Agency (EPA). Wastewater disposal volumes in Kansas were obtained from the Kansas Geological Survey (https://www.kgs.ku.edu). All websites were last accessed in July 2024. Plug back information for Kansas wells was obtained from the Kansas Corporation Commission (KCC) through a Kansas Open Records Act request.

The authors acknowledge that there are no conflicts of interest recorded.

Elizabeth Cochran and Kayla Kroll provided helpful peer reviews that improved the article. The authors thank Colin Brooks from the Oklahoma Corporation Commission (OCC) for compiling information and providing guidance about Oklahoma well plug backs. Jeanne Eckhart of the U.S. Environmental Protection Agency (EPA) kindly provided injection data and information on well plug backs within Osage County, Oklahoma. The authors are appreciative of Seth Hanes and Brian Varela’s efforts to find historical disposal volumes.

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.