The possibility that a moderate earthquake may be followed by an equal or larger one (foreshock probability) increases the hazard in its immediate vicinity for a short time by an order of magnitude or more. Thus, foreshock probabilities are of interest for time-dependent seismic hazard forecasts. We calculate the probability of an initial earthquake (a foreshock) being followed by a mainshock in New Zealand, considering the parameters of elapsed time and distance and magnitude differences between foreshock and mainshock. We use nonaftershock events between 1964 and 2007, with magnitude ≥4.0 and shallower than 40 km, separating the catalog into events within and outside the Taupo volcanic zone (TVZ). We provide a model for the probability P(t,r,δM) that at time t after a potential foreshock (FS) of magnitude MFS and at distance r, a mainshock with magnitude MFS+δM will occur: P(t,r,δM)=P0×10(-BδM)(t+ct)-pt(r+cr)-pr, where P0, B, pt, ct, pr, and cr are constants to be determined.
We find that (1) binning data using fixed intervals of time or space before fitting the parameters returns different values than a more robust approach of fitting directly the entire range, (2) foreshock probabilities decrease with increasing interevent time as described by a modified Omori law with an exponent pt close to 1 (0.9±0.2 [TVZ] and 0.8±0.1 elsewhere—uncertainty estimates are 95% confidence intervals throughout this study), (3) foreshock probabilities decrease with increasing epicentral distance also following a modified Omori type decay with exponent pr of 0.9±0.2 (non-TVZ) and 1.7±0.6 (TVZ), and (4) the mainshock magnitude distribution follows the Gutenberg–Richter relationship (B=1.0±0.17 [non-TVZ] and 1.5±0.5 [TVZ]). The differences between the TVZ and the rest of New Zealand are consistent with higher attenuation in the region, deduced from previous studies.