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

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?CRichter magnitude?Cfrequency 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?CRichter 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?=?2t _S at a constant Gutenberg?CRichter 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?=?2t _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%.