Perspectives on Clustering and Declustering of Earthquakes

Clustering is a fundamental feature of earthquakes that impacts basic and applied analyses of seismicity. Events included in the existing short-duration instrumental catalogs are concentrated strongly within a very small fraction of the space–time volume, which is highly amplified by activity associated with the largest recorded events. The earthquakes that are included in instrumental catalogs are unlikely to be fully representative of the long-term behavior of regional seismicity. We illustrate this and other aspects of space–time earthquake clustering, and propose a quantitative clustering measure based on the receiver operating characteristic diagram. The proposed approach allows eliminating effects of marginal space and time inhomogeneities related to the geometry of the fault network and regionwide changes in earthquake rates, and quantifying coupled space–time variations that include aftershocks, swarms, and other forms of clusters. The proposed measure is used to quantify and compare earthquake clustering in southern California, western United States, central and eastern United States, Alaska, Japan, and epidemic-type aftershock sequence model results. All examined cases show a high degree of coupled space–time clustering, with the marginal space clustering dominating the marginal time clustering. Declustering earthquake catalogs can help clarify long-term aspects of regional seismicity and increase the signal-to-noise ratio of effects that are subtler than the strong clustering signatures. We illustrate how the high coupled space–time clustering can be decreased or removed using a data-adaptive parsimonious nearest-neighbor declustering approach, and emphasize basic unresolved issues on the proper outcome and quality metrics of declustering. At present, declustering remains an exploratory tool, rather than a rigorous optimization problem, and selecting an appropriate declustering method should depend on the data and problem at hand.