Nowcasting ETAS Earthquakes: Information Entropy of Earthquake Catalogs

Abstract

Earthquake nowcasting has been proposed as a means of tracking the change in large earthquake potential in a seismically active area. The method was developed using observable seismic data, in which probabilities of future large earthquakes can be computed using Receiver Operating Characteristic (ROC) methods. Furthermore, analysis of the Shannon information content of the earthquake catalogs has been used to show that there is information contained in the catalogs, and that it can vary in time. So an important question remains, where does the information originate? In this paper, we examine this question using statistical simulations of earthquake catalogs computed using Epidemic Type Aftershock Sequence (ETAS) simulations. ETAS earthquake simulations are currently in widespread use for a variety of tasks, in modeling, analysis and forecasting. After examining several of the standard ETAS models, we propose a version of the ETAS model that conforms to the standard ETAS statistical relations of magnitude-frequency scaling, aftershock scaling, Bath's law, and the productivity relation, but with an additional property. We modify the model to introduce variable non-Poisson aftershock clustering, inasmuch as we test the hypothesis that the information in the catalogs originates from aftershock clustering. We find that significant information in the catalogs arises from the non-Poisson aftershock clustering, implying that the common practice of de-clustering catalogs may remove information that would otherwise be useful in forecasting and nowcasting. We also show that the nowcasting method provides similar results with the the ETAS models as it does with observed seismicity.