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Department of Earth and Planetary Sciences
Harvard University
20 Oxford St.
Cambridge, Massachusetts 02138
(K.R.F., G.E.)
Department of Earth Sciences
Boston University
685 Commonwealth Ave.
Boston, Massachusetts 02215
(R.E.A.)
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 c10
M, where
c is a productivity constant and 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.
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