Induced earthquakes and the ETAS model

The epidemic type aftershock sequence (ETAS) model is widely used in the modelling of earthquake catalogues that include aftershocks. The model has be used successfully in describing tectonic seismicity where the usable catalogue sizes are large. The model is more difficult to apply to induced earthquakes, where catalogue sizes are typically much smaller and the seeding rate of main shocks cannot be assumed to be constant. In both cases, the parameters of the ETAS model are highly correlated under the conventional parameterisation and the resulting log-likelihood function has many flat regions, which can make inference difficult. We will introduce issues that arise when modelling induced seismicity caused by gas extraction and put forward an alternative parameterisation for the aftershock component of the ETAS model. The standard ETAS model is nested within our alternative but the correlation of aftershock parameters is greatly reduced. This means that that inference can be made on a broader class of models and more effectively, allowing more model uncertainty to be propagated into earthquake forecasts and simplified parameter interpretation.