Differences between spontaneous and triggered earthquakes: Their influences on foreshock probabilities

In this study we investigate the foreshock probabilities calculated from earthquake catalogs from Japan, southern California, and New Zealand. Unlike conventional studies on foreshocks, we use a probability-based declustering method to separate each catalog into stochastic versions of family trees, such that each event is classified as either having been triggered by a preceding event or being a spontaneous event. The probabilities are determined from parameters that provide the best fit of the real catalogue using a space-time epidemic-type aftershock sequence (ETAS) model. The model assumes that background and triggered earthquakes have the same magnitude-dependent triggering capability. A foreshock here is defined as a spontaneous event that has one or more larger descendants, and a triggered foreshock is a triggered event that has one or more larger descendants. The proportion of foreshocks in spontaneous events of each catalog is found to be lower than the proportion of triggered foreshocks in triggered events. One possibility is that this is due to different triggering productivity in spontaneous versus triggered events, i.e., a triggered event triggers more children than a spontaneous events of the same magnitude. However, further analysis on simulated data shows that such difference might be caused by the events triggered by smaller events below the magnitude threshold of the catalog. Even if the physical interpretation is unclear, a clustering model where spontaneous events and triggered events have different triggering behaviors can be used to assess the risk of foreshocks, and to avoid overpredicting.