An empirically constrained forecasting strategy for induced earthquake magnitudes using extreme value theory

Induced seismicity magnitude models seek to forecast upcoming magnitudes of induced earthquakes during the operation of subsurface industries such as hydraulic fracturing, geothermal stimulation, wastewater disposal, and carbon capture and storage. Accurate forecasting models could guide operational decision-making in real time, for example operations could be reduced or paused if forecast models indicate that magnitudes may exceed acceptable levels. Robust and transparent testing of forecasting models is required if they are to be adopted by operators and regulators of such industries. We develop and test a suite of models based on extreme value estimators to forecast the magnitudes of upcoming induced seismic events based on observed seismicity. We apply these models to multiple induced seismicity cases from wastewater disposal in Oklahoma and in western Texas, as well as other cases of seismicity caused by subsurface fluid injection in North America, Europe, and China. In total, our testing dataset consists of more than 80 individual sequences of induced seismicity. We find that all the models produce strong correlation between observed and modelled magnitudes, indicating that the forecasting provides useful information about upcoming magnitudes. However, some models are found to systematically over-predict the observed magnitudes, while others tend to under-predict. As such, the combined suite of models can be used to define upper and lower estimators for the expected magnitudes of upcoming events, as well as empirically constrained statistical expectations for how these magnitudes will be distributed between the upper and lower values. We conclude by demonstrating how our empirically constrained distribution can be used to produce probabilistic forecasts of upcoming induced earthquake magnitudes, applying this approach to two recent cases of induced seismicity.