Reply to comment by J. Greenhough et al. on “Relationship between accelerating seismicity and quiescence, two precursors to large earthquakes”

[1] The existence of Accelerating Seismic Release (ASR) prior to large earthquakes has been largely debated in the last decade and opponents are even stronger since the landmark paper by Hardebeck et al. [2008] (personal communication from StatSeis 2007, 2008 and 2009 meetings attendees). In this reply, we discuss the limits of approaches employed to verify the ‘non-existence’ of ASR and we emphasize the advantages of the method proposed by Mignan and Di Giovambattista [2008] to identify ASR, over the classic ASR regression method [e.g., Bowman et al., 1998]. [2] Since Greenhough et al. [2009] start arguing against the ASR hypothesis by citing the paper by Hardebeck et al. [2008], we believe we need to address some concerns about the methodology used to demonstrate that the significance level of ASR is too low to reject a range of alternative hypotheses. Our main criticisms are as follows: (1) accelerating patterns are defined by only a minimum of 10 data points. Mignan [2008a] showed that spurious cases are likely to be found by optimization procedures if the minimum number of events that form ASR is less than 20–50. In real examples, accelerations can be formed by more than 80 events [e.g., Mignan and Di Giovambattista, 2008]. (2) No example of simulated ASR obtained from random processes is illustrated, which unfortunately avoids any comparison with ASR observed in natural cases. Finally (3) claimed observations of decelerating seismicity correspond whether to a jump of seismicity at the beginning of the defined sequence or to under sampling (<15 events). [3] Criticisms to the ASR hypothesis were already made by Gross and Rundle [1998], who found that a Poisson model better explains the observed seismicity than the ASR model, based on a systematic power-law fit search in catalogues. However, both studies [Gross and Rundle, 1998; Hardebeck et al., 2008] fail to take into account the fact that ASR may require some specific physical and tectonic conditions to emerge from background seismicity. Jaumé and Sykes [1999] note that there are examples where ASR is not observed before large earthquakes and give three potential conditions for its appearance: a certain degree of heterogeneity in the fault system, a sufficient density of faults, and a fault hosting the main shock with a length/width ratio greater than one. These conditions are in agreement with the models proposed by Mignan et al. [2006] and Mignan [2008b]. As discussed by Jaumé and Sykes [1999], if the necessary conditions for the existence of an ASR sequence are not always met, it is clear that a study such as that conducted by Gross and Rundle [1998] would likely yield inconclusive results. One decade later, we can use the same argument over Hardebeck et al. [2008] study. [4] The cautionary comment by Greenhough et al. [2009] about regression on cumulative data, although relevant to many ASR studies [e.g., Bowman et al., 1998; Mignan et al., 2006], does not fully apply to the work by Mignan and Di Giovambattista [2008]. Indeed, in that paper, the authors use the Region-Time-Length (RTL) algorithm [Soboliev and Tyupkin, 1999] to determine the ASR space-time window instead of the classic regression method proposed by Bowman et al. [1998], which is criticized by both Hardebeck et al. [2008] and Mignan [2008b]. As observed by Greenhough et al. [2009], a least-square curve fitting is used to describe the ASR pattern of Mignan and Di Giovambattista [2008, Figure 3b]. However, the purpose of this regression (on cumulative data) is to quantify the degree of curvature of the sequence only. As noted by Vere-Jones et al. [2001], this method gives a reasonable visual fit to the data. [5] By not applying standard regression methods to the studied cumulative data, Mignan and Di Giovambattista [2008] do not fully test the reliability of their results and a more rigorous approach should be encouraged in future ASR studies, following advices from Greenhough et al. [2009] or Vere-Jones et al. [2001]. Nevertheless, Mignan and Di Giovambattista [2008] show that an independent algorithm (for quiescence identification) helps identifyingASR patterns and emphasize the possible link between these two different patterns and how it can be explained physically. Figure 1 shows the observed supposed precursory pattern (cumulative data) preceded by a constant background trend. A simple inspection shows what appears to be a change of seismogenic regime after t = 1996.85. A comparison with Figure 1 from Greenhough et al. [2009] shows that a random walk is very unlikely to produce such pattern. A next step could be to determine the probability of getting a similar signal as observed by Mignan and Di Giovambattista [2008], for a GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L17304, doi:10.1029/2009GL039871, 2009