Recognizing the waveform of a foreshock

The 2011 Mw9.1 Tohoku, Japan, earthquake is the paradigmatic example of an earthquake anticipated by a signiﬁcant foreshock activity, with a Mw7.3 earthquake occurred two days before, within about 10 km 1 . Recent results 2 show that statistically relevant changes can be found in the magnitude distribution after the Mw7.3 foreshock but the discrimination between normal and foreshock activity still remains a scientiﬁc challenge 3 . Here we show that the envelope of the ground velocity recorded after the Mw7.3 foreshock presents an atypical sawtooth proﬁle very different from the one observed after other earthquakes 4 . We interpret this proﬁle as the consequence of the locked state of the mainshock fault which reduces the possibility of the foreshock to trigger its own aftershocks. We ﬁnd a similar sawtooth proﬁle after other Mw6+ foreshocks followed within 10 days by a larger earthquake, as in the case of the 2014 Mw8.1 Iquique, Chile, sequence. This observation allows us to deﬁne a level of concern, simply extracted from the ﬁrst 45 minutes of the recording waveform, associated to the occurrence of a larger earthquake. A test of the method for 47 Mw6+ worldwide earthquakes gives precise warning in time and space after all the 10 earthquakes followed by a

The 2011 Mw9.1 Tohoku, Japan, earthquake is the paradigmatic example of an earthquake anticipated by a significant foreshock activity, with a Mw7.3 earthquake occurred two days before, within about 10 km 1 . Recent results 2 show that statistically relevant changes can be found in the magnitude distribution after the Mw7.3 foreshock but the discrimination between normal and foreshock activity still remains a scientific challenge 3 . Here we show that the envelope of the ground velocity recorded after the Mw7.3 foreshock presents an atypical sawtooth profile very different from the one observed after other earthquakes 4 . We interpret this profile as the consequence of the locked state of the mainshock fault which reduces the possibility of the foreshock to trigger its own aftershocks. We find a similar sawtooth profile after other Mw6+ foreshocks followed within 10 days by a larger earthquake, as in the case of the 2014 Mw8.1 Iquique, Chile, sequence. This observation allows us to define a level of concern, simply extracted from the first 45 minutes of the recording waveform, associated to the occurrence of a larger earthquake. A test of the method for 47 Mw6+ worldwide earthquakes gives precise warning in time and space after all the 10 earthquakes followed by a 1 larger one with only 2 false alerts.
The coseismic slip during a large earthquake causes a shear stress reduction in regions which 1 have experienced large slips and, at the same time, concentrates residual shear stress near the slip 2 zone margins 5 . This stress redistribution promotes the occurrence of aftershocks with an abrupt 3 increase of the seismic rate. During normal activity the aftershock magnitudes get smaller for 4 increasing time, but, occasionally, aftershocks larger than the mainshock are observed. In these 5 cases the mainshock is relabeled foreshock, the largest earthquake becomes the mainshock and 6 the key question becomes if it is possible to distinguish foreshocks from normal seismic activity. 7 Focusing on moderate up to intermediate (Mw<5) mainshock magnitudes, after the original pa-8 per by Brodsky 6 , several studies [7][8][9][10][11][12] have shown that the number of foreshocks in instrumental 9 catalogs is larger than the one expected according to normal earthquake clustering models. This 10 result is also in agreement with a recent study 13 , before Mw4 mainshocks, which uses a high-11 resolution earthquake catalog. Statistically relevant deviations from normal seismicity has been 12 also found 7 before Mw6+ mainshocks but the first clear proof of the relevance of foreshocks in 13 improving the forecast of large (Mw6.5+) mainshocks has been only recently obtained by Gu- 14 lia & Wiemer (GW) 2 . Indeed, GW demostrated that the b-value of the Gutenberg-Richter (GR) 15 law decreases during foreshock activity whereas previous studies 14 [15][16][17] and they have been interpreted 19 2 as precursors according to the pre-slip model 18,19 . Other observations 20 , conversely, support the 20 cascade model 21,22 where foreshocks are no different from other sets of clustered earthquakes. 21 In this article we show that it is possible to discriminate between foreshocks and normal 22 seismic sequences from the profile of the envelope µ(t), defined as the logarithm of the envelope 23 of the ground velocity (see Methods). Immediately before an earthquake, µ(t) starts from the 24 background level µ B and rapidly raises up to the time t M , when it reaches its maximum value µ M . 25 This value corresponds to the perceived magnitude close to the recording station and represents 26 the mainshock magnitude apart from an additive term. The presence of aftershocks is clearly 27 visible 4, 23-26 in the decay of the envelope function µ(t), at times t > t M . We present two limit  Mw6.1 Platanos earthquake, for times t > t M , µ(t) fast decays and then remains stationary around 31 µ(t) µ B . Conversely, after the Kos earthquake, µ(t) does not go back to µ B but fluctuates around 32 a plateau with a minimum value µ L significantly larger than µ B . To understand the origin of the 33 plateau, we must take into account that if an aftershock has occurred at time t 1 , with percieved 34 magnitude µ 1 , it produces a peak µ(t 1 ) = µ 1 in the envelope. After this peak, µ(t) would decrease 35 towards µ B but if an other afteshock with perceived magnitude µ 2 occurrs at the time t 2 > t 1 , 36 the envelope raises again reaching a second peak µ(t 2 ) = µ 2 . If the aftershock productivity is 37 very high then the temporal distance (t 2 − t 1 ) between two subsequent aftershocks is very short 38 and µ(t) is not able to decay below a level of the plateau µ L µ 2 . In particular, in ref. 25   probability from µ(t), in the first minutes after t M , can be found in Ref. 4 .

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In Fig.1 probable to occur during an intense aftershock activity. Accordingly, the normal behavior of the 47 envelope function ( Fig.1[1a]) would have suggested a high plateau level with a large value of n af t .

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Instrumental data (black line in Fig.1[1b]), conversely, show exactly the opposite trend with µ(t) with zero events (valleys) interrupted by large earthquakes (peaks). This is incompatible with the 57 GR law which predicts thousands of events with µ i µ B + 1 for each event with µ i µ B + 4.

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According to previous observations, foreshock activity exhibits a much larger number of 120 events n obs with high peak values (µ i > µ M − 2) compared to its expected number n af t . The 121 quantity n obs /n af t should be therefore exhibit abnormal large values during foreshock sequences 122 and Q = (n obs /n af t )10 −βµ M can be used to define the level of concern associated to the occurrence 123 of a subsequent earthquake with peak magnitude larger than µ M (see Methods). We consider as defined as the fraction of events with Q > Q th and NOT followed by a larger earthquake. By 135 changing Q th we obtain a diagram (Fig.3) with points close to the perfect prediction (T P R = 136 1, F AR = 0) and well above the random prediction, which can be discarded with a confidence 137 level above the 99.99999%.

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In Suppl. Fig.1 we show that there exists a specific Q th = 0.18 which allows us to score all the evaluation of Coulomb stress changes 38 . As a consequence it appears reasonable that one can 160 achieve more accurate forecasting by combining the two approaches: the Q value can be adopted as 161 an initial discriminant and the b-value can be used to identify higher stressed regions, which will be we usually consider the closest station compatible with the above constraint on µ B . We have also 190 verified that the value of µ M is not affected by staturation problems.

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The selection of earthquakes 192 We adopt the searching criterion of the USGS earthquake hazard program to obtain the occur-193 rence time and epicentral coordinates of an Mw6+ earthquake. We next consider regional networks 194 to verify this information and to identify the stations closest to the earthquake epicenter. Once the 195 waveform with the ground velocity has been downloaded, the procedures to obtain the envelope 196 and to evaluate Q, illustrated above, are automatically implemented.

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The peak distribution 198 We identify aftershocks from the envelope function µ(t) by means of the procedure devel-199 oped by Peng et al. 23 . We define the quantity n obs as the number of aftershocks producing a peak   (FAR) for the method based on the Q-value with β = 1 (black circles) and with β extracted from data (green diamonds). The dashed blue diagonal represents random prediction (the nullhypothesis) whereas for points above the continuous red line, the null hypothesis can be rejected with a confidence level larger than 99.99999%.