Physics-Based Forecasting of Induced Seismicity at Groningen Gas Field, The Netherlands: Post Hoc Evaluation and Forecast Update

The problem

Gas extraction from the Groningen field in the Netherlands has caused earthquakes since the early 1990s. Forecasts that link extraction plans to earthquake rates could help reduce impacts on nearby communities. By July 2022, 840 events of magnitude 1.0 or more had been detected, and the largest was a magnitude 3.6 in 2012.

In 2016, the field operator, Nederlandse Aardolie Maatschappij (NAM), convened a workshop to estimate the largest earthquake that could occur in the field. Our forecast (Dempsey and Suckale, 2017) was one contribution. However, the accuracy of forecasts like this was unknown, and actual extraction has since differed from the plans they assumed. NAM held a second workshop in 2022. This study, under contract to NAM, was our contribution. Our goal was to evaluate the 2017 forecast and then update it.

What we did

Mean reservoir pressure has fallen by more than 25 MPa, about 250 times atmospheric pressure. The reservoir rock would contract as pressure falls if it were free. Because it is attached to the surrounding rock, it cannot contract sideways. Instead, the horizontal stress in it falls. This moves the faults closer to slipping (Segall and Fitzgerald, 1998). We assume that earthquakes start on each fault at a rate proportional to how fast stress on it is increasing towards failure.

The 2017 forecast covered February 2017 to January 2025 for three extraction rates: 21, 27, and 33 billion cubic metres a year. We compared it with the earthquakes up to 1 July 2022, the first 5.5 years. Over that time, 72.5 billion cubic metres were extracted, about 35% less per year than the lowest scenario. In the 2017 model, earthquake rates were in proportion to extraction rates. We therefore scaled the earthquake count of the lowest scenario, which assumed 168 billion cubic metres over the full eight years, by the volume ratio 72.5/168, or 43%.

We then updated the model with (1) a new pressure scenario from NAM, (2) fault heights that follow the thickness of the reservoir, (3) earthquake magnitudes drawn from two statistical distributions in place of the 2017 simulation of how far each rupture spreads, and (4) calibration to earthquake locations as well as times. One distribution, a tapered Gutenberg-Richter law (Bourne and Oates, 2020), has fewer large earthquakes and represents ruptures confined to the reservoir. The other, an unbounded Gutenberg-Richter law, represents ruptures that can extend into the rock beneath it.

For an out-of-sample test of the updated model, we calibrated it on earthquakes before 1 February 2017 and compared its forecast with the 2017 to 2022 record. We then recalibrated it on earthquakes up to 1 January 2021 and forecast 2021 to 2030.

What we found

After scaling, the 2017 forecast gave a 50% chance of 6 or more earthquakes of magnitude 2.5 or more, and a 5% chance of 9 or more. Ten occurred. This is about the 2% exceedance level, a 1 in 50 outcome. This suggests the 2017 model slightly underestimated the number of these earthquakes. We consider three explanations: (1) a rare but plausible outcome, (2) a scaling that is less accurate at lower extraction rates, or (3) a deficiency in the model.

The largest event in the period, a magnitude 3.4, was consistent with the 2017 forecast. Across scenarios, the forecasts of the largest event differed by only about 0.05 magnitude units. This is because the earthquake rates in the 33 and 21 billion cubic metre scenarios differed by a factor of about 1.6, while about ten times as many earthquakes are needed to raise the largest event by one magnitude unit.

The updated model reproduced past earthquake rates, although its onset was about two years late. In the out-of-sample test, 10 earthquakes of magnitude 2.5 or more had a 9% chance of being exceeded under the tapered distribution and 11% under the unbounded one. The largest observed event, a magnitude 3.4, had a 34% chance of being exceeded under the tapered distribution and 60% under the unbounded one. Together with a test of earthquake timing, these results gave no clear evidence to reject the model.

For 2021 to 2030, the forecast rate falls from 20 to 10 earthquakes of magnitude 1.0 or more per year. Both distributions give a 10% chance of more than 8 earthquakes of magnitude 2.5 or more, and a 1% chance of more than 11.

At 10%, 1%, and 0.1% chances of exceedance, the largest event is magnitude 3.6, 3.8, and 3.9 for the tapered distribution, and 4.3, 5.4, and 6.5 for the unbounded one. We consider the tapered distribution more likely, consistent with earlier studies (e.g., Smith et al., 2020; Muntendam-Bos and Grobbe, 2022). Groningen's magnitude-frequency distribution shows a clear rollover, and few earthquakes appear to start beneath the reservoir. The expert panel at the 2022 workshop assigned a probability of 10% to the scenario of ruptures below the reservoir (Coppersmith et al., 2022).

Limitations

Because a forecast is a probability distribution, a single observed period cannot confirm it. Our model also omits the stress that uneven compaction of the reservoir adds to faults. The model's best-fitting stress path coefficient is also higher than values reported for real reservoirs. We suggest this reflects physical processes missing from the model.

We cannot rule out the unbounded distribution, because no direct stress measurements exist for the rock beneath the reservoir. Drilling into it, with pressure tests, borehole imaging, and friction tests on core, could reduce this uncertainty.

Glossary

Magnitude is a logarithmic measure of earthquake size.

Calibration is the adjustment of model parameters until the model reproduces past earthquakes.

A magnitude-frequency distribution describes how the number of earthquakes falls as magnitude increases.

The Gutenberg-Richter law is a magnitude-frequency distribution in which each unit increase in magnitude makes earthquakes rarer by a fixed factor.

A tapered distribution follows the Gutenberg-Richter law at small magnitudes but has progressively fewer large earthquakes.

A rollover is a bend in the magnitude-frequency distribution, with fewer large earthquakes than the Gutenberg-Richter law predicts.

An exceedance probability is the chance that a quantity, such as the largest magnitude, is higher than a given value.

An out-of-sample test checks a model against data withheld from its calibration.

The stress path coefficient is the ratio of the change in horizontal stress to the change in reservoir pressure.