correspondence Artificial seismic acceleration To the Editor — In their 2013 Letter, magnitude of completeness threshold of earthquake catalogues from California, Bouchon et al.1 claim to see a significant M = 2.5 (Supplementary Information), can produce acceleration comparable acceleration of seismicity before magnitude either in individual sequences or when to the data used by Bouchon et al. ≥6.5 mainshock earthquakes that occur combined. As a result, we argue the (Supplementary Information). Although in interplate regions, but not before statistical analysis of the data, such the ETAS parameters for California may not intraplate mainshocks. They suggest as their finding that the Gutenberg– be applicable to other regions that are part that this accelerating seismicity reflects Richter value b = 0.63, and simulations of the data set used by Bouchon et al., they a preparatory process before large plate- based on that analysis are flawed (see demonstrate the existence of reasonable boundary earthquakes. We concur that Supplementary Information). parameters that produce different behaviour their interplate data set has significantly Bouchon and colleagues compare their than the simulations in Bouchon et al. more foreshocks than their intraplate data with simulations that use the cascade- Bouchon and colleagues also compare data set; however, we disagree that the model-based epidemic type aftershock the acceleration seen before the mainshocks foreshocks indicate a precursory phase that sequence (ETAS) model5. The individual with activity seen before nearby smaller is predictive of large events in particular. data sets are too small to constrain the ETAS earthquakes. The cascade model predicts Acceleration of seismicity in stacked parameters, so Bouchon et al. combine that these stacks should be statistically foreshock sequences has been seen before2,3 them. However, stacking incomplete identical. Unfortunately, Bouchon and and has been explained by the cascade sequences does not correct for the missing colleagues only use a single set of smaller model, in which earthquakes occasionally events. Bouchon and colleagues use a controls that are of unknown interplate or trigger aftershocks larger than themselves4. joint maximum-likelihood inversion to intraplate origin, and again the analysis In this model, the time lags between the simultaneously determine ETAS parameters. uses an incomplete data set. We cannot smaller mainshocks and larger aftershocks Although common, this technique often determine the interplate versus intraplate follow the inverse power law common leads to an erroneously low α value6 — origin of the small earthquakes, but using to all aftershock sequences, creating an the value that determines the relative more controls and a higher completeness apparent acceleration when stacked (see aftershock productivity between small threshold brings the mainshocks and Supplementary Information). and large mainshocks (see Supplementary controls into agreement (Fig. 1). A fundamental problem is that the Information). In simulations, this low value In summary, we find that the tests catalogues used by Bouchon et al. — causes high rates of secondary aftershocks, performed by both Bouchon et al. and by seismicity recorded in a 50-km radius slow sequence decay, and a weakening of us do not provide compelling evidence prior to each mainshock — do not contain the apparent acceleration due to foreshocks. for precursory activity that could be all earthquakes down to their chosen We show that ETAS parameters, fit to used to predict large earthquakes at ab 1 1 Random controls (mean & 95% confidence) Random controls, M≥3 (mean & 95% confidence) ed) 0.9 Controls (ref. 1) ed) 0.9 Controls, M≥3 (ref. 1) Mainshocks (ref. 1) 0.8 0.8 Mainshocks, M≥3 (ref. 1) 0.7 0.7 es (normaliz es (normaliz 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 e number of earthquak e number of earthquak 0.2 0.2 0.1 0.1 Cumulativ Cumulativ 0 0 543210 543210 Time before earthquakes (days) Time before earthquakes (days) Figure 1 | Stacked earthquakes prior to the mainshocks discussed by Bouchon et al. compared with stacked earthquakes prior to randomly selected earthquakes. a, The mean of the randomized controls (blue) with 95% confidence bounds in grey (determined by Monte Carlo sampling random subsets the size of the data set compiled by Bouchon et al.), compared with the mainshocks from Bouchon et al. (red). More strict control earthquakes defined by Bouchon and colleagues (see text) are shown in green. b, Same asleft panel, but using only earthquakes with M ≥ 3. While the mainshocks discussed by Bouchon et al. are marginally consistent with the random controls at M ≥ 2.5, at M ≥ 3 they are much more consistent. 82 NATURE GEOSCIENCE | VOL 8 | FEBRUARY 2015 | www.nature.com/naturegeoscience © 2015 Macmillan Publishers Limited. All rights reserved correspondence plate boundaries. Although some large the seismic acceleration observed prior to 7. Kato, A. et al. Science 335, 705–708 (2012). earthquakes may be preceded by slow interplate earthquakes can be explained by 8. Yagi, Y. et al. Geophys. Res. Lett. 41, 4201–4206 (2014). slip and/or migration of seismicity, these normal foreshock processes. ❐ Additional information processes have not been shown to be Supplementary information is available in the online precursory for interplate M ≥ 6.5 events in References version of the paper. particular. For example, the foreshocks of 1. Bouchon, M., Durand, V., Marsan, D., Karabulut, H. & Schmittbuhl, J. Nature Geosci. 6, 299–302 (2013). Karen R. Felzer1, Morgan T. Page1* and the 2011 M = 9.0 Tohoku-Oki earthquake 2. Papazachos, B. C. Bull. Seis. Soc. Am. 96, 389–399 (1973). 2 in Japan and the 2014 M = 8.1 Iquique 3. Jones, L. M. & Molnar, P. J. Geophys. Res. 84, 3596–3608 (1979). Andrew J. Michael earthquake in Chile abutted the mainshock 4. Helmstetter, A., Sornette, D. & Grasso, J-R. J. Geophys. Res. 1US Geological Survey, Pasadena, California hypocenter7,8, thus aseismic slip is not 108, 2046 (2003). 91106, USA. 2US Geological Survey, Menlo 5. Ogata, Y. J. Am. Stat. Assoc. 83, 9–27 (1988). required to connect the foreshocks and 6. Helmstetter, A., Kagan, Y. Y. & Jackson, D. D. J. Geophys. Res. Park, California 94025, USA. mainshocks. We therefore suggest that 110, B05S08 (2005). *e-mail: [email protected] Reply to ‘Artificial seismic acceleration’ Bouchon et al. reply — In our study1, we Californian catalogues used by Felzer et al. of events both in time and in space. The show that most large magnitude M ≥ 6.5 is better than one based on the actual observations we reported show that most interplate earthquakes are preceded catalogues from the specific regions we of the foreshocks in our subduction data by an acceleration of seismic activity. studied. Regarding catalogue completeness, set, which makes up the majority of our The Correspondence from Felzer et al. our hypothesis is that we can invert database, do not cluster near the main questions our interpretation of this the ETAS parameters by mixing all the shock hypocentre or near each other, acceleration. It has long been recognized earthquake sequences because ETAS is a but instead are spread over a broad area. that one characteristic of seismic events linear model. We suggest that this linearity Because these foreshocks cluster in time is their natural tendency to cluster justifies the inference of one magnitude but do not cluster in space, as the ETAS both in space and time, as evidenced by of completeness for the set of sequences. model implicitly assumes, the ETAS model the presence of aftershocks following Imposing a magnitude cut-off of M = 3.0, cannot provide a correct description of an earthquake. The debate raised by as Felzer and colleagues advocate, would them. Indeed, the simple observation Felzer et al. is whether foreshocks result eliminate the majority of foreshocks. of the non-spatial clustering of many only from this tendency to cluster, that is, Felzer et al. also suggest that our foreshocks (Fig. 4e in ref. 1) demonstrates, a first shock triggers others and eventually value for the productivity parameter α independently of the use of any model, that one of them triggers a large earthquake is too low. However, inversions of ETAS foreshocks are not generally the result of by something akin to a random throw. parameters based on a likelihood function the tendency of seismic events to cluster Felzer and colleagues advocate this systematically provide values lower than both spatially and temporally. In physical interpretation. Alternatively, foreshocks α = 2.3 obtained by Felzer et al. using the terms, this means that many foreshocks are may indicate an underlying mechanical weakly constrained Bath’s Law, a statistical too distant from each other and too distant process, such as slow fault slip, in which the law relating the magnitudes of the main from the main shock hypocentre to trigger foreshocks are simply the seismically visible shock and largest aftershock. For example, one another. ❐ signature — an interpretation we claim our Zhuang et al.3 analysed the Japanese observations favour. catalogue, which covers an important References Felzer and colleagues mostly question part of the subduction zone we analysed, 1. Bouchon, M., Durand, V., Marsan, D., Karabulut, H. & Schmittbuhl, J. Nature Geosci. 6, 299–302 (2013). our calculation of two curves in our and obtained α values in the range 1.33 to 2. Felzer, K. R., Page, M. T. & Michael, A. J. Nature Geosci. original Fig. 4a,b (shown in blue) and in 1.36. Similarly, in their study of worldwide 8, 82–83 (2015). Supplementary Fig. S15. These curves seismicity, Chu et al.4 obtained an α value 2. Ogata, Y. J. Am. Stat. Assoc. 83, 9–27 (1988). 3. Zhuang J., Ogata, Y. &Vere-Jones, D. J. Geophys. Res. are intended to give an estimate of the of 0.89 for subduction zones. Finally, even 109, B05301 (2004).