J Seismol (2009) 13:53–72 DOI 10.1007/s10950-008-9115-1 ORIGINAL ARTICLE Sensitivity analysis of the parameters of earthquake recurrence time power law scaling Abdelhak Talbi · Fumio Yamazaki Received: 31 December 2007 / Accepted: 5 June 2008 / Published online: 10 July 2008 © Springer Science + Business Media B.V. 2008 Abstract The stability of the power law scaling of earthquake recurrence time distribution in a given space–time window is investigated, taking into account the magnitude of completeness and the effective starting time of aftershock sequences in earthquake catalogs from Southern California and Japan. A new method is introduced for sam- pling at different distances from a network of target events. This method allows the recurrence times to be sampled many times on the same area. Two power laws with unknown exponents are as- sumed to govern short- and long-recurrence-time ranges. This assumption is developed analytically and shown to imply simple correlation between these power laws. In practice, the results show that this correlation structure is not satisfied for short magnitude cutoffs (m c = 2.5, 3.5, 4.5), and hence the recurrence time distribution departs from the power law scaling. The scaling parame- ters obtained from the stack of the distributions corresponding to different magnitude thresholds are quite different for different regions of study. It is also found that significantly different scaling parameters adjust the distribution for different A. Talbi (B ) · F. Yamazaki Department of Urban Environment System, Graduate School of Engineering, Chiba University, 1–33, Yayoi-cyo, Inage-ku, Chiba-shi, Chiba, 263–8522, Japan e-mail: abdelhak_t@graduate.chiba-u.jp magnitude thresholds. In particular, the power law exponents decrease when the magnitude cut- off increases, resulting in a slower decrease of the recurrence time distribution, especially for short time ranges. For example, in the case of Japan, the exponent p 2 of the power law scaling at large recurrence times follows roughly the re- lation: p 2 (m c ) =−0.07m c + 2.7; m c ≥ 3.5, where m c is the magnitude cutoff. In case of Southern California, it is shown that Weibull distribution provides a better alternative fit to the data for moderate and large time scales. Keywords Recurrence times · Scaling · Power laws · Universality · Magnitude of completeness 1 Introduction Quite recently, a new scaling law for earthquake recurrence time distribution, D, has been intro- duced and claimed to be universal for broad areas and different magnitude thresholds (Bak et al. 2002; Christensen et al. 2002; Corral 2003, 2004a, b, 2007). The law we refer to, in short, as “Bak’s scaling law” consists of two power laws (PLs), one for short time ranges and the other for long time ranges. According to its authors, this law reveals a complex spatiotemporal organization of seismic- ity, which may be viewed as an intermittent flow of