Improved aftershock forecasts using mainshock information in the framework of the ETAS model

The Epidemic Type Aftershock Sequence (ETAS) model is the most widely used and powerful statistical model for aftershock forecasting. While the distribution of aftershocks around the mainshock is anisotropic, the spatial probability density function of the ETAS model is commonly assumed to be isotropic due to insufficient information. In addition, its parameter estimation can be highly biased due to catalog incompleteness after the mainshock. Thus, we extended the recently developed 2D temporal ETASI, which accounts for short-term incompleteness, to 2D and 3D spatiotemporal ETASI, considering additional spatial occurrence probabilities in the framework of ETAS and ETASI to improve aftershock forecasting. We replaced the isotropic spatial kernel with anisotropic kernels estimated by a spatial probability map of stress scalars, including Coulomb stress changes on master fault orientation (MAS), Coulomb stress changes on variable mechanisms (VM), maximum shear (MS), and von Mises stress (VMS), and the nearest distance to the ruptured fault of the mainshock (R). The fit to six prominent mainshock-aftershock sequences in California demonstrates that the ETASI model outperforms the standard ETAS model. Furthermore, positive information gains indicate that using stress calculations as additional input information can improve the parameter fit. This improvement is weaker in 3D, which is likely related to greater positional uncertainty in the depth domain. However, incorporating the probability map calculated as a function of the nearest distance to the mainshock rupture leads to the best performance in all model variants.