A common origin for aftershocks, foreshocks, and multiplets

We demonstrate that the statistics of earthquake data in the global Centroid Moment Tensor (CMT) and National Earthquake Information Center (NEIC) catalogs and local California Council of the National Seismic System (CNSS) catalog are consistent with the idea that a single physical triggering mechanism is responsible for the occurrence of aftershocks, foreshocks, and multiplets. Specifically, we test the hypothesis that tectonic earthquakes usually show clustering only as a result of an initial earthquake triggering subsequent ones and that the magnitude of each triggered earthquake is entirely independent of the magnitude of the triggering earthquake. Therefore a certain percentage of the time, as determined by the Gutenberg-Richter magnitude-frequency relationship, an earthquake should by chance be larger than or comparable in size to the earthquake that triggered it. This hypothesis predicts that the number of times foreshocks or multiplets are observed should be a fixed fraction of the number of aftershock observations. We find that this is indeed the case in the global CMT and NEIC catalogs; the average ratios between foreshock, aftershock, and multiplet rates are consistent with what would be predicted by the Gutenberg-Richter relationship with b = 1. We give special attention to the Solomon Islands, where it has been claimed that unique fault structures lead to unusually high numbers of multiplets. We use Monte Carlo trials to demonstrate that the Solomon Islands multiplets may be explained simply by a high regional aftershock rate and earthquake density. We also verify our foreshock results from the more complete recordings of small earthquakes available in the California catalog and find that foreshock rates for a wide range of foreshock and mainshock magnitudes can be projected from aftershock rates using the Gutenberg-Richter relationship with b = 1 and the relationship that the number of earthquakes triggered varies with triggering earthquake magnitude M as clO(alphaM), where alpha is a productivity constant and a is equal to 1. Finally, we test an alternative model that proposes that foreshocks do not trigger their mainshocks but are instead triggered by the mainshock nucleation phase. In this model, the nucleation phase varies with mainshock magnitude, so we would expect mainshock magnitude to be correlated with the magnitude, number, or spatial extent of the foreshocks. We find no evidence for any of these correlations.