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Appendices
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A. Different grouping for small and large eruptions
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We tested the properties of the p' and p-value when we modify the grouping by
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choosing small eruptions as VEI<=1 and large eruptions as VEI>=2. With this different
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grouping, we still find a clear dependence of the p’-value with eruptions sizes. p’ and p-
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values and error bars are reported in table A. Even within the 2-sigma error bar (which
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is a proxy for the 95% confidence level) the p’-values for VEI>=1 eruptions is accepted
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to be smaller than the p’-value for VEI>=2 eruptions (red values in table A) at a 95%
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confidence level.
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figure A : Foreshocks (a) and aftershocks (b) patterns as a function of trigger size. Light to
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dark grey: mainshocks are earthquakes from worldwide catalog for magnitude ranges in
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[5.5; 7.5]. Light to dark blue (a) or red (b): mainshocks are eruptions from worldwide
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catalog for small VEI<2, all and large VEI>=2. <N> is the averaged number of seismic
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events per day (normalized by the number of eruption in each class). We used a Gaussian
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smoothing function [Helmstetter et al., 2003]. The p' and p values are the Omori law
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exponents estimated with the maximum likelihood method [Ogata et Katsura, 1993] on the
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seismicity starting from eruption time to the day when it merges with noise level.
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p'
p'
p' +/- σp' (66%)
p'+/- 2σp' (95%)
p
σp
VEI<=1
0.40
0.28
0.12-0.68
-0.16-0.96
0.71
0.27
All VEI
0.93
0.10
0.83-1.03
0.73-1.13
0.74
0.15
VEI>=2
1.55
0.09
1.46-1.64
1.37-1.73
0.76
0.18
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Table A: p’ and p-value of the Omori law for three different datasets of eruptions. The p'
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and p-values and error bars are estimated with the maximum likelihood method [Ogata et
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Katsura, 1993]. The standard deviation  is used as a proxy for the 66% confidence level,
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and 2is the proxy for the 95% confidence level.
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B. Subdivision of the data
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The second test consists in subdividing randomly each class into three groups with the
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same number of events in each group and in computing the p' and p-value for each
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subdivisions. We retrieve similar values for all the subdivisions (figure B1 for small
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eruptions and B2 for large eruptions).
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figure B1 : Stacked foreshocks (a) and aftershocks (b) patterns for small eruptions
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(VEI<=2). Light to dark grey: mainshocks are earthquakes from worldwide catalog for
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magnitude ranges in [5.5; 7.5]. Dark blue (a) and dark red (b): mainshocks are all the
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small eruptions from worldwide catalog (978 events of VEI<=2). Light blue (a) and light
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red (b) : three random subdivisions of the small eruptions (with 326 eruptions in each
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dataset). <N> is the averaged number of seismic events per day (normalized by the number
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of eruption in each class). We used a Gaussian smoothing function [Helmstetter et al.,
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2003]. The p' and p values are the Omori law exponents estimated with the maximum
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likelihood method [Ogata et Katsura, 1993] on the seismicity starting from eruption time
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to the day when it merges with noise level.
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figure B2 : Stacked foreshocks (a) and aftershocks (b) patterns for large eruptions
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(VEI>=3). Light to dark grey: mainshocks are earthquakes from worldwide catalog for
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magnitude ranges in [5.5; 7.5]. Dark blue (a) and dark red (b): mainshocks are all the large
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eruptions from worldwide catalog (172 events of VEI>=3). Light blue (a) and light red (b) :
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three random subdivisions of the large eruptions (with 57 eruptions in each dataset). <N>
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is the averaged number of seismic events per day (normalized by the number of eruption in
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each class). We used a Gaussian smoothing function [Helmstetter et al., 2003]. The p' and p
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values are the Omori law exponents estimated with the maximum likelihood method
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[Ogata et Katsura, 1993] on the seismicity starting from eruption time to the day when it
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merges with noise level.
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N
p'-value
p-value
All VEI<=2
978
0.51 +/- 0.26
0.70 +/- 0.16
1st subcatalog
326
0.53 +/- 0.20
0.71 +/- 0.15
2d subcatalog
325
0.49 +/- 0.15
0.66 +/- 0.22
3d subcatalog
326
0.51 +/- 0.18
0.68 +/- 0.18
All VEI>=3
172
2.06 +/- 0.08
0.78 +/- 0.26
1st subcatalog
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2.23 +/- 0.18
0.83 +/- 0.15
2d subcatalog
57
1.85 +/- 0.41
0.55 +/- 0.18
3d subcatalog
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2.18 +/- 0.28
0.73 +/- 0.32
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Table B: p’ and p-value of the Omori law for three random and independent subdivisions of
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each group (small and large eruptions). The p' and p-values and error bars are estimated
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with the maximum likelihood method [Ogata et Katsura, 1993]. N is the number of
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eruptions in each class.
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C. Bootstrap test
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Lastly we performed a bootstrap analysis for the large eruptions, and showed that no
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individual foreshock sequence dominates the stacking pattern before eruptions (figure
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C(a)) or after eruptions (figure C(b)).
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For that purpose, we successively retrieved all the 172 eruptions one by one from the
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catalog and carried the analysis on the 171 remaining eruptions of the subsequent
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datasets. Figure C shows the stacked patterns for the 172 bootstrapped catalogs (light
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lines) and dark lines are the stacked patterns for the complete dataset (either before or
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after eruptions, respectively in blue and red). Only a few light curves are visible on the
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plots, the other ones being hidden by the dark ones. The clustering of all the stacked
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pattern around the complete catalog stack, supports no single eruption drives the
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stacked pattern.
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figure C : Foreshocks (a) and aftershocks (b) patterns for large eruptions (VEI>=3). Light
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to dark grey: mainshocks are earthquakes from worldwide catalog for magnitude ranges
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in [5.5;7.5]. Dark blue (a) and dark red (b): mainshocks are the large eruptions from
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worldwide catalog. Light blue (a) and light red (b) correspond to the 172 bootstrap results
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when testing the seismicity patterns by retrieving one different eruption for each dataset.
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<N> is the averaged number of seismic events per day (normalized by the number of
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eruption in each class). We used a Gaussian smoothing function [Helmstetter et al., 2003].
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