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Prevalence of viscoelastic relaxation after the 2011 Tohoku-oki earthquake


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.


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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.

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Authors and Affiliations



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).

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