REFERENCES AND NOTES

1. S. L. Johnson, E. Vorobeva, P. Beaud, C. J. Milne, G. Ingold,Phys. Rev. Lett. 103, 205501 (2009).

2. V. Juvé et al., Phys. Rev. Lett. 111, 217401 (2013).3. D. M. Fritz et al., Science 315, 633–636 (2007).4. B. J. Siwick, J. R. Dwyer, R. E. Jordan, R. J. D. Miller, Science

302, 1382–1385 (2003).5. P. Baum, D.-S. Yang, A. H. Zewail, Science 318, 788–792 (2007).6. M. Eichberger et al., Nature 468, 799–802 (2010).7. A. H. Zewail, Science 328, 187–193 (2010).8. T. LaGrange et al., Ultramicroscopy 108, 1441–1449 (2008).9. O. F. Mohammed, D.-S. Yang, S. K. Pal, A. H. Zewail,

J. Am. Chem. Soc. 133, 7708–7711 (2011).10. M. Chergui, Acta Crystallogr. A 66, 229–239 (2010).11. F. Carbone, O.-H. Kwon, A. H. Zewail, Science 325, 181–184

(2009).12. J. M. Kosterlitz, D. J. Thouless, J. Phys. Chem. 6, 1181–1203 (1973).13. P. M. Chaikin, T. C. Lubensky, Principles of Condensed Matter

Physics (Cambridge University Press, Cambridge, 2000).14. A. Hanisch-Blicharski et al., Ultramicroscopy 127, 2–8 (2013).15. M. A. Van Hove, W. H. Weinberg, C.-M. Chan, Low-Energy

Electron Diffraction (Springer, Berlin Heidelberg, 1986).16. S. Schäfer, W. Liang, A. H. Zewail, J. Chem. Phys. 135, 214201

(2011).17. R. S. Becker, G. S. Higashi, J. A. Golovchenko, Phys. Rev. Lett.

52, 307–310 (1984).18. C. Cirelli et al., Europhys. Lett. 85, 17010 (2009).

19. R. Karrer, H. J. Neff, M. Hengsberger, T. Greber, J. Osterwalder,Rev. Sci. Instrum. 72, 4404 (2001).

20. M. Krüger, M. Schenk, P. Hommelhoff, Nature 475, 78–81 (2011).21. G. Herink, D. R. Solli, M. Gulde, C. Ropers, Nature 483,

190–193 (2012).22. A. Paarmann et al., J. Appl. Phys. 112, 113109 (2012).23. E. Quinonez, J. Handali, B. Barwick, Rev. Sci. Instrum. 84,

103710 (2013).24. J. C. H. Spence, T. Vecchione, U. Weierstall, Philos. Mag. 90,

4691–4702 (2010).25. H. Park, J. M. Zuo, Appl. Phys. Lett. 94, 251103 (2009).26. Materials and methods are available as supplementary

materials on Science Online.27. R. K. Raman, Z. Tao, T.-R. Han, C.-Y. Ruan, Appl. Phys. Lett. 95,

181108 (2009).28. M. Tress et al., Science 341, 1371–1374 (2013).29. J. A. Forrest, K. Dalnoki-Veress, Adv. Colloid Interfac. 94,

167–195 (2001).30. O. M. Braun, Y. S. Kivshar, The Frenkel-Kontorova Model:

Concepts, Methods, and Applications (Springer, Berlin,Heidelberg, 2004).

31. A. N. Rissanou, V. Harmandaris, J. Nanopart. Res. 15, 1589(2013).

32. Y.-C. Lin et al., Nano Lett. 12, 414–419 (2012).33. A. K. Geim, I. V. Grigorieva, Nature 499, 419–425 (2013).34. J. Kumaki, T. Kawauchi, E. Yashima, J. Am. Chem. Soc. 127,

5788–5789 (2005).

35. J. S. Ha et al., J. Vac. Sci. Technol. B 12, 1977–1980(1994).

36. Whereas the (10) diffraction spot of PMMA overlaps with thatof graphene, the (3/2 0) PMMA spot is not observed, whichis most likely a result of the chain form factor or disorder.

ACKNOWLEDGMENTS

We thank M. Müller for helpful discussions on polymer dynamics.Supporting sample characterizations by H. Schuhmann, M. Seibt,S. Strauch, H. Stark (TEM imaging), S. Dechert, and M. Sivis(Raman spectroscopy), as well as James E. Evans and Nigel D. Browning(high-resolution TEM, Pacific Northwest National Laboratory),are gratefully acknowledged. This work was partially funded bythe Deutsche Forschungsgemeinschaft (DFG-ZuK 45/1 andDFG-SFB 1073). M.G. was financially supported by theGerman National Academic Foundation. A.M.W. and H.K.Y.gratefully acknowledge support from the Alexander vonHumboldt Foundation.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/345/6193/200/suppl/DC1Materials and MethodsFigs. S1 to S8References (37–48)

9 January 2014; accepted 22 May 201410.1126/science.1250658

EARTHQUAKE DYNAMICS

Supershear rupture in a Mw 6.7aftershock of the 2013 Sea ofOkhotsk earthquakeZhongwen Zhan,1,2* Donald V. Helmberger,2 Hiroo Kanamori,2 Peter M. Shearer1

Earthquake rupture speeds exceeding the shear-wave velocity have been reported forseveral shallow strike-slip events. Whether supershear rupture also can occur in deepearthquakes is unclear, because of their enigmatic faulting mechanism. Using empiricalGreen's functions in both regional and teleseismic waveforms, we observed supershearrupture during the 2013 moment magnitude (Mw) 6.7 deep earthquake beneath the Seaof Okhotsk, an aftershock of the large deep earthquake (Mw 8.3). The Mw 6.7 eventruptured downward along a steeply dipping fault plane at an average speed of 8 kilometersper second, suggesting efficient seismic energy generation. Comparing it to the highlydissipative 1994Mw 8.3 Bolivia earthquake, the two events represent end members of deepearthquakes in terms of energy partitioning and imply that there is more than one rupturemechanism for deep earthquakes.

Most earthquakes rupture at speeds lessthan the shear-wave speed (VS). Theoryand laboratory experiments indicate thatrupture speeds in excess of VS are pos-sible (1–3), and supershear ruptures have

now occasionally been reported for large strike-slip events (mode II), including the 1979 ImperialValley (4), 1999 Izmit (5), 2001 Kunlun (6–8), 2002Denali (7, 9), 2010 Yushu (10), and 2013 Craig (11)earthquakes. All of these documented occurrenceswere shallow earthquakes with a simple fault geo-

metry (12), and mostly with surface breaks, whichis consistent with theoretical studies that the freesurface helps promote supershear rupture (13, 14).No definitive evidence has yet been obtained for

supershear rupture in deep earthquakes (depth >300 km) (15). However, the rupture speeds ofthese events are difficult to estimate becauseof a general absence of near-field observations,and they appear highly variable. For example,the rupture speeds of the two largest deep earth-quakes observed to date, the 1994 moment mag-nitude (Mw) 8.3 Bolivia earthquake and the 2013Mw 8.3 Sea of Okhotsk earthquake (16–18), wereabout 0.2 to 0.4 and 0.7 VS, respectively. About80% of the rupture velocities for deep earth-quakes fall between 0.3 and 0.9 VS (19), a greaterrange than is seen for shallow earthquakes (15).The rupture speed may depend on the slab ther-

mal state (20, 21), with ruptures propagatingmoreslowly inwarm slabs than in cold slabs, but seismicobservations have been inconclusive (22, 23). Theone previous example of observed supershear rup-ture during the 1990 Mw 7.1 Sakhalin deep earth-quake neglected to take into account waveformchanges from attenuation and the high-velocitysubducted slab (24, 25).The 24May 2013Mw 8.3 Sea of Okhotsk event

(depth, 607 km) was the largest deep earth-quake ever recorded (Fig. 1), slightly larger thanthe 1994 Bolivia earthquake. On the same day,an Mw 6.7 earthquake at a depth of 642 km oc-curred about 300 km southwest of themainshockand was recorded by many teleseismic stationsand one regional station (Fig. 1). An extraordi-nary feature of the Mw 6.7 event was its sharpteleseismic P waves, which had displacementpulse widths atmost azimuths of 1 to 2 s (Fig. 1).These are much less than the expected sourceduration of 8 s, based on its magnitude and pre-vious studies of scaled durations of deep earth-quakes (26, 27). If taken as a rough estimate ofthe Mw 6.7 earthquake’s source duration, thesevery short teleseismic P-wave durations implyextremely high stress drops in a range from157 MPa to 5.856 GPa (17). On the other hand,the regional station PET (distance ≈ 495 km) onthe Kamchatka Peninsula to the east displayed amuch longer direct Pwavetrain of about 5 s (Fig.1). Because the Pwave to the PET station left thesource along an upgoing ray path, instead of thedowngoing rays for the teleseismic stations, thislonger P-wave duration at PET suggests possibledownward rupture directivity during theMw 6.7earthquake. However, to test this possibility wefirst need to account for possible path effects suchas wave diffractions along the high-velocity slabinwhich the earthquake occurred and site effectsat the stations.We used waveforms from two nearby smaller

earthquakes (Fig. 1; the 24 June 2013 Mw 4.3

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1Institute of Geophysics and Planetary Physics, ScrippsInstitution of Oceanography, University of California, SanDiego, La Jolla, CA 92093–0225, USA. 2SeismologicalLaboratory, California Institute of Technology, 1200 EastCalifornia Boulevard, Pasadena, CA 91125, USA.*Corresponding author. E-mail: zwzhan@ucsd.edu, zwzhan@gmail.com

RESEARCH | REPORTS

event and the 30 August 1996 Mw 5.5 event) asempirical Green’s functions (EGFs) to calibratethe paths. The Mw 4.3 earthquake’s small mo-ment, similar depth, and probably similar focalmechanism as the Mw 6.7 earthquake (fig. S1)make it an ideal EGF event. Its direct P wave

recorded at the PET station displays two dis-tinct arrivals separated by about 2 s (Fig. 2), dueto diffraction along the dipping high-velocityslab in the upper mantle (25). Therefore, theapparent 5-s P duration of the Mw 6.7 earth-quake at the PET station was partly caused by

the structural path effect. We deconvolved theEGF waveform from the Mw 6.7 earthquake Pwave to remove the path effect and obtained amore accurate source-time function (STF) (28).Most of the energy then concentrated in thefirst ~2 s, which we measured as the STF dura-tion at the PET station (Fig. 2; red shading intop STF).Because teleseismic records of theMw 4.3 event

are noisy, we used the 1996Mw 5.5 event at some-what shallower depth (~590 km) with a slightlyrotated focal mechanism (Fig. 1) as the tele-seismic EGF event. Because we only used tele-seismic directPwaveforms (no absolute amplitude),these small differences in depth and radiationpattern did not significantly affect the accuracyof the EGFs. TheMw 4.3 and 5.5 EGF events hadhighly similar waveforms at the regional stationPET and several quiet teleseismic stations (fig. S2),despite their difference inmoment. This suggeststhat both EGF events can be regarded as delta-function–like point sources and their waveformsare mostly controlled by path effects. We choseteleseismic stations with clean direct P wavesfromboth theMw 6.7 and theMw 5.5 earthquakes(Fig. 1 inset) and then deconvolved to estimateSTFs and their durations (Fig. 2 and fig. S3).The resulting teleseismic STF durations rangefrom ~0.5 to ~1 s. For both regional and tele-seismic stations, relatively simple and compactSTFs convolved with the EGFs produce good fitsto the direct P and P-coda waveforms of theMw 6.7 earthquake, which suggests effective cor-rection of the path effects. We also attempted toinclude two more stations, MA2 and YSS, at dis-tances of about 818 and 858 km, respectively(fig. S4). Direct P waves from these stations leftthe source along approximately horizontal raypaths. However, because of waveform complex-ities caused by triplications due to the 660-kmdiscontinuity (figs. S4 to S6), we were unable tofind an appropriate EGF event to correct for thesestructural effects.After removing the path effects with EGFs, we

inverted the resulting STF durations for earth-quake rupture parameters. The path-corrected STFduration of the PET station (~2.1 s) is still morethan two times longer than those of the teleseismicstations (0.5 to~1 s), suggestingdownward rupturedirectivity. For three-dimensional unilateral rup-ture (fig. S7), the STF duration of the i-th station Ti

can be written as a function of rupture duration t,horizontal rupture azimuth qr, and horizontal andvertical dimensions L and H, as Ti = t + xi(qr)L +hiH, where xi(qr)L and hiH are the corrections forazimuthal and vertical directivity, respectively.Note that xiðqrÞ ¼ − cosðqi−qrÞ

cipis the horizontal

directivity parameter for the i-th station withazimuth qi and P-wave phase velocity cip ¼ a

sinϕi

(18, 29). Here ϕi is the takeoff angle for the i-thstation, and a is the P-wave speed. Therefore,the azimuthal variations in STF durationsresolve the rupture direction qr and horizontalextent L. In the final term, hi ¼ − a

cosϕiis the

vertical slowness, negative for teleseismic sta-tions (with down-going rays) and positive forregional stations (with up-going rays). This sign

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148˚E 150˚E 152˚E 154˚E 156˚E 158˚E 160˚E 162˚E

50˚N

52˚N

54˚N

56˚N

PET

Kuril

−Kam

chat

ka T

renc

h

Kamchatka Peninsula

2013/05/24Mw 6.7

1996/08/30, Mw 5.5

2013/06/23, Mw 4.3

2013/05/24, Mw 8.3

AAK

HRV

PMG

PET

10 s

Fig. 1. Earthquake and station locations. The 2013 Okhostk Mw 8.3 mainshock and Mw 6.7aftershock are displayed as the black and red beachballs, respectively. The two red stars connectedwith two smaller beachballs represent the EGF events used in this study. Slab contours from the Slab1.0 model (31) are shown as dashed lines.The inset shows teleseismic and regional stations with fourrepresentative P vertical displacement seismograms (green lines).

0 2 4 6 8 10

Time (s)

2013 Mw 6.7

HRV31.0/78.4

PMG184.8/61.6

AAK291.5/50.6

PET77.0/4.5

0 2 4 6 8 10

Time (s)

EGF

0 1 2 3 4 5

Time (s)

STF

Fig. 2. EGF and deconvolution.The three columns display vertical-component seismograms of the Mw

6.7 earthquake, EGFs, and the deconvolved STFs. To ensure high signal-to-noise ratio and enhance high-frequency energy, we used acceleration seismograms filtered between 0.5 and 1 Hz. Seismograms of theMw 6.7 event and EGFs are flipped to have the samepolarity before deconvolution.The black and red tracesin the first column are the data and predictions, respectively.The two numbers beneath station names aredistances and azimuths in degrees. In the third column, we show the STF durations defined by the redshading, which includes most of the energy.

RESEARCH | REPORTS

difference in hi accounts for the major observeddifference between teleseismic and regionalSTF durations.We used a grid-searchmethod to invert for the

rupture parameters (t, qr, L, and H). The least-squares misfit of the STF durations, as a functionof rupture vertical extentH and rupture azimuthqr, has a well-defined global minimum at H =11 km and qr = 130° (Fig. 3A). With these opti-mal values, the STF durations corrected for thedownward vertical directivity (Fig. 3B) fall neara straight line with a slope of L = 4 km and zero-crossing duration of t = 1.5 s. With L = 4 kmand H = 11 km, we estimated the rupture dipto be ~70°, coincident with the steeper faultplane's dip of ~69° (17). Because the rupture di-rection qr = 130° is roughly perpendicular to thefault strike (~26°), we conclude that the Mw 6.7earthquake features a downward mode II rup-ture on the fault plane dipping steeply to thesoutheast (Fig. 4A). The rupture propagatedffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

L2 þH2p

or ~12 km in t = 1.5 s, from whichwe estimate an average rupture speed of about8 km/s. This speed is about

ffiffiffi

2p

VS , which is sub-stantially higher than the local shear wave speed(VS ~5.5 km/s, based on the Preliminary Refer-enceEarthModel). Contouring the average rupturespeeds for all grid-searched rupture parameters(Fig. 3A) shows that within the region withreasonablemisfit (inside the dark blue contours),the rupture speed is always higher than VS andlower than VP. Within 95% confidence limits, theaverage rupture speed is 8.0 T 0.7 km/s. Anom-alously broad teleseismic depth phases (pP) alsoare roughly consistent with the downward super-shear rupture model (figs. S8 and S9). However,pP pulse widths exhibit much larger scatter thanP pulse widths, and their behavior appears to beheavily influenced by complicated path effects,

thus we cannot invert the pPwaveforms for rup-ture parameters with any confidence.Previously identified extremely high-stress

drops (157 MPa to 5.856 GPa) of the Mw 6.7earthquake and subsequently low radiation ef-

ficiency (0.005 < hR < 0.15) (16, 17) depict thisevent as mechanistically distinct from the OkhotskMw 8.3 mainshock (Ds ≈ 15 MPa, hR ≈ 0.6) andmore similar to the 1994 Mw 8.3 Bolivia earth-quake (Ds ≈ 114 MPa, hR ≤ 0.036) in a warmer

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0.6 0.8 1 3 5 101

102

103

104

105

Str

ess

Dro

p (M

Pa)

Radius of Rupture Area (km)

1994 Mw 8.3 Bolivia earthquake

2013 Mw 8.3 Okhotsk earthquake

Vr=1.5km/s

Vr=4.5km/s

Radiated Energy 2.36 ×1015 J

1015

1016

1017

1018

Ava

ilabl

e S

trai

n E

nerg

y (J

)

4 km

11 km

Up

70o

Vr=8 km

/s

Vr=8km/sMap View

Fig. 4. Earthquake stress drop and energy partitioning. (A) Rupture geometry of the Mw 6.7earthquake. In the focal mechanism in map view, the thick red line marks the steep fault plane onwhich the rupture is inferred to occur. The orange arrow shows the estimated rupture direction,almost perpendicular to the fault strike. In the side view along the fault strike from the southwest, theearthquake ruptured along the steeper fault plane downward at a speed of 8 km/s. The horizontaland vertical rupture extents are 4 and 11 km, respectively. (B) Stress drop and available strain energyas a function of rupture area radius. Assuming a rupture speed from 1.5 to 4.5 km/s, Ye et al. (17)obtained rupture radii of 1 to 3 km (thick black line), which correspond to stress drops higher thanthose of the 2013 Okhostk Mw 8.3 mainshock and the 1994 Bolivia earthquake (dashed blue lines asreferences, left vertical axis). The resulting available strain energy is also significantly higher than theradiated energy (dashed red line, right vertical axis) (17), which suggests low radiation efficiency. Ourpreferred result with a supershear rupture speed of 8 km/s is marked as the red dot, assuming acircular crack. The stress drop is about 32 MPa, and the available strain energy is close to theradiated energy, suggesting a radiation efficiency of near unity.

0 1 2 3−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

STF Duration (s)

Hor

izon

tal D

irect

ivity

Par

amet

er (

s/km

)

PETPET

STF durationWith vertical correctionBest fitting line

0 5 10 15 2090

100

110

120

130

140

150

160

170

180

Vertical Rupture Extent H (km)

Rup

ture

Azi

mut

h θ r (

°)

Mis

fit

0.4

0.6

0.8

1

1.2

1.4

1.6

Fig. 3. Inversion forearthquake ruptureparameters. (A) Mis-fit as a function ofthe grid-searchedvertical ruptureextent H and ruptureazimuth qr. The reddot at (11 km, 130°)marks the optimalsolution without asubstantial tradeoff.The dashed contoursshow the rupturespeeds for all grid-searched solutions atreference speeds ofVS,

ffiffiffi

2p

VS, and VP.(B) STF durationswith and withoutvertical directivitycorrections, assumingthe optimal valuesfrom (A). The corrected STF durations (blue dots) fall near a straight line with a slope of L = 4 km, and zero-crossing duration of t = 1.5 s (red cross).The green dots show the STF durations without the vertical directivity corrections, in which the PET station has a longer STF duration than all theteleseismic stations.

RESEARCH | REPORTS

slab (Fig. 4B). This complexity suggests strongstress heterogeneity in subducted slabs (17). How-ever, supershear rupture during theMw 6.7 earth-quake brings its stress drop down to 32 MPa andits radiation efficiency to about 1.0 (Fig. 4B),which are much closer to values for the Mw 8.3Okhotsk mainshock. Therefore, strong stress het-erogeneity inside subducted slabs is not requiredto explain the 2013 Okhotsk mainshock and itsMw 6.7 aftershock. However, the difference in rup-ture speed (subshear versus supershear) indicatessubstantial spatial heterogeneity in the fracturestrength or fracture energy within the slab.Compared with shallow supershear events,

this deep event has a relatively small rupturedimension and higher static stress drop (by afactor of ~10). Our estimate of high radiationefficiency (hR ≈1.0) during the Mw 6.7 event isalso consistent with theoretical predictions oflow fracture energy during supershear ruptures(30). This constraint of low fracture energy bearson the question of deep earthquake faultingmechanisms, which is still enigmatic (15, 19).The 1994 Bolivia earthquake involved a largeamount of fracture/thermal energy and radiatedrelatively little energy in seismic waves (16). Interms of energy partitioning, the supershearMw

6.7 earthquake represents the opposite end mem-ber from the Bolivia earthquake, with almost allthe available strain energy being radiated asseismic waves. This contrast is consistent withthe idea of more than one rupture mechanism fordeep earthquakes in slabs with different thermalstates (18, 20, 21). The Okhotsk mainshock andaftershock in a cold slab ruptured with the trans-formational faulting mechanism, whereas theBolivia earthquake in a warm slab was dominatedby shear melting (18).

REFERENCES AND NOTES

1. R. Burridge, Geophys. J. R. Astron. Soc. 35, 439–455 (1973).2. D. Andrews, J. Geophys. Res. 81, 5679–5687 (1976).3. K. Xia, A. J. Rosakis, H. Kanamori, Science 303, 1859–1861

(2004).4. R. J. Archuleta, J. Geophys. Res. 89, 4559–4585 (1984).5. M. Bouchon et al., Geophys. Res. Lett. 28, 2723–2726

(2001).6. M. Bouchon, M. Vallée, Science 301, 824–826 (2003).7. K. T. Walker, P. M. Shearer, J. Geophys. Res. 114 (B2), B02304

(2009).8. M. Vallée, E. M. Dunham, Geophys. Res. Lett. 39, L05311

(2012).9. E. M. Dunham, R. J. Archuleta, Bull. Seismol. Soc. Am. 94,

S256–S268 (2004).10. D. Wang, J. Mori, Bull. Seismol. Soc. Am. 102, 301–308 (2012).11. H. Yue et al., J. Geophys. Res. 118, 5903–5919 (2013).12. M. Bouchon et al., Tectonophysics 493, 244–253 (2010).13. H. Zhang, X. Chen, Geophys. J. Int. 167, 917–932 (2006).14. Y. Kaneko, N. Lapusta, Tectonophysics 493, 272–284 (2010).15. H. Houston, in Treatise on Geophysics, G. Schubert, Ed.

(Elsevier, Amsterdam, 2007), pp. 321–350.16. H. Kanamori, D. L. Anderson, T. H. Heaton, Science 279,

839–842 (1998).17. L. Ye, T. Lay, H. Kanamori, K. D. Koper, Science 341,

1380–1384 (2013).18. Z. Zhan, H. Kanamori, V. C. Tsai, D. V. Helmberger, S. Wei,

Earth Planet. Sci. Lett. 385, 89–96 (2014).19. C. Frohlich, Deep Earthquakes (Cambridge Univ. Press,

Cambridge, 2006).20. D. A. Wiens, Phys. Earth Planet. Inter. 127, 145–163 (2001).21. R. Tibi, G. Bock, D. A. Wiens, J. Geophys. Res. 108, 2091

(2003).22. S.-C. Park, J. Mori, J. Geophys. Res. 113, B08303 (2008).23. M. Suzuki, Y. Yagi, Geophys. Res. Lett. 38, L05308 (2011).

24. K. Kuge, J. Geophys. Res. 99 (B2), 2671–2685 (1994).25. Z. Zhan, D. Helmberger, D. Li, Phys. Earth Planet. Inter.

232, 30–35 (2014).26. S. E. Persh, H. Houston, J. Geophys. Res. 109, B04311

(2004).27. A. Tocheport, L. Rivera, S. Chevrot, J. Geophys. Res. 112,

B07311 (2007).28. Materials and methods are available in the supplementary

materials.29. C. J. Ammon et al., Science 308, 1133–1139 (2005).30. R. Madariaga, K. B. Olsen, Pure Appl. Geophys. 157, 1981–2001

(2000).31. G. P. Hayes, D. J. Wald, R. L. Johnson, J. Geophys. Res. 117,

B01302 (2012).

ACKNOWLEDGMENTS

We thank two anonymous reviewers for their helpful comments.The Incorporated Research Institutions for Seismology (IRIS)provided the seismic data. This work was supported by NSF(grants EAR-1142020 and EAR-1111111). All data used are availablefrom the IRIS data center at www.iris.edu.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/345/6193/204/suppl/DC1Materials and MethodsFigs. S1 to S9

27 February 2014; accepted 2 June 201410.1126/science.1252717

OCEAN MICROBES

Multispecies diel transcriptionaloscillations in open oceanheterotrophic bacterial assemblagesElizabeth A. Ottesen,1,2,3 Curtis R. Young,1,2 Scott M. Gifford,1,2

John M. Eppley,1,2 Roman Marin III,4 Stephan C. Schuster,5

Christopher A. Scholin,4 Edward F. DeLong1,2,6*

Oscillating diurnal rhythms of gene transcription, metabolic activity, and behavior arefound in all three domains of life. However, diel cycles in naturally occurring heterotrophicbacteria and archaea have rarely been observed. Here, we report time-resolvedwhole-genome transcriptome profiles of multiple, naturally occurring oceanic bacterialpopulations sampled in situ over 3 days. As anticipated, the cyanobacterialtranscriptome exhibited pronounced diel periodicity. Unexpectedly, several differentheterotrophic bacterioplankton groups also displayed diel cycling in many of their genetranscripts. Furthermore, diel oscillations in different heterotrophic bacterial groupssuggested population-specific timing of peak transcript expression in a variety ofmetabolic gene suites. These staggered multispecies waves of diel gene transcriptionmay influence both the tempo and the mode of matter and energy transformationin the sea.

The coordination of biological activities intodaily periodic cycles is a common featureof eukaryotes and is widespread amongplants, fungi, and animals, including man(1). Among single celled noneukaryotic

microbes, diel cycles have been well documentedin cyanobacterial isolates (2–4), one halophilicarchaeon (5), and bacterial symbionts of fish andsquid (6, 7). Some evidence for diel cycling inmicrobial plankton has also been suggested onthe basis of bulk community amino acid incor-poration, viral production, or metabolite consump-tion (8–10). However, the existence of regular diel

oscillations in free-living heterotrophic bacterialspecies has rarely been assessed.Microbial community RNA sequencing tech-

niques now allow simultaneous determinationof whole-genome transcriptome profiles amongmultiple cooccurring species (11, 12), enablinghigh-frequency, time-resolved analyses of mi-crobial community dynamics (12, 13). To betterunderstand temporal transcriptional dynamicsin oligotrophic bacterioplankton communities,we conducted a high-resolution multiday timeseries of bacterioplankton sampled from theNorthPacific Subtropical Gyre (14).To facilitate repeated sampling of the same

planktonic microbial populations through time,automated Lagrangian sampling of bacterio-planktonwas performed every 2 hours over 3 daysby using a free-drifting robotic EnvironmentalSample Processor (ESP) (13, 15) (fig. S1). Afterinstrument recovery, planktonic microbial RNAwas extracted, purified, converted to cDNA, andsequenced to assess whole-genome transcriptomedynamics of predominant planktonic microbialpopulations (tables S1 and S2). The recoveredcDNAs were dominated by transcripts from

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1Department of Civil and Environmental Engineering,Massachusetts Institute of Technology, Cambridge, MA02139, USA. 2Center for Microbial Oceanography: Researchand Education (C-MORE), University of Hawaii, Honolulu, HI96822, USA. 3Department of Microbiology, University ofGeorgia, Athens, GA 30602, USA. 4Monterey Bay AquariumResearch Institute, Moss Landing, CA 95039, USA.5Singapore Centre on Environmental Life SciencesEngineering, Nanyang Technological University, 637551Singapore. 6Department of Biological Engineering,Massachusetts Institute of Technology, Cambridge, MA02139, USA.*Corresponding author. E-mail: edelong@hawaii.edu

RESEARCH | REPORTS

www.sciencemag.org/content/345/6193/204/suppl/DC1

Supplementary Materials for

Supershear rupture in a Mw 6.7 aftershock of the 2013 Sea of Okhotsk earthquake

Zhongwen Zhan,* Donald V. Helmberger, Hiroo Kanamori, Peter M. Shearer

*Corresponding author. E-mail: zwzhan@ucsd.edu, zwzhan@gmail.com

Published 11 July 2014, Science 345, 204 (2014) DOI: 10.1126/science.1252717

This PDF file includes: Materials and Methods

Figs. S1 to S9

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Materials and Methods

Deconvolution We derive the source-time functions (STFs) 𝑥(𝑡) by deconvolving the EGFs 𝑢(𝑡) from the Mw 6.7 earthquake waveforms 𝑤(𝑡) with an optimization-based method. The convolution

𝑢 𝑡 ∗  𝑥 𝑡 = 𝑤 𝑡 where ∗ is a convolution operator can also be written in a linear matrix form

𝑈𝑥 = 𝑤 where 𝑥 and 𝑤 are 𝑛!×1 and 𝑛!×1 matrices, 𝑈 is a 𝑛!×𝑛! matrix with each row as a time-shifted 𝑢(𝑡). 𝑛! and 𝑛! are the number of samples of 𝑢(𝑡) and 𝑤(𝑡). For 𝑛! > 𝑛!, we can solve the over-determined inverse problem for 𝑥 by minimizing the L2 norm of data residuals and model norm:

∥ 𝑈𝑥 − 𝑤 ∥!!+ 𝜆 ∥ 𝑥 ∥!! where 𝜆 is a regularization parameter chosen by trial-and-error to ensure reasonably good waveform fitting and compact STFs.

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Fig. S1. Complete seismograms of the Mw 6.7 earthquake and two EGF events (1996 Mw 5.5 and 2013 Mw 4.3) at the PET station. In the USGS NEIC catalog, the Mw 6.7 event and the Mw 4.3 event are located very close in location (Fig. 1) and depth (623 km vs. 625 km), while the Mw 5.5 event is shallower (580 km). Here we plot the velocity seismograms of the three events in the 20-100 s period band (black traces), aligned on the P-wave onset picked before filtering (red traces). The S waves of the Mw 6.7 and Mw 4.3 events arrive at similar times, while the S wave of the Mw 5.5 event arrives earlier, consistent with its shallower depth. At this long period band, P and S waveforms and P/S amplitude ratios are mostly controlled by earthquake focal mechanisms. Note that the top and middle traces have similar P and S waveforms and P/S amplitude ratios. Although the Mw 4.3 event waveform is a little noisy, we can still see that the Mw 4.3 event probably has a similar focal mechanism as the Mw 6.7 event. In contrast, the bottom trace has a similar P waveform to the top two traces, but a much weaker S wave with a different shape. This difference is also consistent with its different GCMT focal mechanism from the Mw 6.7 event (Fig. 1).

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Fig. S2 Comparison of the Mw 4.3 and Mw 5.5 EGF events. As discussed in Fig. S1, the Mw 5.5 event has a different depth and focal mechanism than the Mw 6.7 and Mw 4.3 events. However, for teleseismic stations, the Mw 5.5 event is still a good EGF event. In the left panel, direct P waves of the Mw 5.5 and Mw 4.3 earthquakes at three quiet stations (so that the Mw 4.3 is visible) are plotted in black and red, respectively. The seismograms are filtered between 1 and 2 Hz, and their amplitudes are normalized to the maximum amplitudes. Note that the two EGF events have very similar waveforms, even in the coda. This is because teleseismic direct P waveforms are mostly controlled by path effects, and probably less by small differences in depth or radiation pattern. The numbers following station names are station azimuths. However, the depth difference matters at the regional station PET. Both EGF events' broadband P waves display two separate pulses, due to wave diffraction along the subducted high-velocity slab. The depth difference between the two events (~60 km) changes the time interval between the two pulses. Because of this waveform dependence on depth, we only use the Mw 4.3 earthquake as the EGF event for deconvolution at the PET station. For both teleseismic and regional stations, the two EGF events have similar frequency content, in spite of their different moments and expected difference in source durations. This means that both events are sharp enough that path effects mostly control their waveforms.

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Fig. S3 Similar to Fig. S2 but for the complete dataset. The three columns display seismograms of the Mw 6.7 earthquake, EGFs, and the deconvolved source time functions (STF). To ensure high signal-to-noise ratios and enhance high-frequency energy, we use the acceleration seismograms filtered between 0.5 and 1 Hz. Seismograms of the Mw 6.7 event and EGFs are flipped to have the same polarity before deconvolution. The black and red traces in the first column are the data and predictions, respectively. The two numbers beneath station names are distances and azimuths in degrees. On the third column, we show the STF durations defined by the red shading, which includes most of the energy.

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Fig. S4 Map of the three closest stations PET (~495 km), MA2 (~818 km) and YSS (~858 km).

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Fig. S5 Observed P waves of the 2013/06/24 Mw 4.3 earthquake at the PET, MA2 and YSS stations displayed in Fig. S4. The red arrows mark the predicted P wave arrival times. The seismograms are high-pass filtered above 0.5 Hz. Only the closest PET station shows a good signal-to-noise ratio. Thus, the 2013 Mw 4.3 earthquake can only be used as the EGF event for the PET station.

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Fig. S6 The 1996/08/30 Mw 5.5 earthquake is recorded clearly at the MA2 and YSS stations. However, because of the different depths and focal mechanisms between the Mw 5.5 earthquake and the Mw 6.7 earthquake (based on the global CMT solutions), the Mw 5.5 event is not an appropriate EGF event for the Mw 6.7 earthquake at either MA2 or YSS. To illustrate this point, we plot the synthetic velocity seismograms at the YSS station for both earthquakes, assuming the same impulsive source-time function (STF) and PREM 1D Earth velocity model. Although we assume the same STF, their P waveforms are still different due to differences in depths and focal mechanisms. Specifically, the Mw 6.7 earthquake shows a significant triplication phase related to the 660-km discontinuity right after the direct P waves.

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Fig. S7 Rupture geometry and parameter definitions. We assume unilateral rupture from O to A shown by the red arrow, with a rupture azimuth of 𝜃!, and horizontal and vertical rupture extents of 𝐿 and 𝐻, respectively.

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Fig. S8 Examples of teleseismic P and pP waveforms at the same time scale. Due to both downward rupture directivity and attenuation, teleseismic pP waveforms are significantly broader than their corresponding P waves. Polarities are flipped to be positive for all examples.

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Fig. S9 In this figure, we attempt to separate the source effect and attenuation effect in teleseismic pP waveforms. As shown in Fig. 3B, the average STF durations for teleseismic P waves are ~0.75 s. If we assume no downward rupture directivity, teleseismic pP waves should have the same average STF duration (~0.75 s). If we instead assume downward rupture directivity as suggested by the PET station, the average pP STF duration should be about 2.25 s (Fig. 3B). We then grid-search the optimal t* values for the two STF durations (2.25 s and 0.75 s) to best fit the observed pP waveforms. We produce synthetic pP waveforms by convolving triangle STFs with the Futterman t* operators and cross-correlate with the observed pP waveforms. (A) shows an example for

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the BHZ component of the MNTX station. The STF durations of 2.25 s and 0.75 s require t* of 1.09 s and 1.57 s to explain the observed pP waveform, respectively. We apply this procedure to 823 teleseismic stations with distances larger than 60° to avoid intersections of other seismic phases with pP. To avoid noisy data and unstable t* estimates, we remove stations with best cross-correlation coefficients less than 0.75. (B) shows the histograms of the resulted 660 t* values for each STF duration (2.25s and 0.75 s in blue and red, respectively). The average t* values are 0.95 s and 1.46 s for STF durations of 2.25 s and 0.75 s, respectively. As a reference, we also plot the expected t* range 0.9±0.3 s for pP (S1,17) as the vertical black line and the shaded zone around it. Clearly, average pP STF duration of 2.25 s with the assumption of downward rupture directivity produces t* values more consistent with previous studies. To explain global pP waveforms without the downward rupture, we will need significantly higher attenuation (t*~1.46 s) than expected. Therefore, we conclude that teleseismic pP waveforms support our supershear rupture model for the 2013 Mw 6.7 earthquake based on teleseismic and regional P waves.

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Supplementary References S1. L. M. Warren, P. M. Shearer, Mapping lateral variations in upper mantle attenuation by stacking P and PP spectra, J. Geophys. Res., 107(B12), 2342 (2002).