Time-, Distance-, and Magnitude-Dependent Foreshock Probability Model for New Zealand

Abstract

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 FS and at distance r , a mainshock with magnitude M FS+ δM will occur: P ( t , r , δM )= P ×10(- BδM )( t + c t )- p t ( r + c r )- p r , where P , B , p t , c t , p r , and c r 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 t 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 r 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.