Importance of rheological heterogeneity for interpreting viscoelastic relaxation at a subduction earthquake

Guest post by Hisashi Suito

Postseismic deformation is commonly observed following large earthquake. This postseismic deformation is thought to be caused by three mechanisms: afterslip, viscoelastic relaxation, and poroelastic rebound. Short-term deformation near the rupture zone is considered to be caused mainly by the afterslip or, at times, poroelastic rebound. It is commonly interpreted that the viscoelastic relaxation plays an important role only in long-term or far-field deformation.

Many researchers have studied the early postseismic deformation following the 2011 Tohoku-Oki earthquake. There are dense GNSS array onshore and a several Seafloor Geodetic Observation sites offshore in and around the Japan Trench. Among them, the seafloor deformation is the most important data. In comparison with the onshore GNSS sites, which move seaward in the same direction as the coseismic motion, the seafloor sites move landward in the opposite direction. Sun et al. (2014) explained this landward deformation as an effect of viscoelastic relaxation, stressing that viscoelastic relaxation plays an important role even in short-term deformation. Subsequent studies have also identified viscoelastic relaxation as an important mechanism when interpreting postseismic deformation.

However, despite the importance of viscoelastic relaxation, it is unclear which elements of the viscoelastic media affect the observed surface deformation. In order to complement previous modeling efforts and to understand the process of viscoelastic relaxation, Suito (2017) developed a three dimensional viscoelastic model of the 2011 Tohoku-Oki earthquake and clarified which elements of the viscoelastic media affect the observed surface deformation.

Firstly, the individual effect of two different viscoelastic media, the mantle wedge and the oceanic mantle (Fig. 1) is examined. The mantle wedge relaxation controls dominantly onshore eastward motion, and uplift of the Pacific coastal and offshore regions (Fig. 1a). In contrast, the oceanic mantle controls dominantly offshore westward motion, subsidence across a broad area, and minor uplift of the surrounding areas (Fig. 1b). In a word, these two media produce almost opposite deformation patterns. These differences are the most important issues for understanding the viscoelastic relaxation caused by subduction earthquakes.

Fig. 1 Computed displacements cumulative for 5 years, due to viscoelastic relaxation. a) the mantle wedge only. b) the oceanic mantle only. Black arrows and contoured color map represent the horizontal and vertical displacements, respectively. (Bottom) Conceptual representations of the viscoelastic structure; the colored areas represent the viscoelastic media. η is the viscosity.
Fig. 1 Computed displacements cumulative for 5 years, due to viscoelastic relaxation. a) the mantle wedge only. b) the oceanic mantle only. Black arrows and contoured color map represent the horizontal and vertical displacements, respectively. (Bottom) Conceptual representations of the viscoelastic structure; the colored areas represent the viscoelastic media. η is the viscosity.

Then, four different models are developed to clarify which elements of the viscoelastic media affect the observed surface deformation (Fig. 2). The simplest model, with uniform viscosity for all viscoelastic media (Fig. 2a), could explain the horizontal deformation but not the vertical deformation. The second model, with different viscosities for the mantle wedge and the oceanic mantle (Fig. 2b), could explain the onshore observations but could not explain the seafloor observations. The third model, which includes a thin weak layer beneath the subducting slab (Fig. 2c), could essentially explain the near-field onshore and seafloor observations but could not explain the far-field data. The final depth-dependent model (Fig. 2d) was able to explain the far-field data as well as the near-field data.

Fig. 2 Computed displacements, cumulative for 5 years, due to viscoelastic relaxation. a) Model 1. b) Model 2. c) Model 3. d) Model 4. The symbols are same as Figure 1.
Fig. 2 Computed displacements, cumulative for 5 years, due to viscoelastic relaxation. a) Model 1. b) Model 2. c) Model 3. d) Model 4. The symbols are same as Figure 1.

In these typical models, it is of particular importance to consider the different viscosities between the mantle wedge and the oceanic mantle, and to include a thin weak layer beneath the slab, which has a dramatic impact on the seafloor deformation. Far-field data as well as near-field data are also important for constraining the viscoelastic structure; the former is sensitive to viscoelastic relaxation at greater depths.

It is clear that viscoelastic relaxation alone cannot explain the observations. Substantial viscoelastic flow is produced in areas of very high coseismic slip. Therefore, viscoelastic relaxation plays an important role in neighboring areas, where it is the dominant deformation mechanism. In contrast, viscoelastic relaxation is minor in areas of relatively low coseismic slip. Afterslip is likely generated and plays an important role in these areas. A combined viscoelastic and afterslip model is necessary for constructing a complete postseismic deformation model.

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