• journal_title：Bulletin of the Seismological Society of America
• Contributor：Thessa Tormann ; Martha K. Savage ; Euan G. C. Smith ; Mark W. Stirling ; Stefan Wiemer
• Publisher：Seismological Society of America
• Date：2008-
• Format：text/html
• Language：en
• Identifier：10.1785/0120060217
• journal_abbrev：Bulletin of the Seismological Society of America
• issn：0037-1106
• volume：98
• issue：5
• firstpage：2149
• section：Articles

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 M<sub>FSsub> and at distance r, a mainshock with magnitude M<sub>FSsub>+δM will occur: P(t,r,δM)=P<sub>0sub>×10<sup>(-BδM)sup>(t+c<sub>tsub>)<sup>-p<sub>tsub>sup>(r+c<sub>rsub>)<sup>-p<sub>rsub>sup>, where P<sub>0sub>, B, p<sub>tsub>, c<sub>tsub>, p<sub>rsub>, and c<sub>rsub> 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 p<sub>tsub> 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 p<sub>rsub> 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.