# Probability of earthquake occurrence and magnitude estimation in the post shut-in phase of geothermal projects

## Abstract

Induced seismicity in geothermal projects is observed to continue after shut-in of the fluid injection. Recent experiments show that the largest events tend to occur after the termination of injection. We use a probabilistic approach based on Omori’s law and the Gutenberg–Richter magnitude–frequency distribution to demonstrate that the probability of exceeding a certain maximum magnitude still increases after shut-in. This increase is governed by the exponent of Omori’s law *q* and the Gutenberg–Richter *b* value. For a reduced *b* value in the post-injection phase, the probability of occurrence directly after shut-in can be even higher than the corresponding probability for an ongoing injection. For the reference case of *q* = 2 and a 10% probability at shut-in time *t* _{S} to exceed a given maximum magnitude, we obtain an increase to 14.6% for *t* = 2*t* _{S} at a constant Gutenberg–Richter *b* value after shut-in. A reduction of the *b* value by one quarter leads to a probability of 20.5%. If we consider a constant probability level of occurrence for an event larger than a given magnitude at shut-in time, this maximum magnitude increases by 0.12 units for *t* = 2*t* _{S} (0.26 units for a reduced *b* value). For the Soultz-sous-Forêts (France) injection experiment in 2000, recent studies reveal *q* = 9.5 and a *b* value reduction by 14%. A magnitude 2.3 event 9 h after shut-in falls in the phase with a probability higher than for the continued injection. The probability of exceeding the magnitude of this post-injection event is determined to 97.1%.

## Keywords

Induced seismicity Shut-in Post-injection Probability EGS*b*value Soultz-sous-Forêts Basel

## Notes

### Acknowledgement

We thank an anonymous reviewer for helpful and constructive remarks. Figures were made using GMT (Wessel and Smith 1998).

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