Supplementary Information

The debate on the prognostic value of earthquake foreshocks: A meta-analysis

Arnaud Mignan1

1: Swiss Seismological Service, ETH Zurich, NO H66, Sonneggstrasse 5, CH-8092 Zurich

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1. Data

I have reviewed almost one hundred references on accelerating seismic release, relying mostly on the comprehensive review made by Ref. 18, and approximately one hundred references on short-term foreshocks. In order to build a comprehensive database, I have used the following approach: (i) Select all relevant references provided by the Google Scholar search engine based on keywords, such as “foreshock” or “accelerating moment release”; (ii) Select all relevant references listed in the reference list of each one of the articles already in the database; (iii) Repeat step (ii) until no more new reference is found. In that approach, only articles not cited by any of the references contained in the database may have been missed. Even if the completeness of the database cannot be averred, the database should nonetheless be representative of the foreshock literature. Of all the published studies, I have only found 37 in which foreshocks are observed and their possible origin explained, whether by earthquake triggering or loading due to aseismic slip (Table S1). I have not considered studies that infer one theory or the other based on changes of the slope of the GR law, on power-law time-to-failure fitting, or on event migration, since these patterns can be explained indiscriminately by both theories5,6,18. Such studies form the bulk of the two hundred references investigated. It should be noted that the results presented in Table S1 are based on the conclusions of the different peer-reviewed studies, whether they really do or do not represent the true foreshock process. No attempt has been made to rank the studies by the quality of their analyses. All 37 studies are considered equally valid in the present work.

Supplementary Table S1: Data used in the meta-analysis. Mainshock and minimum foreshock magnitudes are represented by M and mmin, respectively. T and L refer to earthquake triggering and to loading due to aseismic slip, respectively.

No. / Ref. / Data source / Data type / M / mmin / Foreshock / Method / Result
1 / 1 / 1975 Haicheng, China / Sequence / 7.3 / 0.6 / Anomalous / Physics / No T
“The increase in shear stress on the mainshock fault caused by the foreshocks is very small and […] direct triggering of the mainshock by the foreshocks is unlikely”, p. 4575
2 / 31 / 1979 Petatlan, Mexico / Sequence / 7.6 / 1.6 / Anomalous / Heuristic / L
“[aseismic region 10 km wide between foreshocks and mainshock epicentre] suggests an influence of the pre-main shock activity by an asperity existing along the Benioff zone. The stress […] probably is transmitted from below”, p. 4261
3 / 32 / San Andreas, California / Sequences / 5.0
5.2
5.4
5.5
5.8
6.4 / 2.0 / Anomalous / Heuristic / No T
“If [the model of foreshocks triggering the mainshock] were true, the durations of the sequences should decrease as the magnitudes of the foreshocks increase. No such dependence is seen in these data”, p. 1377
4 / 33 / California / Sequences / 6.5
6.8
7.1
8.3 / 5.0 / Anomalous / Heuristic / L
“This type of precursor [over extended area] seems to require the presence of several major faults in close enough proximity to one another that moderate-size shocks are selectively triggered on surrounding faults during the latter stages of the cycle of strain buildup to large earthquakes”, p. 595
5 / 34 / Central and Northern California / Stacking / 2.4 / 1.5 / Normal / Statistics / T
“Foreshocks were explained as events which had an afterevent which happened to be bigger than the triggering event”, p. 910
6 / 26 / 1992 Landers, California / Sequence / 7.3 / 1.5 / Anomalous / Physics / No T
“Modeling of the Coulomb stress changes due to all previous foreshocks indicates that the foreshocks probably did not trigger each other”, p. 9865
7 / 35 / California / Sequences / 4.7
5.2
5.5
6.1
6.4
7.3 / 1.0 / Anomalous / Physics / No T
“In general, these foreshock sequences are not compatible with a cascading failure nucleation model”, p. 22371
8 / 36 / San Francisco Bay, California / Sequences / 7.0
7.1
7.9 / 5.5 / Anomalous / Physics / L
“We find that the changes in moderate seismicity during this time period are broadly consistent with our model of elastic strain accumulation and release on the major faults”, p. 786
9 / 37 / California / Sequences / 6.8
6.9
7.0
7.1
7.3
7.5 / 5.1 / Anomalous / Heuristic / No T
“There is no evidence [precursors distributed over large distances] to suggest that the precursor earthquakes directly influence the time and location of the subsequent strong earthquake”, p. 5794
10 / 38 / Japan / Stacking / 5.0 / 3.0 / Normal / Statistics / T
“[Foreshocks as mainshock triggers] is compatible with the relationship between a mainshock and aftershocks […]. However the values of exponent of the power law […] are significantly smaller than those for similarly stacked aftershocks”, p. 381
11 / 39 / Global / Stacking / 6.0
7.0 / 5.0 / Normal / Statistics / T
“The world generic [aftershock cluster] model would better represent worldwide foreshock-related conditional probabilities”, p. 4766
12 / 40 / New Zealand / Stacking / 4.0 / 4.0 / Normal / Statistics / T
“Our results are consistent with models in which foreshocks are a manifestation of the same process as aftershocks, but the huge range allowed makes such consistency less meaningful”, p. 467
13 / 41 / California, Nevada / Stacking / 5.0 / 2.0 / Normal / Statistics / T
“The data are consistent with our hypothesis that main shock and aftershock magnitude are independent, and that foreshocks are simply small main shocks with large aftershocks”, p. 5
1999 Hector Mine, California / Sequence / 7.1 / 2.0 / Normal / Statistics / T
“It is probable [described as “circumstantial evidence”, p. 1] that the 1999 M7.1 Hector Mine earthquake was not triggered directly by the 1992 M7.3 Landers earthquake but rather by its own foreshocks, which were themselves triggered directly or indirectly by the Landers earthquake”, p. 12
14 / 42 / 1998 Sendai, Japan / Sequence / 5.0 / 1.4 / Anomalous / Physics / No T
“Cumulative Coulomb stress changes at the hypocenters of those foreshocks and the mainshock do not support the cascade model for generation of the foreshocks and the mainshock”, p. 2476
15 / 6 / Southern California / Stacking / 3.0 / 3.0 / Normal / Statistics / T
“The cascade model described here [ETAS] is sufficient to explain the properties of foreshocks in time, space and magnitude”, p. 9
16 / 27 / 1999 Hector Mine, California / Sequence / 7.1 / 1.3 / Anomalous / Heuristic / No T
“Qualitatively, the lack of triggering in the foreshock sequence, the foreshock mechanisms and the mainshock location in the stress shadow of the foreshocks do not suggest static stress triggering”, p. 4
17 / 7 / Global
California / Stacking / 6.0
2.2;4.8 / 5.6
2.2 / Normal / Statistics / T
“A single physical triggering mechanism is responsible for the occurrence of aftershocks, foreshocks, and multiplets”, p. 88
18 / 43 / Southern California / Stacking / 5.4 / 2.5 / Normal / Statistics / T
“The SCEDC statistics satisfy an ETAS model with a = 0.8-0.9, consistent with previous catalogue studies”, p. 459
East Pacific Rise / Stacking / 5.4 / 2.5 / Anomalous / Statistics / No T
“We can reject the ETAS hypothesis that the clustering of foreshocks, mainshocks and aftershocks […] can be described by the same triggering mechanism”, p. 459
19 / 44 / 2003 Tokachi-oki, Japan / Sequence / 8.0 / 0.0
1.5 / Anomalous / Physics / L
“Each anomaly [deviation from ETAS] is explained by change in Coulomb failure stress, caused by aseismic slip”, p. 1
20 / 45 / Sumatra / Sequences / 9.0
8.7 / 4.5 / Anomalous / Physics / L
“The outlined region corresponds to the 0.02 bar Coulomb-pre-stress contour […]. The earthquakes within this contour demonstrate AMR”, p. 642
21 / 46 / California / Sequences / 6.5
6.6
6.7
7.0
7.1
7.3
7.5 / 3.5 / Anomalous / Physics / L
“AMR is shown to occur preferentially in the lobes of the backslip stress field predicted by the stress accumulation model”, p. 1
22 / 19 / 2004 Niigata-Ken-Chuetsu, Japan / Sequence / 6.6 / 2.0 / Anomalous / Physics / L
“The quiescence and activation, which took place in the zone of negative and positive increments of the Coulomb failure stress, respectively, were possibly caused by aseismic slip on or near the focal fault plane”, p. 1
23 / 47 / Southern California, global / Stacking / 2.0
5.7 / 2.0
5.7 / Normal / Statistics / T
“The ability of foreshocks to trigger larger earthquakes is consistent with the triggering capability of mainshocks. Thus, […] foreshocks have no more predictive power than other earthquakes”, p. 2147
24 / 24 / California, Nevada / Stacking / 6.5 / 4.0 / Normal / Statistics / T
“These tests [comparison to ETAS simulations] demonstrate that apparent AMR may arise from […] normal foreshock and aftershock activity”, p. 1
25 / 48 / 1997 Umbria-Marche, Italy / Sequence / 6.0 / 2.3 / Anomalous / Statistics / L
“We then show that background events located in that spatiotemporal window [quiescence due to aseismic slip] form a clear acceleration, as expected by the Non-Critical PAST”, p. 1
26 / 49 / New Zealand / Stacking / 4.0 / 4.0 / Normal / Statistics / T
“New Zealand’s foreshock probabilities follow this generic law [Gutenberg-Richter law and modified Omori law] with slightly smaller decay exponents compared to Californian foreshocks and New Zealand aftershocks”, p. 2158
27 / 50 / Japan
New Zealand
Southern California / Stacking / 4.3
4.1
3.5 / 4.2
4.0
3.4 / Normal / Statistics / T
“Even if the physical interpretation is unclear, a clustering model where spontaneous events and triggered events have different triggering behaviors can be used to assess the risk of foreshocks”, p. 1
28 / 51 / Greece / Sequences / 6.4
6.5
6.6 / 3.5 / Anomalous / Physics / L
“Studying the annual rate of occurrence it is found that in areas of positive pre-stress changes a sharp increase of the number of earthquakes is observed several years before the occurrence of the main shock”, p. 367
29 / 20 / 1999 Izmit, Turkey / Sequence / 7.6 / 0.3 / Anomalous / Heuristic / L
"The signal consisted of a succession of repetitive seismic bursts, accelerating with time, [...] These observations show that the earthquake was preceded for 44 minutes by a phase of slow slip", p. 877
30 / 52 / Southern California / Stacking / 3.0 / 2.0 / Normal / Statistics / T
“These foreshocks are an expected consequence of earthquake interaction and clustering. Their existence and location near the eventual rupture does not in itself indicate a preparatory strain accumulation process beyond ordinary earthquake triggering”, p. 5
31 / 21 / 2011 Tohoku, Japan / Sequence / 9.0 / 2.0 / Anomalous / Heuristic / L
"The time history of quasi-static slip along the plate interface, based on small repeating earthquakes that were part of the migrating seismicity, suggests that two sequences involved slow-slip transients", p. 705
32 / 53 / Southern California / Stacking / 2.0 / 2.0 / Anomalous / Statistics / No T
“We show that the linear density probability of earthquakes occurring before and after […] mainshocks displays a symmetrical behavior […]. This observation can be used to discriminate spatial clustering due to foreshocks from the one induced by aftershocks”, p. 1
33 / 54 / 2011 Tohoku, Japan / Sequence / 9.0 / 1.2 / Normal / Statistics / T
“The whole sequence [2 day-long foreshock sequence initiated by a Mw7.3 earthquake] can be readily explained without the need to invoke aseismic transients”, p. 1
34 / 25 / Italy, Southern California / Stacking / 5.5
6.0 / 4.0 / Normal / Statistics / T
“The results indicate that the foreshock activity observed in the real catalogs is compatible with what is expected by the ETAS model”, p. 1
35 / 5 / 2009 L’Aquila, Italy / Sequence / 6.3 / 1.8;3.3 / Anomalous / Statistics / L
“Based on the computation of the temporal joint log-likelihood, we found that the theoretical time series [predicted by the NC PAST] provides a good match to the observations”, p. 4
2009 L’Aquila, Italy / Sequence / 6.3 / 3.4;6.3 / Normal / Statistics / No L
“Only for a minimum magnitude cutoff Mco ≥ 3.4 is the time series better fitted by a Poisson process [95% of events shown not to produce any aftershock]”, p. 4
36 / 55 / California / Stacking / 2.0 / 1.5 / Normal / Statistics / T
“We can distinguish among three different kinds of spatial clustering […] (i) Direct triggering. […] (ii) Correlated triggering. […]”, p. 12
California / Stacking / 2.0 / 1.5 / Anomalous / Statistics / L
[…] (iii) Correlations originating from some underlying physical process”, p. 12
37 / 28 / North Pacific / Stacking / 6.5 / 2.5 / Anomalous / Statistics / No T
“The observed pattern seems to preclude triggering of the mainshock by foreshocks for most of the subduction earthquakes of the data set”, p. 302

2. Additional references

31. Hsu, V., Gettrust, J. F., Helsley, C. E. & Derg, E. Local Seismicity Preceding the March 14, 1979, Petatlan, Mexico Earthquake (Ms = 7.6). J. Geophys. Res. 88, 4247-4262 (1983).

32. Jones, L. M. Foreshocks (1966-1980) in the San Andreas System, California. Bull. Seismol. Soc. Am. 74, 1361-1380 (1984).