Characteristic Magnitude and Spatiotemporal Relationships of Aftershocks and Background Earthquakes

Abstract

Aftershocks, background earthquakes, and their spatiotemporal parameters have been studied for decades for the purpose of hazard assessment and forecasting. Methods for determining these parameters or seismic attributes are becoming increasingly sophisticated and varied; some optimize the results to fit observations using trial and error, while others do the same by giving prescriptions for a limited region. Here, we propose a method that is potentially useful in general hazard assessment and forecasting applications. We categorized the earthquakes into two groups, aftershocks (triggered events) and background earthquakes, by introducing the network distance, i.e., the shortest distance between two events of equal magnitude within a modified interevent time, into the k-means clustering, which couples the modified interevent time and magnitude hierarchically. Our results show a bimodal distribution consisting of a power law at shorter network distances and a lognormal distribution at longer network distances, implying that earthquakes of magnitudes larger than the characteristic magnitude, found to be 4.5 for Taiwan and 4.3 for California, may be only weakly linked to other same magnitude earthquakes and hence are hard to be triggered even by events of larger size.