Hyperbolic property of earthquake networks

Karla Henricksen, & Ilya Zaliapin

Published September 15, 2019, SCEC Contribution #10047

We examine the geometry of earthquakes in time-space-magnitude domain using the Gromov hyperbolic property of metric spaces. Gromov delta-hyperbolicity quantifies the curvature of a metric space via four point condition, which is a computationally convenient analog of the famous slim triangle property. We estimate the delta-hyperbolicity for the observed earthquakes in Southern California during 1981–2017. A set of earthquakes is represented by a point field in space-time-magnitude domain. The separation between earthquakes is quantified by the Baiesi-Paczuski proximity that has been shown efficient in applied cluster analyses of natural and human-induced seismicity and acoustic emission experiments. The Gromov delta is estimated in the earthquake space and in the proximity graphs obtained by connecting pairs of earthquakes within a given proximity. All experiments result in the values of delta that are bounded from above and do not tend to increase as the examined region expands. This suggests that the earthquake field has hyperbolic geometry. We discuss the properties naturally associated with hyperbolicity in terms of the examined earthquake field. The results improve the understanding of the dynamics of seismicity and further expand the list of natural processes characterized by underlying hyperbolic geometry.

Henricksen, K., & Zaliapin, I. (2019). Hyperbolic property of earthquake networks. In JSM Proceedings, Statistics and the Environment Section. Alexandria, VA: American Statistical Association, 2024 – 2047. http://hdl.handle.net/11714/6719