A 3D ETAS model for forecasting spatio-temporal distribution of induced seismic events
Authors: Ebrahimian Hossein , Jalayer Fatemeh , Convertito Vincenzo 
Published: March 2022

&lt;p&gt;&lt;strong&gt;&lt;em&gt;Methodology:&lt;/em&gt;&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;Induced earthquakes have peculiar characteristics such as, relatively shallow depths, small magnitude, correlation with field operations, non-GR recurrence law, and eventually non-homogenous Poisson recurrence time. Indeed, induced seismicity tends to cluster in limited volumes near the wells where field operations (e.g., fluids injection, extraction, fracking, etc.) are performed. A novel and fully-probabilistic simulation-based procedure is presented for providing temporal and volumetric predictions of induced events&amp;#8217; occurrence in a prescribed forecasting time interval (in the order of hours or days). The procedure aims at exploiting the information provided by the ongoing sequence in quasi-real time (even in the presence of very limited registered data) to adaptively update the seismicity forecasts based on the incoming information as it becomes available. The clustering of seismic events in volume (3D seismicity) and time is modelled based on an Epidemic Type Aftershock Sequence (ETAS) model. The proposed 3D ETAS model encompasses a decoupled depth-area volumetric probabilistic kernel that incorporates kernel density functions for areal extent as well as the focal depth. The ETAS parameters are going to be re-calibrated in order to take into account non-GR long-term temporal boundary conditions in case of induced seismicity. Moreover, exact spatial integrals will be used to consider the 3D boundary conditions. The proposed procedure considers the uncertainties in the earthquake occurrence model parameters in a Bayesian updating framework. Pairing up the Bayesian inference and the suitable efficient simulation schemes (using Markov Chain Monte Carlo Simulation) provides the possibility of performing the forecasting procedure with minimum (or no) need of human interference.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;&lt;em&gt;Application:&lt;/em&gt;&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;The procedure is demonstrated through retrospective forecasting of induced seismicity recorded at the Geysers geothermal field in northern California in the time period of 2011-2015. Injection of cold water and heavier liquids in the hot reservoir caused induced earthquakes with moment magnitudes in the range of [0.0, 4.0] and depth ranging up to 5 km. The proposed procedure is examined for both Bayesian updating of the proposed 3D ETAS model parameters and forecasting of the number of events of interest expected to occur in various time intervals before and after a number of main events within the seismic sequence. The seismicity is predicted within a confidence interval from the mean estimate. Adding a kernel density for the focal depth and moving towards the 3D seismicity forecasting leads to the forecasted number of events that better match the events that actually took place in the forecasting interval, as compared to the 2D ETAS model. Therefore, it is concluded that the proposed 3D ETAS model is quite effective in case of induced seismicity.&lt;/p&gt;