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Prevalence of viscoelastic relaxation after the 2011 Tohoku-oki earthquake

Abstract

After a large subduction earthquake, crustal deformation continues to occur, with a complex pattern of evolution1. This postseismic deformation is due primarily to viscoelastic relaxation of stresses induced by the earthquake rupture and continuing slip (afterslip) or relocking of different parts of the fault2,3,4,5,6. When postseismic geodetic observations are used to study Earth’s rheology and fault behaviour, it is commonly assumed that short-term (a few years) deformation near the rupture zone is caused mainly by afterslip, and that viscoelasticity is important only for longer-term deformation6,7. However, it is difficult to test the validity of this assumption against conventional geodetic data. Here we show that new seafloor GPS (Global Positioning System) observations immediately after the great Tohoku-oki earthquake provide unambiguous evidence for the dominant role of viscoelastic relaxation in short-term postseismic deformation. These data reveal fast landward motion of the trench area, opposing the seaward motion of GPS sites on land. Using numerical models of transient viscoelastic mantle rheology, we demonstrate that the landward motion is a consequence of relaxation of stresses induced by the asymmetric rupture of the thrust earthquake, a process previously unknown because of the lack of near-field observations. Our findings indicate that previous models assuming an elastic Earth will have substantially overestimated afterslip downdip of the rupture zone, and underestimated afterslip updip of the rupture zone; our knowledge of fault friction based on these estimates therefore needs to be revised.

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Figure 1: Coseismic and postseismic deformation of the 2011 Tohoku-oki earthquake.
Figure 2: Numerical models of short-term viscoelastic relaxation.
Figure 3: Observed (red) and model-predicted (blue) time series of the east component of postseismic displacements.

References

  1. 1

    Wang, K., Hu, Y. & He, J. Deformation cycles of subduction earthquakes in a viscoelastic Earth. Nature 484, 327–332 (2012)

    CAS  ADS  Article  Google Scholar 

  2. 2

    Hu, Y., Wang, K., He, J., Klotz, J. & Khazaradze, G. Three-dimensional viscoelastic finite element model for post-seismic deformation of the great 1960 Chile earthquake. J. Geophys. Res. 109, B12403 (2004)

    ADS  Article  Google Scholar 

  3. 3

    Pollitz, F. F., Bürgmann, R. & Banerjee, P. Post-seismic relaxation following the great 2004 Sumatra-Andaman earthquake on a compressible self-gravitating Earth. Geophys. J. Int. 167, 397–420 (2006)

    ADS  Article  Google Scholar 

  4. 4

    Suito, H. & Freymueller, J. T. A viscoelastic and afterslip postseismic deformation model for the 1964 Alaska earthquake. J. Geophys. Res. 114, B11404 (2009)

    ADS  Article  Google Scholar 

  5. 5

    Kogan, M. G. et al. Rapid postseismic relaxation after the great 2006–2007 Kuril earthquakes from GPS observations in 2007–2011. J. Geophys. Res. 118, 3691–3706 (2013)

    ADS  Article  Google Scholar 

  6. 6

    Pritchard, M. E. & Simons, M. An aseismic slip pulse in northern Chile and along-strike variations in seismogenic behavior. J. Geophys. Res. 111, B08405 (2006)

    ADS  Google Scholar 

  7. 7

    Hsu, Y.-J. et al. Frictional afterslip following the 2005 Nias-Simeulue earthquake, Sumatra. Science 312, 1921–1926 (2006)

    CAS  ADS  Article  Google Scholar 

  8. 8

    Sato, M. et al. Displacement above the hypocenter of the 2011 Tohoku-Oki earthquake. Science 332, 1395 (2011)

    CAS  ADS  Article  Google Scholar 

  9. 9

    Kido, M., Osada, Y., Fujimoto, H., Hino, R. & Ito, Y. Trench-normal variation in observed seafloor displacements associated with the 2011 Tohoku-Oki earthquake. Geophys. Res. Lett. 38, L24303 (2011)

    ADS  Article  Google Scholar 

  10. 10

    Ozawa, S. et al. Coseismic and postseismic slip of the 2011 magnitude-9 Tohoku-Oki earthquake. Nature 475, 373–376 (2011)

    CAS  ADS  Article  Google Scholar 

  11. 11

    Fujii, Y., Satake, K., Sakai, S., Shinohara, M. & Kanazawa, T. Tsunami source of the 2011 off the Pacific coast of Tohoku earthquake. Earth Planets Space 63, 815–820 (2011)

    ADS  Article  Google Scholar 

  12. 12

    Iinuma, T. et al. Coseismic slip distribution of the 2011 off the Pacific Coast of Tohoku Earthquake (M9.0) refined by means of seafloor geodetic data. J. Geophys. Res. 117, B07409 (2012)

    ADS  Article  Google Scholar 

  13. 13

    Shao, G., Chen, J. & Archuleta, R. Quality of earthquake source models constrained by teleseismic waves: using the 2011 M9 Tohoku-oki earthquake as an example. (Poster 93, presented at Incorporated Research Institutions for Seismology Workshop, Boise, Idaho, 13–15 June, 2012); available at http://www.iris.edu/hq/iris_workshop2012/scihi/WebPages/0115.html

  14. 14

    Tajima, F., Mori, J. & Kennett, B. L. N. A review of the 2011 Tohoku-oki earthquake (Mw 9.0): large-scale rupture across heterogeneous plate coupling. Tectonophysics 586, 15–34 (2013)

    ADS  Article  Google Scholar 

  15. 15

    Ozawa, S. et al. Preceding, coseismic, and postseismic slips of the 2011 Tohoku earthquake, Japan. J. Geophys. Res. 117, B07404 (2012)

    ADS  Article  Google Scholar 

  16. 16

    Japan Coast Guard & Tohoku University. Seafloor movements observed by seafloor geodetic observations after the 2011 off the Pacific coast of Tohoku earthquake. Rep. Coord. Committee Earthquake Prediction 90, 3–4 (2013)

  17. 17

    Watanabe, S. et al. Evidence of viscoelastic deformation following the 2011 Tohoku-oki earthquake revealed from seafloor geodetic observation. Geophys. Res. Lett. (in the press); preprint at http://onlinelibrary.wiley.com/doi/10.1002/2014GL061134/abstract

  18. 18

    DeMets, C., Gordon, R. G. & Argus, D. F. Geologically current plate motions. Geophys. J. Int. 181, 1–80 (2010)

    ADS  Article  Google Scholar 

  19. 19

    Hu, Y., Burgmann, R., Freymueller, J. F., Banerjee, P. & Wang, K. Contributions of poroelastic rebound and a weak volcanic arc to the postseismic deformation of the 2011 Tohoku earthquake. Earth Planets Space 66, 106 (2014)

    ADS  Article  Google Scholar 

  20. 20

    Sun, T. et al. Viscoelastic landward motion of the trench area following a subduction earthquake. Abstr. G14A–08 (Fall Meeting, AGU, San Francisco, 9–13 December, 2013); available at http://adsabs.harvard.edu/abs/2013AGUFM.G14A..08S

  21. 21

    Wada, I. & Wang, K. Common depth of decoupling between the subducting slab and mantle wedge: reconciling diversity and uniformity of subduction zones. Geochem. Geophys. Geosyst. 10, Q10009 (2009)

    ADS  Article  Google Scholar 

  22. 22

    Yamamoto, Y., Hino, R. & Shinohara, M. Mantle wedge structure in the Miyagi Prefecture forearc region, central northeastern Japan arc, and its relation to corner-flow pattern and interplate coupling. J. Geophys. Res. 116, B10310 (2011)

    ADS  Article  Google Scholar 

  23. 23

    Hu, Y. & Wang, K. Spherical-Earth finite element model of short-term postseismic deformation following the 2004 Sumatra earthquake. J. Geophys. Res. 117, B05404 (2012)

    ADS  Google Scholar 

  24. 24

    Peltier, W. R., Wu, P. & Yuen, D. A. in Anelasticity in the Earth (eds Stacey, F. D., Paterson, M. S. & Nicolas, A. ) 59–77 (Geodynamics Ser. Vol. 4, American Geophysical Union, 1981)

    Book  Google Scholar 

  25. 25

    Peltier, W. R. The impulse response of a Maxwell Earth. Rev. Geophys. Space Phys. 12, 649–668 (1974)

    ADS  Article  Google Scholar 

  26. 26

    Melosh, H. J. & Raefsky, A. A simple and efficient method for introducing faults into finite element computations. Bull. Seismol. Soc. Am. 71, 1391–1400 (1981)

    Google Scholar 

  27. 27

    Nakajima, J. & Hasegawa, A. Anomalous low-velocity zone and linear alignment of seismicity along it in the subducted Pacific slab beneath Kanto, Japan: reactivation of subducted fracture zone? Geophys. Res. Lett. 33, L16309 (2006)

    ADS  Article  Google Scholar 

  28. 28

    Kita, S., Okada, T., Hasegawa, A., Nakajima, J. & Matsuzawa, T. Anomalous deepening of a seismic belt in the upper-plane of the double seismic zone in the Pacific slab. Earth Planet. Sci. Lett. 290, 415–426 (2010)

    CAS  ADS  Article  Google Scholar 

  29. 29

    Zhao, D., Wang, Z., Umino, N. & Hasegawa, A. Mapping the mantle wedge and interplate thrust zone of the northeast Japan arc. Tectonophysics 467, 89–106 (2009)

    ADS  Article  Google Scholar 

  30. 30

    Wada, I., Rychert, C. A. & Wang, K. Sharp thermal transition in the forearc mantle wedge as a consequence of nonlinear mantle wedge flow. Geophys. Res. Lett. 38, L13308 (2011)

    ADS  Article  Google Scholar 

  31. 31

    Noda, H. & Shimamoto, T. Transient behavior and stability analyses of halite shear zones with an empirical rate-and-state friction to flow law. J. Struct. Geol. 38, 234–242 (2012)

    ADS  Article  Google Scholar 

  32. 32

    Kawakatsu, H. et al. Seismic evidence for sharp lithosphere-asthenosphere boundaries of oceanic plates. Science 324, 499–502 (2009)

    CAS  ADS  Article  Google Scholar 

  33. 33

    Rychert, C. A. & Shearer, P. M. A global view of the lithosphere-asthenosphere boundary. Science 324, 495–498 (2009)

    CAS  ADS  Article  Google Scholar 

  34. 34

    Fischer, K. M., Ford, H. A., Abt, D. L. & Rychert, C. A. The lithosphere-asthenosphere boundary. Annu. Rev. Earth Planet. Sci. 38, 551–575 (2010)

    CAS  ADS  Article  Google Scholar 

  35. 35

    Karato, S. On the origin of the asthenosphere. Earth Planet. Sci. Lett. 321–322, 95–103 (2012)

    ADS  Article  Google Scholar 

  36. 36

    Sakamaki, T. et al. Ponded melt at the boundary between the lithosphere and asthenosphere. Nature Geosci. 6, 1041–1044 (2013)

    CAS  ADS  Article  Google Scholar 

  37. 37

    Schmerr, N. The gutenberg discontinuity: melt at the lithosphere-asthenosphere boundary. Science 335, 1480–1483 (2012)

    CAS  ADS  Article  Google Scholar 

  38. 38

    Fulton, P. M. et al. Low coseismic friction on the Tohoku-oki fault determined from temperature measurements. Science 342, 1214–1217 (2013)

    CAS  ADS  Article  Google Scholar 

  39. 39

    Spiess, F. N. Suboceanic geodetic measurements. IEEE Trans. Geosci. Remote Sens. GE-23, 502–510 (1985)

    ADS  Article  Google Scholar 

  40. 40

    Fujimoto, H. Seafloor geodetic approaches to subduction thrust earthquakes. Monogr. Environ. Earth Planets 2, 23–63 (2014)

    ADS  Article  Google Scholar 

  41. 41

    Kido, M. et al. Seafloor displacement at Kumano-nada caused by the 2004 off Kii Pen-insula earthquakes, detected through repeated GPS/acoustic surveys. Earth Planets Space 58, 911–915 (2006)

    ADS  Article  Google Scholar 

  42. 42

    Sato, M. et al. Interplate coupling off northeastern Japan before the 2011 Tohoku-oki earthquake, inferred from seafloor geodetic data. J. Geophys. Res. 118, 3860–3869 (2013)

    ADS  Article  Google Scholar 

  43. 43

    Kido, M., Osada, Y. & Fujimoto, H. Temporal variation of sound speed in ocean: a comparison between GPS/acoustic and in situ measurements. Earth Planets Space 60, 229–234 (2008)

    ADS  Article  Google Scholar 

  44. 44

    Osada, Y. et al. Seafloor crustal movement observed off Miyagi after the 2011 Tohoku earthquake using GPS-acoustic observation system. Abstr. T13F-2693 (Fall Meeting, AGU, 2012); available at http://adsabs.harvard.edu/abs/2012AGUFM.T13F2693O

  45. 45

    Obana, K. et al. Aftershocks near the updip end of the 2011 Tohoku-Oki earthquake. Earth Planet. Sci. Lett. 382, 111–116 (2013)

    CAS  ADS  Article  Google Scholar 

  46. 46

    Kubota, T. et al. Source models of M-7 class earthquakes in the rupture area of the 2011 Tohoku-Oki earthquake by near-field tsunami modeling. Abstr. T13B-2594 (Fall Meeting, AGU, 2012); available at http://adsabs.harvard.edu/abs/2012AGUFM.T13B2594K

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Acknowledgements

We thank the Japan Coast Guard for making available digital values of published data. Comments from M. Sato improved the manuscript. K.W. was supported by Geological Survey of Canada core funding and a Natural Sciences and Engineering Research Council of Canada Discovery Grant through the University of Victoria. T.S. was supported by a University of Victoria PhD Fellowship and a Howard E. Petch Scholarship. The Tohoku University seafloor observation study was supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan under its Earthquake and Volcano Hazards Observation and Research Program. This is Geological Survey of Canada contribution 20140167.

Author information

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Authors

Contributions

T.S. carried out the numerical modelling. K.W. designed the study. K.W. and T.S. together did most of the writing. T.I. processed land GPS data. R.H., H.F., M.K., Y. Osada, S.M. and Y. Ohta collected and processed GJT3 seafloor GPS data. J.H. wrote the modelling code and contributed to the modelling. Y.H. constructed fault geometry and initiated the modelling.

Corresponding author

Correspondence to Kelin Wang.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Illustration of the Burgers rheology used in this work.

The Burgers rheology is represented by a serial connection of a Maxwell fluid of viscosity ηM and rigidity µM and a Kelvin solid of viscosity ηK and rigidity µK. τM and τK are Maxwell and Kelvin relaxation times, respectively.

Extended Data Figure 2 Central part of the finite element mesh for modelling deformation associated with the Tohoku-oki earthquake.

Darker layers represent elastic plates. The LAB layer is highlighted in yellow. Structural details are shown in Fig. 2c. GPS sites used to constrain the model in this work are shown in red. Elements near the trench are too fine to be discerned at this plotting scale and hence collectively appear as a blue region.

Extended Data Figure 3 Postseismic (1 year) deformation results of model B in Extended Data Table 1.

Otherwise the figure is the same as Fig. 1b. Time series at sites marked with a green circle are shown in Extended Data Fig. 4.

Extended Data Figure 4 East component of postseismic displacements of model B in Extended Data Table 1.

Otherwise the figure is the same as Fig. 3. Locations of the GPS sites are shown in Extended Data Fig. 3.

Extended Data Figure 5 Layout of PXPs (precision transponders) at seafloor GPS site GJT3.

Grey filled circles are PXPs installed for testing purposes9, not used in this work.

Extended Data Figure 6 Postseismic survey results for seafloor GPS site GJT3.

a, East component Dx. b, North component Dy. Open symbols for the first measurement show array position before the effect of the Mw 7.0 intraslab earthquake on 10 July 2011 was removed. Sub-array 1 includes PXP EJ12, EJ13 and EJ15, and sub-array 2 includes PXP EJ12, EJ13 and EJ22 (Extended Data Fig. 5). The straight solid and dashed lines show linear trends of survey results of sub-array 1 and sub-array 2, respectively, with resultant average velocities Vx and Vy for the east and north components, respectively. The red curves show a logarithmic function fit to the survey results.

Extended Data Table 1 3D model parameters

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Sun, T., Wang, K., Iinuma, T. et al. Prevalence of viscoelastic relaxation after the 2011 Tohoku-oki earthquake. Nature 514, 84–87 (2014). https://doi.org/10.1038/nature13778

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