Earthquake productivity law

Peter Shebalin^{1}, **Sergey Baranov ^{2}**

^{1}Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences^{2}Kola Branch of Geophysical Survey of Russian Academy of Sciences

bars.vl@gmail.com

The mechanisms responsible for stress transmission and probabilistic models were widely studied to explain earthquake clustering, but these approaches are still far from being able to reveal the cause-and- effect relationship between individual events. In this study we used an alternative approach which is based on proximity measures in the space-time-magnitude domain to construct hierarchical cluster trees and to identify pairs of events that are the nearest neighbors between two successive hierarchical levels. For declustering seismic catalog and identifying triggering and triggered earthquakes we used nearest-neighbor approach by I. Zaliapin and Y. Ben-Zion.

For each triggering earthquake, we count the number of triggered events at the lower hierarchical level using a relative magnitude threshold ΔM to account for scale invariance in the triggering process (M_{triggering} - M_{triggered}<ΔM). This number of triggered events is defined as the ΔM-productivity (hereafter the productivity). The distribution of the number of triggered events for an earthquake population is defined as the productivity distribution with a mean denoted L_{ΔM} and called the clustering factor.

Using global and regional earthquake statistics for many years we showed that earthquake productivity obeys exponential distribution F(x) = P(x<L) = 1 - exp(x/L_{ΔM}),
where L_{ΔM} is a clustering factor. This ΔM-productivity law is independent of the magnitude of triggering events and characterizes the earthquake clustering process across scales according to the relative magnitude threshold. We also showed that L_{ΔM} decreases drastically with the depth, but the distribution remains exponential.

The law of earthquake productivity, together with other laws of seismology (Gutenberg-Richter law and Omori-Utsu law), is important for assessing seismic hazard after strong earthquake. This research was supported by Russian Science foundation, project No. 20-17-00180.