Articleshttps://doi.org/10.1038/s41561-018-0144-2

Earthquake nucleation and fault slip complexity in the lower crust of central AlaskaCarl Tape   1*, Stephen Holtkamp   1, Vipul Silwal   1, Jessica Hawthorne   2, Yoshihiro Kaneko   3, Jean Paul Ampuero   4,5, Chen Ji   6, Natalia Ruppert   1, Kyle Smith   1 and Michael E. West   1

1Geophysical Institute, University of Alaska Fairbanks, Fairbanks, AK, USA. 2Department of Earth Sciences, University of Oxford, Oxford, UK. 3GNS Science, Lower Hutt, New Zealand. 4Seismological Laboratory, California Institute of Technology, Pasadena, CA, USA. 5Université Côte d’Azur, IRD, CNRS, Observatoire de la Côted’Azur, Géoazur, France. 6Department of Earth Science, University of California, Santa Barbara, CA, USA. *e-mail: ctape@alaska.edu

© 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

SUPPLEMENTARY INFORMATION

In the format provided by the authors and unedited.

NATuRE GEoSCiENCE | www.nature.com/naturegeoscience

Supplementary Information for

Earthquake nucleation and fault slip complexity in the lower crust

of central Alaska

Carl Tape, Stephen Holtkamp, Vipul Silwal, Jessica Hawthorne, Yoshihiro Kaneko,

Jean Paul Ampuero, Chen Ji, Natalia Ruppert, Kyle Smith, Michael E. West

correspondence to: ctape@alaska.edu

Contains: Supplementary Figures 1–23,

Supplementary Tables 1–5, and Supplementary Text

S1 The 2015 VLFE spectra as a sum of smaller events

It is possible to model the 2015 MW 3.8 VLFE as the sum of about 10 MW 3.2 earthquakes

occurring over the course of about 10 seconds, following the approach Gomberg et al. (2016)

used to model VLFEs as sums of much smaller LFEs.

To see this, imagine the VLFE is the sum of N subevents, all of which have moment M0s

and corner frequency fcs, and source spectra

Ss(f) = M0s

1

1 + (f/fcs)2. (S1)

At frequencies much lower than 0.05 Hz—far lower than 1 over the VLFE duration—all of the

subevents will occur during a small portion of the period of interest and combine constructively,

giving low-frequency VLFE spectral amplitude proportion to the VLFE moment

Sv(f ≪ 0.05 Hz) = NSs(f) = NM0s. (S2)

At frequencies much higher than 0.05 Hz—far higher than 1 over the VLFE duration—the

subevents will occur during random portions of the period of interest and may combine con-

structively or destructively. In this case, the VLFE amplitude will be given by

Ss(f ≫ 0.05 Hz) =√NSs(f) =

√NM0s

1

1 + (f/fcs)2. (S3)

These are the two end member regimes in the approach of Gomberg et al. (2016). At intermediate

frequencies, the VLFE amplitude Sv(f) will be between√NSs(f) and NSs(f).

These VLFE source spectra may be observed via displacement spectra at the station. The

1

displacement spectra at a given frequency are given by the source spectra Sv(f) multiplied by

a path effect G(f). So to analyze the 2015 VLFE, it is useful to compare its spectra with the

spectra of a nearby MW 3.5 earthquake. We model the spectra of the MW 3.5 earthquake with

moment M0e and corner frequency fce as

Se(f) = M0e

1

1 + (f/fce)2. (S4)

At frequencies larger than 1 Hz, the 2015 VLFE and MW 3.5 earthquake have similar displace-

ment spectra, as seen in Figure S6d.

Equating the high-frequency VLFE spectrum to the MW 3.5 spectrum and assuming they

have the same path effect gives

Ss(f ≫ 0.05 Hz)G(f) = Se(f)G(f) (S5)√NM0s

1

1 + (f/fcs)2

= M0e

1

1 + (f/fce)2. (S6)

Since the two spectra have similar shapes at high frequency, we may assume that they have

similar corner frequencies fcs and fce, and estimate that

√NM0s = M0e, (S7)

where M0e is the moment of a MW 3.5 earthquake. However, we also have inferred from the

analysis of the low-frequency VLFE signal (or from the ≪ 0.05 Hz VLFE amplitude, if you

prefer) that the VLFE moment M0v is equivalent to a MW 3.8 earthquake. Matching the VLFE

moment with N subevents with moment M0s gives

NM0s = M0v = moment of Mw 3.8 earthquake. (S8)

Combining the high-frequency and moment constraints (equations (S7) and (S8)) gives

√NM0v

N= M0e (S9)

√N =

M0v

M0e

(S10)

N =

(

moment of Mw 3.8 earthquake

moment of Mw 3.5 earthquake

)2

≈ 8. (S11)

So it is possible to match the data by constructing the MW 3.8 VLFE from 8 MW 3.2 earthquakes.

These 8 subevents are consistent with the 10 or so peaks observed in the deconvolution of

the 2015 VLFE (Figure S4a).

To match the spectral shape, those MW 3.2 earthquakes would have to have corner frequen-

cies similar to the MW 3.5 earthquake analyzed for comparison. Commonly observed corner

frequency scaling suggests that MW 3.2 earthquakes should have corner frequencies a factor of

2

1.4 higher than MW 3.5 earthquakes, so the lower subevent corner frequencies might suggest

slightly lower stress drop or rupture velocities for the VLFE subevents, but that level of variation

in the corner frequency, coupled with variability in the spectra, is within the range observed in

earthquakes, so it is plausible that the VLFE subevents could be normal earthquakes.

We note, however, that it is very rare to observe 8 MW 3.2 earthquakes within a 10-second in-

terval without a strong external forcing. So any physical model of VLFEs as a sum of subevents

would likely require a driving mechanism distinct from that commonly seen in normal earth-

quakes, be it fluid diffusion, off-fault microcracking, delayed nucleation, or aseismic slip.

Indeed, we should note that our preferred slow slip interpretation and the VLFE as a sum

of subevents are end members, and one could model part of the VLFE moment via subevents

and part of the moment as aseismic slip. In that case, the total VLFE moment M0v modeled as

subevents in equation (S11) would be smaller, and a larger number of smaller subevents would

be expected. However, if such smaller subevents exist, they would be expected to have higher

corner frequencies, and the VLFE spectra would also be expected to have more power at higher

frequencies—to have a slower high-frequency decay than the MW 3.5 earthquake used for com-

parison. Such a model would appear to contradict the observations. However, the contradiction

could arise because the model is overly simplistic. It may not be appropriate to assume that there

are 100 or more earthquakes of a similar size. If there are many events of different sizes, the

high-frequency spectra could have a different shape, determined by the subevent size distribu-

tion rather than their average corner frequency.

S2 The low-frequency foreshock signal of the 2016 event

S2.1 Low-frequency onset of the 2016 event

Figures S10–S12 show low-frequency causal filtered seismograms and high-frequency envelopes

for all 17 stations within 60 km of the 2016 earthquake. The origin time of the 2016 earthquake

(dashed line corresponding to the origin of the x-axis) is shown along with P and S phase picks

on the envelope plot. On the low-frequency plots, we pick the onset of the low-frequency waves

associated with the event. Low-frequency picks preceding the P-wave arrival of the mainshock—

interpreted as the precursory VLFE—are present on 8 of the 17 closest stations (Table S3, Fig-

ures S10–S12).

S2.2 Relative timing of foreshock signals for the 2016 event

The onset times of HFF and LFF for the 2016 event are listed in Table S4. The column LF-HF

shows the difference between the onsets, while the last column (LF-HF-10) shows the difference

between the onsets, but with a 10-second correction applied to LF on the basis of Figure S9.

Here we consider the three possibilities for the relative timing of the HFF and LFF signals for

the 2016 event.

3

• Option 1 (preferred): HFF and LFF are simultaneous. The last column in Table S4,

which has the 10-second correction (Figure S9), shows values that are near 0 s, indicating

that the HFF and LFF are nearly simultaneous.

• Option 2: LFF before HFF. It is possible that the LFF signals occurred before HFF. Three

factors could promote an earlier initiation of LFF:

1. The delay in the measured onset time is greater than the 8–12 s implied by Figure S9.

This would push the actual LFF onset time earlier.

2. A portion of LFF is below our detection capabilities. This would imply that the

actual LFF started earlier than it was detected. The LFF has a simple long-period

pulse (Figure 2b), but it is barely detectable on even the closest stations, whereas

HFF is easily detected on all stations (Table S3).

3. The delay could be a consequence of differences in seismic velocities. Although

we have rotated the seismograms to analyze the transverse component, the earliest

arriving HFF signal is likely P waves, while the LFF signal is comprised of shear

or surface waves. Given the depth of the event and monitoring network, this could

introduce a delay of the LFF arrivals of a few to several seconds.

• Option 3: HFF before LFF. If the delay in the measured onset time of LFF is less than

the 8–12 s implied by Figure S9, then HFF would appear to start before LFF is observed.

For the 2015 event, option 3 is clearly the case: we see that LF-HF-10 > 20 for most stations

within 50 km of the event (Table S5), indicating a clear delay of LF with respect to HF. We also

see that the low-frequency signal started near or just after the peak in the high-frequency waves,

evidenced from the positive values of LF in Table S5.

Our observations can be reconciled with our interpretations in Figure 4 and Table S2, which

propose that aseismic slow slip was responsible for the growing high-frequency signals of the

2015 and 2016 events. For the 2016 event, the duration of the aseismic slip could have been

absent, since the LFF—representing a VLFE—and HFF are nearly coincident. For the 2015

event, the duration of aseismic slip is inferred to be ∼20 s (Table S5) before transitioning into a

VLFE (e.g., Figure S1).

4

Supplementary Table S1: Events in Minto Flats fault zone in this study and in Tape et al.

(2015). The subregion corresponds to the designation in Tape et al. (2015). The depth is from

the moment tensor inversion, with the catalog depth in parentheses. The duration listed is the one

used within the moment tensor inversion, if performed. The bandpass for each moment tensor

inversion is listed as the periods T1 and T2. VLFE = very-low-frequency earthquake, HFS =

increasing high-frequency signal, EQ = earthquake. Y-I denotes that we interpret the event as a

VLFE based on the HFS.

origin time subregion latitude longitude Mw Ml depth duration T1 T2 VLFE HFS EQ

(km) (s) (s) (s)

events in Tape et al. (2015):

2000-11-29 10:35:47.2 S 63.90 -150.35 5.7 5.8 19 (16.4) 7.1 20 40 – – Y

2000-12-06 18:40:26.0 S 63.89 -150.31 4.9 5.0 10 (11.7) 2.8 20 33.3 – – Y

2001-03-25 11:34:50.9 E 64.63 -149.25 4.4 4.6 20 (22.2) 1.6 16.7 40 – – Y

2001-06-30 09:41:42.3 S 64.04 -150.15 4.6 4.4 16 (14.6) 2.0 14.3 25 – – Y

2008-07-16 10:12:00.6 W 64.59 -149.53 3.9 4.1 23 (30.5) 1.0 16.7 25 – – Y

2009-07-28 12:13:15.7 W 64.61 -149.49 3.8 3.7 23 (22.7) 1.0 14.9 25 – – Y

2012-04-11 09:21:57.4 W 64.92 -148.95 3.8 3.9 16 (19.3) 1.0 1.7 3.3 Y-I Y Y

2013-03-05 21:55:58.4 E 64.84 -148.73 3.4 3.4 20 (17.3) 1.0 16.7 28.6 – – Y

2013-06-05 18:58:23.3 SW 64.64 -149.68 3.9 4.0 10 (13.9) 1.0 16.7 33.3 – – Y

2013-07-12 07:59:17.0 N 65.09 -148.77 3.6 3.4 16 (17.2) 1.0 10 22.2 – – Y

2014-12-13 15:47:31.4 E 64.43 -149.38 3.4 3.3 17 (13.0) 1.0 11.1 28.6 – – Y

events in this study:

2002-12-29 20:38:30.2 E 64.95 -148.61 – 3.4 – (17.6) – – – – – Y

2004-11-17 11:29:00.3 W 64.89 -149.10 – 3.6 – (18.8) – – – – – Y

2011-11-18 10:46:23.5 W 64.94 -148.94 – 3.4 – (11.1) – – – – – Y

2013-03-12 07:39:50.2 E 64.72 -148.95 3.5 2.1 23 (1.0) 12 25 40 Y Y –

2015-09-12 03:24:12.2 N 65.13 -148.67 – 1.4 – (20.4) – – – Y-I Y –

2015-09-12 03:25:12.7 N 65.12 -148.66 3.8 2.6 21 (15.6) 10 20 50 Y Y –

2015-10-22 13:16:15.8 E 64.73 -149.04 2.6 2.7 18 (18.8) 1.0 5 20 – – Y

2015-10-31 02:56:35.6 S 64.43 -149.70 3.4 3.5 25 (23.9) 1.0 10 25 – ? Y

2016-01-14 19:04:10.7 W 64.68 -149.25 3.7 3.8 17 (22.7) 1.0 10 30 Y Y Y

5

Supplementary Table S2: Summary of seismic observations for six events in this study from

high-frequency waveforms (≥ 1 Hz; ) and low-frequency waveforms (≤ 0.1 Hz; ).

Event locations are shown in Figure 1.

stage 2012 2013 2015 2015- 2015- 2016

observation in VLFE EQ VLFE VLFE 10-22 10-31 VLFE EQ

Fig. 4 EQ EQ

growing high-frequency 1

signal (Fig. 1b)

simultaneous large-amplitude 1

low-frequency signal

earthquake 2

(P, S, surface waves)

AEC† catalog magnitude (Ml), 3.9 2.1 2.6 2.7 3.5 3.8

from high frequencies

moment tensor magnitude (Mw), 3.8 3.5 3.8 2.6 3.4 3.7

from low frequencies†Alaska Earthquake Center

6

Supplementary Table S3: Polarities of waves (U = up, D = down) for the 2016-01-14 earth-

quake for stations within 200 km of the epicenter. LFFP = low-frequency foreshock polarity;

HFP = high-frequency P polarity from earthquake; LFP = polarity predicted from low-frequency

waveforms; parentheses denote stations that are nodal for the source mechanism (Fig. S3b). The

LFFP picks are based on waveforms shown in Figures S10–S12, which show the vertical com-

ponent of velocity, bandpass filtered 20–100 s. The amplitude listed is the amplitude at the peak

of the LFFP.

stations distance azimuth LFFP (nm/s) HFP LFP

(km) (◦)

F1TN XV 5.3 127 – – (D)

F2TN XV 6.2 62 – U U

FPAP XV 10.5 138 D (-13.7) D D

F3TN XV 11.0 26 – U (U)

FNN1 XV 12.5 173 D (-38.2) D D

NEA2 AK 13.2 140 D (-20.0) D D

FNN2 XV 15.2 218 U? (11.8) D (U)

FAPT XV 16.8 152 D (-25.2) D D

F4TN XV 17.4 15 D (-21.4) – (D)

FTGH XV 20.1 87 U (24.7) U U

F5MN XV 22.9 8 D (-26.0) D D

F6TP XV 25.6 325 D (-32.1) D D

F7TV XV 33.5 305 – D (D)

F8KN XV 33.8 286 – U U

I23K TA 52.1 354 – D D

BWN AK 56.9 182 – D D

MDM AK 57.3 57 – U U

WRH AK 60.2 112 – – U

CCB AK 69.0 93 – U U

COLA IU 69.3 72 – – U

POKR TA 98.6 60 – – U

BPAW AK 106.1 233 – – U

MCK AK 107.1 172 – – D

HDA AK 114.5 104 – – U

PS08 PS 117.1 97 – – U

I21K TA 140.7 294 – – U

RND AK 143.6 172 – – D

H24K TA 143.7 26 – – D

TRF AK 146.5 201 – – (D)

KTH AK 150.1 214 – – U

CHUM AK 173.3 240 – – U

CAST AK 197.6 226 – – U

PPD AK 198.2 60 – – D

H21K TA 199.0 305 – – U

7

Supplementary Table S4: Time picks for the 2016 event. HF = HFF start time (emerges from

background noise level). LF = LFF start time, only listed for the unequivocal polarity measure-

ments in Table S3. HF and LF are relative to the P time of the Mw 3.7 earthquake. The differential

time LF–HF is the delay in the LF onset relative to the HF onset. The time LF–HF–10 includes

a 10-second correction in LF that is based on Figure S9.

stations distance azimuth HF LF LF-HF LF-HF-10

(km) (◦) (s) (s) (s) (s)

F1TN XV 5.3 127 -19.3 NaN NaN NaN

F2TN XV 6.2 62 -18.8 NaN NaN NaN

FPAP XV 10.5 138 -19.3 -9.5 9.8 -0.2

F3TN XV 11.0 26 -18.3 NaN NaN NaN

FNN1 XV 12.5 173 -19.5 -11.0 8.5 -1.5

NEA2 AK 13.2 140 -20.6 -10.3 10.4 0.4

FNN2 XV 15.2 218 -21.7 NaN NaN NaN

FAPT XV 16.8 152 -16.5 -11.1 5.3 -4.7

F4TN XV 17.4 15 -18.9 -1.3 17.7 7.7

FTGH XV 20.1 87 -20.9 -11.6 9.4 -0.6

F5MN XV 22.9 8 -21.2 -12.1 9.1 -0.9

F6TP XV 25.6 325 -20.3 -10.8 9.5 -0.5

F7TV XV 33.5 305 -18.4 NaN NaN NaN

F8KN XV 33.8 286 -20.9 NaN NaN NaN

I23K TA 52.1 354 -19.6 NaN NaN NaN

BWN AK 56.9 182 -21.0 NaN NaN NaN

MDM AK 57.3 57 -19.6 NaN NaN NaN

WRH AK 60.2 112 -21.4 NaN NaN NaN

CCB AK 69.0 93 -19.6 NaN NaN NaN

COLA IU 69.3 72 -19.7 NaN NaN NaN

POKR TA 98.6 60 -18.4 NaN NaN NaN

BPAW AK 106.1 233 -19.7 NaN NaN NaN

MCK AK 107.1 172 -19.0 NaN NaN NaN

HDA AK 114.5 104 -18.8 NaN NaN NaN

PS08 PS 117.1 97 -18.5 NaN NaN NaN

I21K TA 140.7 294 -19.2 NaN NaN NaN

RND AK 143.6 172 -17.7 NaN NaN NaN

H24K TA 143.7 26 -18.1 NaN NaN NaN

TRF AK 146.5 201 -19.8 NaN NaN NaN

KTH AK 150.1 214 -19.0 NaN NaN NaN

CHUM AK 173.3 240 -14.9 NaN NaN NaN

CAST AK 197.6 226 -19.3 NaN NaN NaN

PPD AK 198.2 60 -15.0 NaN NaN NaN

H21K TA 199.0 305 -14.3 NaN NaN NaN

8

Supplementary Table S5: Time picks for the 2015 event. HF = HF start time. LF = LF start

time. Both times are listed relative to the peak HF signal, which is estimated using a triangle fit

to the 2–8 Hz filtered seismogram (e.g., Figure 1b). The differential time LF-HF is the delay in

the LF onset relative to the HF onset. The time LF-HF-10 includes a 10-second correction in LF

that is based on Figure S9.

stations distance azimuth HF LF LF-HF LF-HF-10

(km) (◦) (s) (s) (s) (s)

MDM AK 27.1 131 -20.9 8.5 29.4 19.4

PS07 PS 27.8 40 -21.8 NaN NaN NaN

I23K TA 32.8 276 -23.2 -10.1 13.1 3.1

F5MN XV 35.8 223 -27.3 2.9 30.1 20.1

F4TN XV 39.4 216 -29.7 4.8 34.5 24.5

F3TN XV 45.1 211 -31.7 5.0 36.7 26.7

TCOL TA 46.8 126 -25.7 4.0 29.6 19.6

COLA IU 46.8 126 -24.8 5.8 30.6 20.6

FTGH XV 48.5 189 -25.4 5.5 31.0 21.0

F6TP XV 50.6 237 -28.1 3.4 31.5 21.5

F2TN XV 51.0 206 -27.4 11.2 38.6 28.6

F1TN XV 57.0 204 -29.5 9.9 39.4 29.4

POKR TA 57.8 90 -26.2 -7.0 19.2 9.2

FPAP XV 60.2 200 -29.7 2.0 31.8 21.8

NEA2 AK 61.9 198 -28.0 4.9 32.9 22.9

F7TV XV 62.4 242 -28.6 9.4 38.0 28.0

FNN1 XV 66.6 204 -34.3 5.5 39.8 29.8

FAPT XV 66.7 198 -31.8 0.9 32.7 22.7

CCB AK 66.8 142 -26.5 12.6 39.1 29.1

FNN2 XV 71.2 212 -30.8 2.5 33.3 23.3

F8KN XV 71.8 237 -27.3 4.9 32.2 22.2

WRH AK 77.3 159 -28.7 3.9 32.6 22.6

H24K TA 87.8 24 -30.4 6.1 36.5 26.5

H23K TA 88.5 333 -30.7 -5.2 25.5 15.5

PS06 PS 95.7 329 -30.9 NaN NaN NaN

MLY AK 98.3 265 -31.5 -4.0 27.5 17.5

PS08 PS 108.7 126 -31.9 NaN NaN NaN

BWN AK 109.9 196 -34.5 -9.7 24.7 14.7

HDA AK 113.9 133 -32.7 1.7 34.4 24.4

PPD AK 152.9 72 -32.5 21.7 54.1 44.1

MCK AK 155.4 185 -39.7 7.6 47.3 37.3

I21K TA 155.8 274 -42.0 -1.8 40.2 30.2

BPAW AK 159.1 225 -40.2 -0.6 39.6 29.6

J25K TA 166.1 108 -40.4 -4.3 36.0 26.0

RND AK 191.4 183 -45.1 9.5 54.6 44.6

9

−100 0 100 200 300 400 500

SII.AK.BHZ (200, 997 km)

OHAK.AT.BHZ (198, 912 km)

KDAK.II.BHZ_00 (196, 842 km)

Q19K.TA.BHZ (203, 735 km)

P19K.TA.BHZ (203, 652 km)

CNP.AK.BHZ (193, 636 km)

HOM.AK.BHZ (196, 627 km)

BRLK.AK.BHZ (192, 608 km)

BRSE.AK.BHZ (191, 608 km)

O20K.TA.BHZ (202, 596 km)

CAPN.AK.BHZ (196, 500 km)

FIRE.AK.BHZ (191, 449 km)

SSN.AK.BHZ (195, 420 km)

SKN.AK.BHZ (203, 377 km)

CUT.AK.BHZ (195, 312 km)

TRF.AK.BHZ (204, 202 km)

FAPT.XV.HHZ (198, 66 km)

FNN1.XV.HHZ (203, 66 km)

NEA2.AK.BHZ (198, 62 km)

FPAP.XV.HHZ (200, 60 km)

F1TN.XV.HHZ (204, 57 km)

F2TN.XV.HHZ (206, 51 km)

Time (s)

2015−09−12 03:23:32 + 600.00 s; F2TN max −8.72e−01 nm / sec at t = 43.5 s BHZ BHZ_00 HHZ [ nm / sec, −−] event 20150912032512711 (2015−09−12, M2.6, −148.7, 65.1, z = 15.6 km)

22 / 22 seismograms (22 stations) ordered by input, norm −−> (sin D)^−0.50

Supplementary Figure S1: Record section of vertical component velocity seismograms, filtered

20–50 s, for the Mw 3.8 2015 VLFE. Amplitudes have been corrected for geometric spreading

of surface waves. The record section shows all stations within an azimuthal sector (here, 190◦ to

210◦), such that the waveforms would be expected to be similar, since the source-station paths

are similar. By cross-correlating all waveforms for this earthquake, we estimate a group velocity

of 3.5 km/s.

10

(a) (b)

0.000

0.006

0.012

0.018

0.024

0.030

ln(V

R_m

ax /

VR

)

0.000

0.006

0.012

0.018

0.024

0.030

ln(V

R_m

ax /

VR

)

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

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VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

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VR

(gr

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10 15 20 25 30

Depth, km

0

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VR

(gr

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10 15 20 25 30

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20

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(gr

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10 15 20 25 30

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0

20

40

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VR

(gr

ay)

10 15 20 25 30

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0

20

40

60

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100

VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

3.80

3.80

3.80

3.80

3.80

3.803.80

3.80

3.803.80 3.80

3.80

3.80

3.80

3.80

3.80

3.80

20150912032512711 | Model tactmod | Best depth 21.2 ± 4.2 km

0.00

0.01

0.02

0.03

0.04

0.05

ln(V

R_m

ax /

VR

)

0.00

0.01

0.02

0.03

0.04

0.05

ln(V

R_m

ax /

VR

)

0

20

40

60

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100

VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

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VR

(gr

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10 15 20 25 30

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(gr

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(gr

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(gr

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10 15 20 25 30

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40

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(gr

ay)

10 15 20 25 30

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20

40

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VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

3.60

3.60

3.70

3.70

3.70

3.70 3.703.70

3.70

3.70

3.80 3.80

3.80

3.80

3.80

3.80

3.80

3.90

20160114190410727 | Model tactmod | Best depth 16.7 ± 4.6 km

(c) (d)

0.000

0.003

0.006

0.009

0.012

0.015

ln(V

R_m

ax /

VR

)

0.000

0.003

0.006

0.009

0.012

0.015

ln(V

R_m

ax /

VR

)

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25 30

Depth, km

3.503.50

3.50

3.50

3.50

3.50 3.50

3.50

3.50

3.50

3.50

3.50

3.503.50 3.50

3.50

3.50

3.60

20130312073950214 | Model tactmod | Best depth 23.3 ± 2.6 km

0.000

0.007

0.014

0.021

0.028

0.035

ln(V

R_m

ax /

VR

)

0.000

0.007

0.014

0.021

0.028

0.035

ln(V

R_m

ax /

VR

)

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25

Depth, km

0

20

40

60

80

100

VR

(gr

ay)

10 15 20 25

Depth, km

3.203.20

3.20

3.203.20 3.20

3.20

3.20

3.20

3.30

3.30

3.30 3.40

3.40

3.40

3.40

20151031025635572 | Model tactmod | Best depth 24.1 ± 2.6 km

Supplementary Figure S2: Grid search over depth for four events in this study. For each depth,

the moment tensor inversion allows the magnitude and orientation to vary. The red arrow is the

AEC catalog depth derived from arrival times. The white arrow is the depth derived from the

moment tensor inversion. (a) Grid search over depth for the 2015 event; the best-fitting depth is

21 ± 4 km. (b) Grid search over depth for the 2016 event; the best-fitting depth is 17 ± 5 km.

(c) Grid search over depth for the 2013 event; the best-fitting depth is 23±3 km. (d) Grid search

over depth for the 2015-10-31 Mw 3.4 earthquake; the best-fitting depth is 18 ± 3 km. This

earthquake is used for comparison in Figure S6. See Silwal (2018) for full results.

11

F1TN

F2TN

FPAP

F3TN

FNN1

NEA2FNN2

FAPT

F4TN

FTGH

F5MN

F6TP

F7TV

F8KN

I23K

BWN

MDM

WRH

CCB

TCOL

PS07

POKRBPAW

MCK

HDA

PS08

PS06

I21K

RND

H24K

TRF

KTH

CHUMPS09

CAST

H21KPPD

MDM

PS07

I23K

FTGH

TCOLCOLA

F6TP

NEA2

POKR

F8KN

H23K H24K

MLY

HDA

J25K

b 2016-01-14 earthquakea 2015-09-12 very low frequency earthquake (VLFE) F6TP

I23K

BWN

WRH

CCB

TCOL

PS07

POKR

BPAW

MCK

HDA

RND

H24K

TRF

CHUM

MDM

PS07

I23K

FTGH

TCOL

F6TP

POKR

F8KN

H23K

H24K

MLY

HDA

J25K

Vertical Radial Transverse

200 s100 s

Supplementary Figure S3: Source mechanisms and waveform fits for the 2015 very-low-

frequency earthquake (VLFE) (a) and the 2016 VLFE+earthquake (b). The beachball is a lower-

hemisphere projection of the P-wave radiation pattern. The subset of waveform fits show the

observations (black) in comparison with the modeled seismograms (red). See Silwal (2018) for

full results.

12

0 5 10 15 20 25 30 35−0.1

0

0.1

0.2

0.3

Time, s

S(t

)

(a) 2015 event (shading fills 84%, dur = 9.8 s)

0 5 10 15 20 25 30 35−0.5

0

0.5

1

Time, s

Cum

ulat

ive

sum

of S

(t)

2015 event (int S(t) = 0.97)

0 5 10 15 20 25 30 35−1

0

1

2

Time, s

S(t

)

(b) 2016 event (shading fills 71%, dur = 1.2 s)

0 5 10 15 20 25 30 35−0.5

0

0.5

1

1.5

Time, s

Cum

ulat

ive

sum

of S

(t)

2016 event (int S(t) = 1.46)

Supplementary Figure S4: Estimated source time functions for the 2015 and 2016 events, using

seismograms filtered with f ≥ 1 Hz. Each pair of plots shows the estimated source time function

(top)—including a shaded portion that represents our interpretation of the source duration—as

well as a cumulative (integrated) version of the source time function (bottom). (a) Source time

function S(t) for the 2015 very-low-frequency earthquake. The estimated duration of ∼10 s is

represented by the shaded maximum pulse, which fills 84% of the integrated area of S(t). The

magnitude of Mw 3.8 estimated from long-period waveforms (Figure S3b) matches the estimated

moment from high-frequency waveforms. (b) Source time function S(t) for the 2016 earthquake,

estimated using the stations shown in Figure S5. The estimated duration of ∼1 s is represented

by the shaded maximum pulse. The magnitude of Mw 3.7 estimated from long-period wave-

forms (Figure S3a) matches the estimated moment from high-frequency waveforms after the

main pulse, indicated by∫

S(t) ≈ 1 (red curve). We attribute the later, lower-amplitude pulses

in S(t) to noise. See Figure S13 for a source time function estimated using higher frequency

waveforms.

13

(a) (b)

-10 0 10 20 30 40 50 60 70 80

POKRZ 8.28e-05

POKRT 8.46e-05

COLAT 1.54e-04

TCOLT 1.75e-04

MDMT 1.87e-04

CCBT 1.22e-04

FTGHT 9.90e-05

-10 0 10 20 30 40 50 60 70 80

FAPTT 8.76e-05

NEA2Z 8.42e-05

NEA2T 8.56e-05

F8KNZ 7.25e-05

F8KNT 1.01e-04

I23KT 2.19e-04

Time, s Time, s

-10 0 10 20 30 40 50 60

MDMZ 3.41e-04

MDMT 8.48e-04

POKRZ 3.06e-04

POKRT 8.40e-04

FTGHT 1.85e-03

CCBT 6.89e-04

F8KNT 2.92e-03

I23KT 9.17e-04

Time, s

Supplementary Figure S5: Corresponding fits between synthetic seismograms (red) and ob-

served seismograms for the source-time functions shown in Figure S4. In order to obtain better

agreement between data and synthetics, they are bandpass filtered 1–50 s; excluding the shorter

periods leads to a source duration estimate that is slightly longer (by ∼0.5 s) than actuality. The

max amplitudes in the data are listed in cm/s for each seismogram. All stations are <100 km

from the epicenter (Tables S4 and S5). (a) The 2015 Mw 3.7 very-low-frequency earthquake.

(b) The 2016 Mw 3.7 earthquake.

14

(a) TA.I23K (32.8 km, 81.8 km) (b) TA.POKR (57.8 km, 132.2 km)

10−2

10−1

100

101

−220

−200

−180

−160

−140

−120

−100

−80

−60

Dis

plac

emen

t Pow

er S

pect

ra [1

0*lo

g10(

m2 /H

z)] (

dB)

Frequency

I23K, BHZ

2015−09−12 VLFE2015−09−12 Noise2015−10−31 EQ2015−10−31 Noise

10−2

10−1

100

101

−220

−200

−180

−160

−140

−120

−100

−80

−60

Dis

plac

emen

t Pow

er S

pect

ra [1

0*lo

g10(

m2 /H

z)] (

dB)

Frequency

POKR, BHZ

2015−09−12 VLFE2015−09−12 Noise2015−10−31 EQ2015−10−31 Noise

(c) AK.NEA2 (61.9 km, 35.3 km) (d) TA.H24K (87.8 km, 178.7 km)

10−2

10−1

100

101

−220

−200

−180

−160

−140

−120

−100

−80

−60

Dis

plac

emen

t Pow

er S

pect

ra [1

0*lo

g10(

m2 /H

z)] (

dB)

Frequency

NEA2, BHZ

2015−09−12 VLFE2015−09−12 Noise2015−10−31 EQ2015−10−31 Noise

10−2

10−1

100

101

−220

−200

−180

−160

−140

−120

−100

−80

−60

Dis

plac

emen

t Pow

er S

pect

ra [1

0*lo

g10(

m2 /H

z)] (

dB)

Frequency

H24K, BHZ

2015−09−12 VLFE2015−09−12 Noise2015−10−31 EQ2015−10−31 Noise

Supplementary Figure S6: Vertical component displacement spectra for four stations (TA.I23K,

TA.POKR, AK.NEA2, TA.H24K), showing the enhancement in low-frequency amplitudes for

the 2015-09-12 Mw 3.8 (depth 21 km) VLFE (solid black) in comparison with the 2015-10-31

Mw 3.4 (depth 25 km) earthquake (solid red). The signal spectra are calculated for a time window

spanning from the origin time to 600 seconds. The noise spectra, plotted as dashed curves, are

calculated for a time window of 600 seconds preceding the origin time. The vertical lines mark

the limits of the bandpass used for the VLFE moment tensor inversion: 20–50 s. The four

stations here are among those used within the moment tensor inversion (Figure S3a). Note that

the two events are separated by 91 km (Figure 1a), resulting in different source-station distances,

as labeled above each subplot. The depths are estimated from moment tensor inversion as 21 km

(VLFE) and 25 km (EQ). The catalog magnitudes, estimated from high-frequency waveforms,

are Ml 2.6 (VLFE) and Ml 3.5 (EQ) (Table S1).

15

a

10 11 12 13 14 15 16 17 18 19 20−1

0

1

2

3

4

5

10 11 12 13 14 15 16 17 18 19 200

20

40

60

80

100

Time (Day of January 2016)

Cu

mu

lative

Se

ism

icity

Ma

gn

itu

de

Accelerating Foreshocks

Ma

insh

ock

b

27 28 29 30 31 01 02 03 04 05 060

1

2

3

4

5

27 28 29 30 31 01 02 03 04 05 060

50

100

150

200

250

300

Time (Day of August/September 2014)

Cu

mu

lative

Se

ism

icity

Ma

gn

itu

de

No Foreshocks

Ma

insh

ock

Supplementary Figure S7: Earthquake sequences associated with (a) the Mw 3.7 2016 earthquake

and (b) a Mw 5.0 earthquake on 2014-08-31. (a) Network matched filter catalog of earthquakes

in the 2016 sequence. (top) Magnitude (Ml) vs. time for the 2016 earthquake sequence. (bot-

tom) Cumulative seismicity over time for the 2016 earthquake sequence. Note that the rate of

foreshocks is accelerating up until the time of the mainshock. Most earthquakes do not have

foreshock sequences, as seen here. (b) Same as (a), but for the 2014 earthquake.

16

T0 10 20 30 40 50 60 70 80

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

BWN

CCB

COLA

F1TN

F2TN

F3TN F4TN

F5MNF6TP

F7TV

F8KN

FAPT

FNN1

FNN2

FPAP

FTGHI23K

MDMNEA2

WRH

distance, km

k fo

r v(

t) =

B*(

t − t 0)k

Z0 10 20 30 40 50 60 70 80

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

BWN

CCB

COLAI23K

MDM

NEA2

WRH

F1TN

F2TN

F3TN

F4TN

F5MNF6TP

F7TV

F8KN

FAPT

FNN1

FNN2

FPAP

FTGH

distance, km

k fo

r v(

t) =

B*(

t − t 0)k

Supplementary Figure S8: Estimated exponent k (Figure S16) for stations <80 km from the

epicenter of the 2016 event. Top is for the transverse component; bottom is for the vertical

component.

17

0.2

0.0

-0.2

-0.4

0.2

0.0

-0.2

-0.4

0.2

0.0

-0.2

-0.4

0.2

0.0

-0.2

-0.4

0.2

0.0

0.6

0.4

1.0

0.8

-300 -200 -100 0 100

Time (seconds)

a

b

c

d

e

Supplementary Figure S9: A synthetic test illustrating the influence of noise levels on the delay

in the LFF onset time pick. (a) An artificial input signal that is a triangle with total width of 20

seconds; the triangle starts at time t = 0. (b) Input signal filtered 20–100 s with no noise. The

LFF time pick is 0 s. (c) Same as (b) but with ∼10% of signal-to-noise (Gaussian noise). The

LFF time pick is 8.3 s. (d) Same as (b) but with ∼20% noise; the time pick is 9.6 s. (e) Same as

(b) but with ∼40% noise; the time pick is 11.2 s. These results indicate that the LFF onset time

pick will be delayed by 8–12 s from the actual LFF onset. See Tables S4 and S5.

18

F1TN F2TN

FPAP F3TN

FNN1 NEA2

D

D D

D

U

Time (seconds) Time (seconds)

Supplementary Figure S10: Additional examples of waveforms for the 2016 event (Figures S10–

S12), similar to Figure 2b. Each subplot has four time series; the dashed line at t = 0 is the

origin time of the Mw 3.7 earthquake. The bottom is the log-scaled envelope of the 2–8 Hz

vertical component seismogram; units show the base-10 exponent of m/s (e.g., −4 is 10−4 m/s).

The top three are the east (top), north (middle), and vertical (bottom) component seismograms

(units m/s), causal-filtered 20–100 s and cut at the P arrival time for the earthquake. Our polarity

measurement for the low-frequency foreshock (LFF) is labeled. The LFF polarity for the vertical

component is listed in Table S3.

19

FNN2 FAPT

F4TN FTGH

F5MN F6TP

D

U

Time (seconds) Time (seconds)

U?

U?

U?

D?

D

D

D D

U

Supplementary Figure S11: Additional examples of waveforms for the 2016 event (Figures S10–

S12), similar to Figure 2b. Each subplot has four time series; the dashed line at t = 0 is the

origin time of the Mw 3.7 earthquake. The bottom is the log-scaled envelope of the 2–8 Hz

vertical component seismogram; units show the base-10 exponent of m/s (e.g., −4 is 10−4 m/s).

The top three are the east (top), north (middle), and vertical (bottom) component seismograms

(units m/s), causal-filtered 20–100 s and cut at the P arrival time for the earthquake. Our polarity

measurement for the low-frequency foreshock (LFF) is labeled. The LFF polarity for the vertical

component is listed in Table S3.

20

F7TV F8KN

I23K BWN

MDM

D?

Time (seconds)

Time (seconds)

U?

Supplementary Figure S12: Additional examples of waveforms for the 2016 event (Figures S10–

S12), similar to Figure 2b. Each subplot has four time series; the dashed line at t = 0 is the

origin time of the Mw 3.7 earthquake. The bottom is the log-scaled envelope of the 2–8 Hz

vertical component seismogram; units show the base-10 exponent of m/s (e.g., −4 is 10−4 m/s).

The top three are the east (top), north (middle), and vertical (bottom) component seismograms

(units m/s), causal-filtered 20–100 s and cut at the P arrival time for the earthquake. Our polarity

measurement for the low-frequency foreshock (LFF) is labeled. The LFF polarity for the vertical

component is listed in Table S3.

21

0 10 20 30 40 50

F5MN

4.20e-02 cmAz= 7

Dist=22.9

F1TN

1.82e-02 cmAz= 126

Dist= 5.3

F8KN

9.48e-03 cmAz= 286

Dist=33.8

F7TV

1.82e-02 cmAz= 305

Dist=33.5

F6TP

9.45e-03 cmAz= 324

Dist=25.6

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.5

1.0

1.5

2.0

2.5

0 5 10 15 20 25 30 35 40

0.0

0.1

0.2

0.3

0.00

0.05

0.10

0.15

0.20

0 5 10 15 20 25 30

-5

0

5

X 1

0-4

2016011419041072

F8KN HHT

JAN 14 (014), 2016

19:04:10.727

-20 -15 -10 -5 0 5 10

(a)

(b)

(c)

(d)

Time, s Time, s

Time, sTime, s

cu

mu

lative

mo

me

nt

mo

me

nt ra

tem

om

en

t ra

tecu

mu

lative

mo

me

nt

Supplementary Figure S13: Source time function estimation for the 2016 event using high-

frequency (f ≤ 4.5 Hz), transverse-component waveforms at five stations within 35 km of the

epicenter: F1TN, F5MN, F6TP, F7TV, F8KN. The data were manually aligned such that the

mainshock initiated at t = 30 s. Synthetic seismograms were calculated using a standard 1D

model for central Alaska (tactmod). (a) Cumulative moment function (top) and its derivative,

the moment rate function (bottom). (b) Zoom-in of (a) showing the first 30 seconds. (c) Com-

parison of recorded seismograms (black) and synthetic seismograms (red) calculated using the

moment rate function in (a). Text labels show the station azimuth, epicentral distance, and peak

amplitude. (d) Transverse displacement seismogram at station F8KN; here t = 0 is the main-

shock origin time. The high-frequency peaks are correlated with the small peaks in the moment

rate function (b). The ramp shape from 7 s to 10 s is partially caused by the near-field term of

the mainshock SH wave, which begins with the mainshock P arrival.

22

−50 0 50

0

2

4

6BPAW [117.5 km]

−50 0 50

0

2

4

6BWN [63.7 km]

−50 0 50

0

2

4

6CCB [59.7 km]

−50 0 50

0

2

4

6CHUM [184.7 km]

−50 0 50

0

2

4

6COLA [58.1 km]

−50 0 50

0

2

4

6F1TN [10.5 km]

−50 0 50

0

2

4

6F2TN [5.2 km]

−50 0 50

0

2

4

6F3TN [6.7 km]

−50 0 50

0

2

4

6F4TN [12.4 km]

−50 0 50

0

2

4

6F5MN [18.3 km]

−50 0 50

0

2

4

6F6TP [29.1 km]

−50 0 50

0

2

4

6F7TV [39.7 km]

−50 0 50

0

2

4

6F8KN [42.6 km]

−50 0 50

0

2

4

6FNN1 [20.0 km]

−50 0 50

0

2

4

6FNN2 [26.2 km]

−50 0 50

0

2

4

6FPAP [13.7 km]

−50 0 50

0

2

4

6FTGH [11.1 km]

−50 0 50

0

2

4

6H23K [124.0 km]

−50 0 50

0

2

4

6H24K [134.5 km]

−50 0 50

0

2

4

6HDA [106.5 km]

−50 0 50

0

2

4

6I21K [147.7 km]

−50 0 50

0

2

4

6I23K [48.6 km]

−50 0 50

0

2

4

6J25K [175.7 km]

−50 0 50

0

2

4

6KTH [160.4 km]

−50 0 50

0

2

4

6MCK [111.8 km]

−50 0 50

0

2

4

6MDM [45.9 km]

−50 0 50

0

2

4

6MLY [87.3 km]

−50 0 50

0

2

4

6NEA2 [15.7 km]

−50 0 50

0

2

4

6POKR [87.2 km]

−50 0 50

0

2

4

6PPD [186.7 km]

nenana_nuc_20151022T_if0

−50 0 50

0

2

4

6PS06 [129.2 km]

−50 0 50

0

2

4

6PS07 [73.6 km]

−50 0 50

0

2

4

6PS08 [108.1 km]

−50 0 50

0

2

4

6RND [148.3 km]

−50 0 50

0

2

4

6TCOL [58.1 km]

−50 0 50

0

2

4

6TRF [155.5 km]

−50 0 50

0

2

4

6WRH [53.9 km]

Supplementary Figure S14: Envelopes of high-frequency seismograms for a normal earthquake

on 2015-10-22. No coherent signal is visible prior to the P arrival, which is denoted by the

vertical red line at t = 0. Station MDM is shown in Figure 1b.

23

−80 −60 −40 −20 0 20 40

0

2

4

6BPAW [134.2 km] k = 1.4

−80 −60 −40 −20 0 20 40

0

2

4

6CCB [62.4 km] k = 5.7

−80 −60 −40 −20 0 20 40

0

2

4

6COLA [51.6 km] k = 3.1

−80 −60 −40 −20 0 20 40

0

2

4

6HDA [111.3 km] k = 2.4

−80 −60 −40 −20 0 20 40

0

2

4

6KTH [180.3 km] k = 0.6

nenana_nuc_20120411T_if4

−80 −60 −40 −20 0 20 40

0

2

4

6MCK [132.7 km] k = 1.2

−80 −60 −40 −20 0 20 40

0

2

4

6MDM [34.0 km] k = 2.3

−80 −60 −40 −20 0 20 40

0

2

4

6MLY [85.8 km] k = 33.0

−80 −60 −40 −20 0 20 40

0

2

4

6PPD [173.3 km] k = 1.7

−80 −60 −40 −20 0 20 40

0

2

4

6PS08 [109.7 km] k = 20.4

−80 −60 −40 −20 0 20 40

0

2

4

6WRH [64.7 km] k = 3.8

Supplementary Figure S15: Envelopes of high-frequency seismograms for all stations within

200 km of the 2012 event. The vertical red lines span the high-frequency foreshock signals that

last approximately 20 s at each station. The estimated value of k, labeled above each subplot,

is based on the best-fitting curve of B(t − t0)k. For comparison with a normal earthquake, see

Figure S14. Station MDM is shown in Figure 1b.

24

−50 0 50

0

2

4

6BPAW [106.1 km] k = 2.1

−50 0 50

0

2

4

6BWN [56.9 km] k = 2.4

−50 0 50

0

2

4

6CAST [197.6 km] k = 3.4

−50 0 50

0

2

4

6CCB [69.0 km] k = 3.4

−50 0 50

0

2

4

6CHUM [173.3 km] k = 2.6

−50 0 50

0

2

4

6COLA [69.3 km] k = 1.9

−50 0 50

0

2

4

6F1TN [5.3 km] k = 2.8

−50 0 50

0

2

4

6F2TN [6.2 km] k = 2.0

−50 0 50

0

2

4

6F3TN [11.0 km] k = 2.7

−50 0 50

0

2

4

6F4TN [17.4 km] k = 2.7

−50 0 50

0

2

4

6F5MN [22.9 km] k = 3.8

−50 0 50

0

2

4

6F6TP [25.6 km] k = 3.8

−50 0 50

0

2

4

6F7TV [33.5 km] k = 3.0

−50 0 50

0

2

4

6F8KN [33.8 km] k = 3.6

−50 0 50

0

2

4

6FAPT [16.8 km] k = 1.7

−50 0 50

0

2

4

6FNN1 [12.5 km] k = 3.5

−50 0 50

0

2

4

6FNN2 [15.2 km] k = 4.2−50 0 50

0

2

4

6FPAP [10.5 km] k = 3.0

−50 0 50

0

2

4

6FTGH [20.1 km] k = 2.4

−50 0 50

0

2

4

6H21K [199.0 km] k = 2.1

nenana_nuc_20160114T_if4

−50 0 50

0

2

4

6H24K [143.7 km] k = 3.2

−50 0 50

0

2

4

6HDA [114.5 km] k = 1.9

−50 0 50

0

2

4

6I21K [140.7 km] k = 3.2

−50 0 50

0

2

4

6I23K [52.1 km] k = 2.5

−50 0 50

0

2

4

6KTH [150.1 km] k = 3.1

−50 0 50

0

2

4

6MCK [107.1 km] k = 1.7

−50 0 50

0

2

4

6MDM [57.3 km] k = 2.8

−50 0 50

0

2

4

6NEA2 [13.2 km] k = 2.9

−50 0 50

0

2

4

6POKR [98.6 km] k = 1.8

−50 0 50

0

2

4

6PPD [198.2 km] k = 5.1

−50 0 50

0

2

4

6PS08 [117.1 km] k = 1.9

−50 0 50

0

2

4

6RND [143.6 km] k = 1.2

−50 0 50

0

2

4

6TRF [146.5 km] k = 2.9

−50 0 50

0

2

4

6WRH [60.2 km] k = 5.6

Supplementary Figure S16: Envelopes of high-frequency seismograms for all 34 stations within

200 km of the 2016 event. The vertical red lines span the high-frequency foreshock signals that

last approximately 20 s at each station. The estimated value of k, labeled above each subplot,

is based on the best-fitting curve of B(t − t0)k. For comparison with a normal earthquake, see

Figure S14. Station MDM is shown in Figure 1b.

25

−100 0 100 200−1

0

1

2

3

4

5

6BPAW [119.9 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6BWN [62.8 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6CCB [55.2 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6CHUM [187.5 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6COLA [54.7 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6DHY [198.6 km] k = 0.1

nenana_nuc_20130312T_if2

−100 0 100 200−1

0

1

2

3

4

5

6HDA [101.9 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6MCK [109.7 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6MDM [43.6 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6MLY [92.0 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6NEA [15.0 km] k = 0.2

−100 0 100 200−1

0

1

2

3

4

5

6POKR [84.6 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6PPD [184.0 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6PS06 [132.1 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6PS08 [103.6 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6RND [146.2 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6TRF [155.5 km] k = 0.1

−100 0 100 200−1

0

1

2

3

4

5

6WAT2 [196.3 km] k = 0.0

−100 0 100 200−1

0

1

2

3

4

5

6WRH [49.4 km] k = 0.1

Supplementary Figure S17: Envelopes of high-frequency seismograms for the 2013 VLFE.

Compare with the 2015 VLFE in Figure S18. Station MDM is shown in Figure 1b.

26

−100 0 100 200

0

2

4

6BPAW [159.1 km] k = 0.1

−100 0 100 200

0

2

4

6BWN [109.9 km] k = 0.1

−100 0 100 200

0

2

4

6CCB [66.8 km] k = 0.1

−100 0 100 200

0

2

4

6COLA [46.8 km] k = 0.1

−100 0 100 200

0

2

4

6F1TN [57.0 km] k = 0.1

−100 0 100 200

0

2

4

6F2TN [51.0 km] k = 0.1

−100 0 100 200

0

2

4

6F3TN [45.1 km] k = 0.1

−100 0 100 200

0

2

4

6F4TN [39.4 km] k = 0.1

−100 0 100 200

0

2

4

6F5MN [35.8 km] k = 0.1

−100 0 100 200

0

2

4

6F6TP [50.6 km] k = 0.1

−100 0 100 200

0

2

4

6F7TV [62.4 km] k = 0.1

−100 0 100 200

0

2

4

6F8KN [71.8 km] k = 0.1

−100 0 100 200

0

2

4

6FAPT [66.7 km] k = 0.1

−100 0 100 200

0

2

4

6FNN1 [66.6 km] k = 0.1

−100 0 100 200

0

2

4

6FNN2 [71.2 km] k = 0.1

−100 0 100 200

0

2

4

6FPAP [60.2 km] k = 0.1

−100 0 100 200

0

2

4

6FTGH [48.5 km] k = 0.1

−100 0 100 200

0

2

4

6H23K [88.5 km] k = 0.1

−100 0 100 200

0

2

4

6H24K [87.8 km] k = 0.1

−100 0 100 200

0

2

4

6HDA [113.9 km] k = 0.1

−100 0 100 200

0

2

4

6I21K [155.8 km] k = 0.1

−100 0 100 200

0

2

4

6I23K [32.8 km] k = 0.1

−100 0 100 200

0

2

4

6J25K [166.1 km] k = 0.1

−100 0 100 200

0

2

4

6MCK [155.4 km] k = 0.1

−100 0 100 200

0

2

4

6MDM [27.1 km] k = 0.1

−100 0 100 200

0

2

4

6MLY [98.3 km] k = 0.1

−100 0 100 200

0

2

4

6NEA2 [61.9 km] k = 0.1

−100 0 100 200

0

2

4

6POKR [57.8 km] k = 0.1

−100 0 100 200

0

2

4

6PPD [152.9 km] k = 0.1

−100 0 100 200

0

2

4

6PS06 [95.7 km] k = 0.1

−100 0 100 200

0

2

4

6PS07 [27.8 km] k = 0.1

−100 0 100 200

0

2

4

6PS08 [108.7 km] k = 0.1

−100 0 100 200

0

2

4

6RND [191.4 km] k = 0.1

nenana_nuc_20150912T_if3

−100 0 100 200

0

2

4

6TCOL [46.8 km] k = 0.1

−100 0 100 200

0

2

4

6WRH [77.3 km] k = 0.1

Supplementary Figure S18: Envelopes of high-frequency seismograms for the 2015 VLFE. Sta-

tion MDM is shown in Figure 1b.

27

−0.05

0

0.05

0.1

inte

r−sta

tio

np

ha

se

co

he

ren

ce

−180

0

180

inte

r−sta

tion

ph

ase

diffe

ren

ce

ve

locity a

t X

V.F

PA

P (μ

m/s

)

−50 −45 −40 −35 −30 −25 −20 −15 −10 −5

−45 −40 −35 −30 −25 −20 −15 −10 −5

−45 −40 −35 −30 −25 −20 −15 −10 −5

−45 −40 −35 −30 −25 −20 −15 −10 −5

−0.5

0

0.5

no

rma

lize

dcro

ss−

co

rre

latio

n / N

co

mp

1/2

time relative to earthquake (s)

0.1

100

0.1

pe

rce

nta

ge

with

am

plit

ud

e

larg

er

by c

ha

nce

−3

0

3

no

rma

lize

d

cro

ss−

co

rre

latio

n / σ

all 30 stations

XV.FPAP

AK.NEA2

XV.F1TN

XV.F2TN

a

b

c

d

5

5

30

0

−30

Supplementary Figure S19: Phase coherence between mainshock and high-frequency foreshocks

of the 2016 event. (a) 1–10 Hz phase coherence between the mainshock and 4-s windows of

the foreshock arrivals. Colored curves for station pairs including the indicated stations. The

black curve averages over all available stations. (b) Averaged phase difference between the

cross-correlations. (c) Velocity seismogram at XV.FPAP. (d) 1–10 Hz cross-correlation between

the mainshock signals and the foreshocks, for individual stations (colors) and averaged over all

stations (black).

28

−2

−1

0

1

2

−25.5 to −21.5 s

de

pth

(km

)

−24.5 to −20.5 s −23.5 to −19.5 s −22.5 to −18.5 s −21.5 to −17.5 s −20.5 to −16.5 s

−2

−1

0

1

2

−19.5 to −15.5 s

de

pth

(km

)

−18.5 to −14.5 s −17.5 to −13.5 s −16.5 to −12.5 s −15.5 to −11.5 s −14.5 to −10.5 s

−2

−1

0

1

2

−13.5 to −9.5 s

de

pth

(km

)

−12.5 to −8.5 s −11.5 to −7.5 s −10.5 to −6.5 s −9.5 to −5.5 s −8.5 to −4.5 s

−2 −1 0 1 2

−2

−1

0

1

2

−7.5 to −3.5 s

distance E (km)

de

pth

(km

)

−2 −1 0 1 2

−6.5 to −2.5 s

distance E (km)−2 −1 0 1 2

−5.5 to −1.5 s

distance E (km)−2 −1 0 1 2

−4.5 to −0.5 s

distance E (km)−2 −1 0 1 2

−3.5 to 0.5 s

distance E (km)−2 −1 0 1 2

−2.5 to 1.5 s

distance E (km)p

ha

se

co

he

ren

ce

−0.1

0

0.1

Supplementary Figure S20: Phase coherence between mainshock and high-frequency foreshocks

of the 2016 event. Phase coherence is plotted as a function of foreshock location in an east-west

oriented vertical plane. This plane has zero north-south offset from the mainshock.

29

−2

−1

0

1

2

−25.5 to −21.5 s

dis

tan

ce

N (

km

)

−24.5 to −20.5 s −23.5 to −19.5 s −22.5 to −18.5 s −21.5 to −17.5 s −20.5 to −16.5 s

−2

−1

0

1

2

−19.5 to −15.5 s

dis

tan

ce

N (

km

)

−18.5 to −14.5 s −17.5 to −13.5 s −16.5 to −12.5 s −15.5 to −11.5 s −14.5 to −10.5 s

−2

−1

0

1

2

−13.5 to −9.5 s

dis

tan

ce

N (

km

)

−12.5 to −8.5 s −11.5 to −7.5 s −10.5 to −6.5 s −9.5 to −5.5 s −8.5 to −4.5 s

−2 −1 0 1 2

−2

−1

0

1

2

−7.5 to −3.5 s

distance E (km)

dis

tan

ce

N (

km

)

−2 −1 0 1 2

−6.5 to −2.5 s

distance E (km)−2 −1 0 1 2

−5.5 to −1.5 s

distance E (km)−2 −1 0 1 2

−4.5 to −0.5 s

distance E (km)−2 −1 0 1 2

−3.5 to 0.5 s

distance E (km)−2 −1 0 1 2

−2.5 to 1.5 s

distance E (km)p

ha

se

co

he

ren

ce

−0.1

0

0.1

Supplementary Figure S21: Phase coherence between mainshock and high-frequency foreshocks

of the 2016 event. Phase coherence is plotted as a function of foreshock location in map view.

This plane has zero vertical offset from the mainshock.

30

Time (ms)

Dis

tan

ce

alo

ng

fa

ult x

, cm

Time, ms

00

10

10

20

20

30

30

rate strengthening, a - b > 0

rate weakening,

a - b < 0

Fault modelLaboratory experiment

fault

viscousputty

Polycarbonate plate

viscousputty

Loading with a manual pump

(a)

(c)

fault

(b)

Rupture length (mm)

Ru

ptu

re s

pe

ed

Vr (

m/s

)

(e)

3210.5

σ (MPa)

Ru

ptu

re s

pe

ed

Vr (

m/s

)

10 15 20 30 50 70 100 150

1

5

10

50

100

500

1000

10 15 20 30 50 70 100 150

0.5

1

5

10

50

100

500

1000

(d)

Laboratory experiments

6

σ (MPa)

acc

ele

ratio

n (

ase

ism

ic)

dynamic propagation (seismic)

quasi-static

propagation

(aseismic)

acc

ele

ratio

n (ase

ism

ic)

dynamic propagation (seismic)

quasi-static

propagation

(aseismic)

Numerical simulations

Rupture length (mm)

nucleation dynamic rupture

σ = 1.58 MPa

Supplementary Figure S22: Schematic diagrams illustrating the set-up of (a) the laboratory ex-

periments of Latour et al. (2013) and (b) the numerical model of Kaneko et al. (2016). (c)

Comparison between simulation results (Kaneko et al., 2016), plotted as the blue dashed line,

with laboratory results from Latour et al. (2013), plotted as the red line and with grayscale to

show the light intensity change indicating the actively slipping zone. The curves show the po-

sition of the rupture front during a transition from quasi-static nucleation to dynamic rupture.

The rupture fronts are defined as the locations of two peak shear stresses: one within the left

rate-strengthening patch and the other within the rate-weakening patch. (d)-(e) Characteristics

of nucleation phase under different σ in numerical simulations and for 47 stick-slip events in

laboratory experiments. Observed and modeled rupture speeds increase with the rupture length.

The rupture length is defined as a distance from the edge of the rate-weakening patch at x = 11cm to the rupture front. The evolution of the rupture front under a range of σ closely matches

the laboratory results.

31

time (ms)-80 -60 -40 -20 0lo

g1

0(r

up

ture

le

ng

th (

mm

))

-1

0

1

2

3

distance along strike (cm)10 15 20 25

tim

e (

ms)

-50

-40

-30

-20

-10

0

10

time (ms)-80 -60 -40 -20 0lo

g1

0(r

up

ture

le

ng

th (

mm

))

-1

0

1

2

3

distance along strike (cm)10 15 20 25

tim

e (

ms)

-60

-40

-20

0

time (ms)-80 -60 -40 -20 0lo

g1

0(r

up

ture

le

ng

th (

mm

))

-1

0

1

2

3

distance along strike (cm)10 15 20 25

tim

e (

ms)

-60

-40

-20

0

time (ms)-80 -60 -40 -20 0lo

g1

0(r

up

ture

le

ng

th (

mm

))

-1

0

1

2

3

distance along strike (cm)10 15 20 25

tim

e (

ms)

-80

-60

-40

-20

0

f = 10-1.8(t + 31)2.5

f = 10-2.1(t + 36)2.5

f = 10-3.1(t + 57)2.7

f = 10-4.8(t + 85)3.2

σ = 0.75 MPa

σ = 0.91 MPa

σ = 1.58 MPa

σ = 2.40 MPa

A

A

B C

AB C

A

B C

A

B C

A

A

A

σ = 0.75 MPa

σ = 0.91 MPa

σ = 1.58 MPa

σ = 2.40 MPa

Supplementary Figure S23: Evolution of rupture front position (left column) and rupture

length (right column) for four simulations from Kaneko et al. (2016) for normal stresses of

σ = 0.75 MPa (top), 0.91 MPa, 1.58 MPa, and 2.40 MPa (bottom). The three stages of rupture

are labeled as A (quasi-static), B (acceleration), and C (dynamic propagation). The onsets of the

quasi-static, acceleration, and dynamic propagation phases are marked by green, black and red

dashed lines, respectively. In this figure, t = 0 is defined as the time at the end of the accel-

eration phase, which is graphically defined from Figure S22d. The magenta dashed curve is a

power function fit (B(t− t0)k), with the best-fitting power function shown by magenta text.

32