Predictability in the ETAS Model of Interacting Triggered Seismicity

As part of an effort to develop a systematic methodology for earthquake forecasts, we use a simple model of seismicity based on interacting events which may trigger a cascade of earthquakes, well-known as the Epidemic-Type Aftershock Sequence model). The ETAS model is constructed on a (bare) Omori’s law, the Gutenberg-Richter law and the idea that large events trigger more numerous aftershocks. We demonstrate the essential role played by the cascade of triggered seismicity in controlling the rate of aftershocks decay as well as the overall level of seismicity in the presence of a constant external seismicity source. The key parameter of this model, which controls the different regimes of the seismic activity, is the branching ratio, defined as the average number of triggered event per earthquake. This parameter is given two observable meanings as the ratio of triggered events over total seismicity and the ratio of secondary aftershocks over total aftershocks. We offer an analytical approach to account for the yet unobserved triggered seismicity adapted to the problem of forecasting future seismic rates at varying horizons from the present. Tests presented on synthetic catalogs validate strongly the importance of taking into account all the cascades of still unobserved triggered events in order to predict correctly the future level of seismicity beyond a few minutes. We find a very strong predictability gain if one accepts to predict less than typically 25% of the large-magnitude targets. However, the probability gains degrade fast when one attempts to predict more than 30% of the targets. This results from the fact that a significant fraction of events remain uncorrelated from past seismicity. This delineates the fundamental limits underlying forecast skills, stemming from an intrinsic stochastic component in these interacting triggered seismicity models.