# Response of Induced Seismicity to Injection Rate Reduction: Models of Delay, Decay, Quiescence, Recovery, and Oklahoma

- **Authors:** David Dempsey (ORCID 0000-0003-2135-5129); Jeremy Riffault (ORCID 0000-0002-0316-7215)
- **Journal:** Water Resources Research, vol. 55(1), pp. 656-681 (2019)
- **Publisher:** American Geophysical Union (AGU)
- **DOI (version of record):** [https://doi.org/10.1029/2018wr023587](https://doi.org/10.1029/2018wr023587)
- **This page:** https://ddempsey.github.io/papers/2019-dempsey-response-induced-seismicity-injection-rate/
- **Open PDF:** [https://ddempsey.github.io/papers/2019-dempsey-response-induced-seismicity-injection-rate/dempsey2019-response-induced-seismicity.pdf](https://ddempsey.github.io/papers/2019-dempsey-response-induced-seismicity-injection-rate/dempsey2019-response-induced-seismicity.pdf) (Accepted manuscript (peer-reviewed, author's version))
- **Full text (Markdown):** [https://ddempsey.github.io/papers/2019-dempsey-response-induced-seismicity-injection-rate/fulltext.md](https://ddempsey.github.io/papers/2019-dempsey-response-induced-seismicity-injection-rate/fulltext.md)
- **Notice:** An edited version of this paper was published by AGU. Published 2019 American Geophysical Union. Version of record: https://doi.org/10.1029/2018wr023587
- **Also in:** UC Research Repository, https://hdl.handle.net/10092/105822
- **Explainer:** all explainers on this site are AI-generated.
- **BibTeX:** https://ddempsey.github.io/papers/2019-dempsey-response-induced-seismicity-injection-rate/citation.bib
- **Topics:** Induced seismicity & faults
- **Keywords:** Induced seismicity; Geology; Seismology; Cabin pressurization; Pore water pressure

## In brief

We modelled how injection-triggered earthquakes respond to a cut in injection rate. The earthquake rate can fall by more than the cut and stop for a time before it partly recovers. For Western Oklahoma, our forecasts suggest the 2016 volume limit is inadequate.

- When faults need a minimum pressure rise before they slip, cutting injection reduces the earthquake rate by more than the size of the cut.
- After a cut, earthquakes can stop for a period and then partly return, reaching up to 25% of the pre-cut rate in the paper's examples.
- Calibrated to Western Oklahoma, our model reproduced the onset of earthquakes in early 2014, the peak in 2016, and the decline to September 2018.
- In our forecasts at the September 2018 rate, the chance of magnitude 5 or larger before 2025 was 14 to 46%, and 81 to 90% at the mandated maximum.
- Halving injection to 1.5 million cubic metres a month returned the earthquake rate to background levels between mid-2019 and mid-2021 in our forecasts.

## The problem

Pumping fluid underground can trigger earthquakes (Ellsworth, 2013). In 2016,
the Oklahoma Corporation Commission ordered a 40% cut in wastewater volumes
injected into two regions with many earthquakes (Langenbruch & Zoback, 2016).
However, at Paradox Valley, Colorado, a 35% injection cut reduced earthquakes
but did not stop them (Ake et al., 2005).

Our goal was to determine what should be expected after an injection cut, and
to test whether the Oklahoma limit protects against earthquakes of magnitude 5
or larger.

## What we did

We built models of how fluid pressure spreads from injection wells, from a
single well in a thin, wide aquifer to injection spread over a circle above
faulted basement rock. In the model, faults fail only once the pressure has
risen by a critical amount, the critical triggering pressure. Above that
threshold, the earthquake rate at a location is proportional to how fast the
pressure there is rising. If pressure falls, earthquakes stop at that location
and restart only when pressure exceeds its previous maximum.

For Western Oklahoma, we spread the injected water evenly over a circle 50 km
in radius, in a 500 m thick layer representing the Arbuckle formation.
Pressure then diffuses down faults into the basement, where most earthquakes
occur at about 4.5 km depth (Schoenball & Ellsworth, 2017). We estimated four
unknowns, including the critical triggering pressure, by comparing 4,680 model
runs with the 914 earthquakes of magnitude 3 or larger recorded in the region
before September 2018.

## What we found

When faults are already at the point of failure (a critical pressure of zero),
the earthquake rate eventually falls in proportion to the cut. When faults
need some pressure rise to fail, the rate falls by more than the cut. This is
because pressure near the well declines for a time after the cut. Earthquakes
there stop until it rises again above its earlier maximum. If the threshold is
high enough, earthquakes stop everywhere for a period. They then return as
pressure rebuilds, towards a new rate below the pre-cut rate. In the paper's
examples, this recovery reached up to 25% of the pre-cut rate. However, a
falling earthquake rate soon after a cut does not reliably indicate the
long-term earthquake rate.

<div class="widget" id="w-rate-cut" role="group" aria-label="Interactive model of how the earthquake rate near a single injection well responds to a cut in the injection rate, for a chosen cut size and critical triggering pressure"></div>

The widget uses our reconstruction of the paper's single-well model. Its
critical pressure is dimensionless. Larger values represent faults further
from failure. Time is counted in multiples of the injection period before the
cut. With a 40% cut and a critical pressure of 1.3, earthquakes stop from 0.16
to 0.59 injection periods after the cut. They then recover towards 24% of the
pre-cut rate. At some other settings, the recovery exceeds the paper's 25%.

In Western Oklahoma, our model reproduced the onset of earthquakes in early
2014, the peak in 2016, and the decline to September 2018. We estimated an
Arbuckle diffusivity of 44 to 277 m²/s, enough for pressure to spread about 40
to 90 km in a year. This is an order of magnitude or more higher than values
used in earlier studies (e.g., Goebel et al., 2017). We estimated a critical
triggering pressure of 0.021 to 0.077 MPa, the extra pressure at the bottom of
2 to 8 m of water, and a pressure rise at 4.5 km depth of up to 0.190 MPa by
September 2018. Once the threshold has been passed, the earthquake rate is
sensitive to changes in injection. In our model, the decline results from
operators cutting injection by more than the mandate required.

In our forecasts, if injection holds at its September 2018 rate of 3.0 million
m³ a month (about 40 Olympic swimming pools a day), the earthquake rate dips
to a minimum in 2021 and then rises to 1.4 to 4.1 magnitude 3 events a month
by 2025. The chance of a magnitude 5 or larger earthquake before 2025 is 14 to
46%. At the mandated maximum of 4.0 million m³ a month, that chance is 81 to
90%. Halving injection to 1.5 million m³ a month returns the earthquake rate
to background levels between mid-2019 and mid-2021, although the chance of
magnitude 5 could still be as high as 10%.

For the same three injection rates, Langenbruch and Zoback (2016) forecast the
same 32% chance of magnitude 5. We argue that the mandate, in its present
form, is inadequate. Operators have been injecting below the limit
voluntarily, and no regulation prevents them from returning to it.

At the diffusivities we estimated, pressure increases from neighbouring wells
overlap. Earthquakes then respond to all the wells together. Regulating wells
one at a time, for example with a traffic light system, may be both unfair and
ineffective. Cutting one well may have no long-term effect on earthquakes
triggered by a regional rise in pressure.

## Limitations

Our models assume uniform rock and a single critical pressure. They treat
hundreds of wells as one evenly spread source, without individual wells, known
faults, or poroelastic effects. As a result, they describe the average
response of many faults. Omitting poroelastic effects may have inflated our
estimate of Arbuckle diffusivity. Alternatively, earlier studies may have
underestimated it.

Our model and that of Langenbruch and Zoback (2016) both fit past earthquakes,
yet their forecasts disagree. This is because theirs uses an injection-rate
threshold and ours a pressure threshold. Agreement with past data alone does
not distinguish between them. We suggest that the physics and assumptions of
each model also need critical assessment.

## Glossary

An **aquifer** is a permeable rock layer that fluid can flow through.

The **Arbuckle formation** is the aquifer that receives most of the wastewater
injected in Oklahoma.

**Basement** is the crystalline rock beneath the Arbuckle formation, where
most of the Oklahoma earthquakes occur.

The **critical triggering pressure** is the pressure rise a fault needs before
it slips.

**Diffusivity** measures how quickly a pressure change spreads through rock.
It rises with permeability.

**Permeability** measures how easily fluid flows through rock.

**Poroelastic effects** are changes in rock stress caused by fluid pressure
changes some distance away.

A **traffic light system** reduces or stops injection at a well when nearby
earthquakes exceed set levels.

A **dimensionless** pressure has no units. It is the pressure rise divided by
a reference pressure set by the injection rate and how easily the well takes
fluid.

**Magnitude** is a logarithmic measure of earthquake size.

The **background rate** is the rate of earthquakes expected without injection.

## Abstract

When injection‐induced seismicity poses a risk to communities, it is common to reduce the injection rate or halt operations. This applies both to individual wells and well clusters, such as those within the Area of Interest for Triggered Seismicity in Western Oklahoma, where in 2016 a 40% volume reduction mandate was imposed by the state regulator. Here we quantify how induced seismicity responds to an injection reduction. We introduce models of pressure diffusion in idealized geometries coupled to steady state pressurization and rate‐state models of earthquake triggering. We find that the delay in seismicity onset and then postreduction behavior—decay, sometimes quiescence, and recovery of the seismicity rate—depend on the critical triggering pressure and on diffusion and rate‐state parameters. We have adapted our model to replicate the timing of onset, peak, and recent pace of decline of seismicity triggered by wastewater injection in Western Oklahoma. Our analysis implies that diffusivity in the Arbuckle formation is high (between 44 and 277 m2/s). The critical triggering pressure is inferred to be between 0.021 and 0.077 MPa, and fluid overpressure at 4.5‐km depth in the basement is estimated to have increased by as much as 0.190 MPa. We simulate future seismicity out to 2025 for three scenarios. Fixing the 2018 injection rate, already less than the limit imposed by the state regulator, we find a high likelihood of further M ≥ 5 earthquakes. This suggests that the volume reduction mandate in Western Oklahoma is, at present levels, inadequate.

## Cite

Dempsey, David, Riffault, Jeremy (2019). Response of Induced Seismicity to Injection Rate Reduction: Models of Delay, Decay, Quiescence, Recovery, and Oklahoma. Water Resources Research, 55(1), 656-681. https://doi.org/10.1029/2018wr023587

```bibtex
@article{dempsey2019response,
  title = {Response of Induced Seismicity to Injection Rate Reduction: Models of Delay, Decay, Quiescence, Recovery, and Oklahoma},
  author = {Dempsey, David and Riffault, Jeremy},
  journal = {Water Resources Research},
  year = {2019},
  volume = {55},
  number = {1},
  pages = {656-681},
  publisher = {American Geophysical Union (AGU)},
  doi = {10.1029/2018wr023587},
  url = {https://ddempsey.github.io/papers/2019-dempsey-response-induced-seismicity-injection-rate/}
}
```