Importance of rheological heterogeneity for interpreting viscoelastic relaxation caused by the 2011 Tohoku-Oki earthquake
© The Author(s) 2017
Received: 21 September 2016
Accepted: 24 January 2017
Published: 31 January 2017
KeywordsViscoelastic relaxation Postseismic deformation The 2011 Tohoku-Oki earthquake Rheological heterogeneity FEM
The Mw9.0 2011 off the Pacific coast of Tohoku Earthquake (hereafter, the 2011 Tohoku-Oki earthquake) was the largest earthquake ever recorded in Japan and triggered substantial and long-lived postseismic deformation. The transient surface deformation that accompanies postseismic stress redistribution can provide new insights into the rheology and mechanics of the lithosphere and asthenosphere. Postseismic deformation is commonly observed following large earthquakes and 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 mechanism or, at times, poroelastic rebound. It is commonly interpreted that the viscoelastic relaxation mechanism plays an important role only in long-term or far-field deformation. Viscoelastic relaxation and rheology estimated from analysis of geodetic data have been reported in studies of the postseismic deformation following inland earthquakes, such as the 1999 Izmit earthquake (Hearn et al. 2009), the 1999 Chi–Chi earthquake (Rousset et al. 2012), the 2002 Denali earthquake (Freed et al. 2006), and the 2004 Parkfield earthquake (Bruhat et al. 2011). In contrast, afterslip has been shown to be the dominant mechanism of postseismic deformation following major M7‒M8 class subduction earthquakes, such as those occurring in the Japan Trench (Heki et al. 1997; Miyazaki et al. 2004), and in the Middle America and Peru‒Chile Trenches (Graham et al. 2014; Remy et al. 2016). Combined afterslip and viscoelastic relaxation models were studied following M9 earthquakes that occurred in Chile (Hu et al. 2004), Alaska (Suito and Freymueller 2009), Sumatra (Broerse et al. 2015), and Maule (Klein et al. 2016).
Many researchers have studied the early postseismic deformation following the 2011 Tohoku-Oki earthquake. For example, Ozawa et al. (2012) argued that afterslip was the dominant mechanism; Diao et al. (2014) and Han et al. (2014) examined the combined effects of afterslip and viscoelastic relaxation; Hu et al. (2014) explored the effect of poroelastic rebound; and several authors showed that viscoelastic relaxation plays an important role even in short-term deformation (Sun et al. 2014; Sun and Wang 2015; Hu et al. 2016a). The most important results from these studies are those obtained using seafloor geodetic observation (SGO) (Watanabe et al. 2014; Tomita et al. 2015). In comparison with the onshore Global Navigation Satellite Systems (GNSS) sites, which move seaward in the same direction as the coseismic motion, the SGO 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 (e.g., Sun and Wang 2015; Yamagiwa et al. 2015; Hu et al. 2016a). 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 postseismic deformation following the 2011 Tohoku-Oki earthquake, this study implements a three-dimensional viscoelastic model using the finite element method (FEM). The question of which elements of the viscoelastic media affect the surface deformation is of particular importance. The individual effects of two viscoelastic media, the mantle wedge and the oceanic mantle, are shown to contribute differently to the surface deformation. In addition, the deformation characteristics of viscoelastic relaxation based on four typical models are briefly summarized, and measurements of postseismic subsidence and landward motion on the seafloor are shown to be highly sensitive to viscoelastic structure, particularly to the inclusion of a thin weak layer beneath the subducting plate. Near-field data as well as far-field data, recorded ~500 km from the rupture area, are both important for constraining viscoelastic structure. It should be noted that the purpose of this paper is not to construct a final postseismic deformation model; rather, the objective is to discuss the importance of rheological heterogeneity for interpreting postseismic deformation at subduction zones. Only the cumulative deformation is summarized; the temporal variation is not discussed in this paper.
Characteristics of postseismic deformation
Onshore GNSS sites show deformation of up to approximately 120 and 50 cm in the horizontal and vertical directions, respectively, for 5 years after the main shock. It should be noted that coseismic offsets due to aftershocks are included at some sites. Each effect ranges between a few centimeters and several centimeters at the maximum, except for the 2011 Fukushima Hamadori and the 2014 Nagano‒Hokubu earthquakes. All sites move approximately eastward (seaward) in the direction of the coseismic motion. The displacement direction is somewhat different in the southern part of the Kanto district, where the orientation is toward the SE, although eastward displacements are dominant in the surrounding areas.
Vertical deformation is more complex than horizontal deformation. The area of coseismic subsidence is now undergoing uplift, except in the northern part of the Tohoku district, with the largest uplift reaching 50 cm at the tip of the Oshika Peninsula. Inland and along the Japan Sea coast, the cumulative subsidence is up to 10 cm, with significantly larger subsidence observed in the Ou Backbone area. In the northern part of the Tohoku district, the cumulative subsidence is approximately 5 cm. However, uplift in this area began 1 year after the earthquake (Fig. 1c). A cumulative uplift of ~10 cm is also observed in the Kanto, Chubu, and southern Hokkaido districts. It should be noted that uplift is also observed on Sado Island and in the north Tohoku district, although these regions are located on the Japan Sea coast.
The cumulative seafloor displacements used in this paper were compiled from Watanabe et al. (2014) with slight modifications. The displacement pattern is significantly different to the results obtained from onshore GNSS data, as mentioned previously. There is a strong along-trench gradient in amount and direction from nearly zero displacement at KAMN station, to tens of centimeters westward (landward) at KAMS and MYGI stations, and 50‒70 cm eastward (seaward) at FUKU and CHOS stations. Although the MYGI station moves westward, the MYGW station, which is located 20 km west of MYGI, moves 20 cm in a SSE direction. All sites except for the FUKU and CHOS stations, which are located in the southern part of the focal area, moved in a different direction to the coseismic motion. In addition, all of the SGO sites, except for CHOS, revealed subsidence of approximately 20‒50 cm, whereas a large uplift is observed onshore along the Pacific coast.
Figure 1b shows the principal strain axes and dilatation for 5 years after the main shock. The strain calculation from the displacement vectors shown in Fig. 1a (onshore GNSS data only) is based on the method developed by Shen et al. (1996). Extensional strain is observed across the entire northeast Japan region, except for the area around the Oshika Peninsula on the Pacific coast, which is characterized by contractional strain. The dominant principal strain axes are E‒W extension in the extensional area and E‒W contraction in the contractional area. N‒S contraction is also observed within the extensional area in the central part of the Tohoku district.
FEM model description
Results and discussion
Viscoelastic relaxation of mantle wedge and oceanic mantle
Viscoelastic relaxation of the mantle wedge produces eastward (seaward) motion across the entire area, uplift of the onshore Pacific coastal region and offshore area, and minor subsidence of the Japan Sea coastal region (Fig. 4b). Extension across a broad area of northeast Japan and contraction across the onshore Pacific coastal region and the offshore area are also produced by the mantle wedge relaxation (Fig. 4c). The dominant principal strain axes are E‒W extension in the Tohoku district and E‒W contraction in the offshore area. N‒S contraction is also produced in the central part of the Tohoku district.
In contrast, viscoelastic relaxation of the oceanic mantle produces an almost opposite deformation pattern to that of the mantle wedge, characterized by westward (landward) motion across the entire area, subsidence in the Tohoku district and offshore area, and uplift in the southern Hokkaido, Kanto, and Chubu districts and in the area beyond the trench (Fig. 4e). Contraction across the Tohoku district and offshore area, with minor extension across the surrounding area, and extension in the area beyond the trench are also produced by the oceanic mantle relaxation (Fig. 4f). The dominant principal strain axes are E‒W contraction in the offshore area and in a limited area along the Pacific coast in the central Tohoku district.
Viscoelastic relaxation according to four typical models
Assuming the same viscosity, 2 × 1018 Pa s, for all viscoelastic media (Model 1), the mantle wedge and oceanic mantle relaxations affect the horizontal surface deformation equally (Fig. 5a), causing eastward motion onshore and westward motion on the seafloor (Fig. 4b, e). Regarding the vertical surface deformation, subsidence was dominant across the entire Tohoku district and was controlled mainly by relaxation in the oceanic mantle (Fig. 4e). This model can explain the observed horizontal deformation, although it cannot explain the vertical deformation characteristics. The main problem with this model is the assumption of the same viscosity for all viscoelastic media. Previous studies of viscoelastic relaxation at subduction zones have reported that the difference in viscosity between the mantle wedge and the oceanic mantle significantly affects the surface deformation (Hu et al. 2004; Wang 2007). In addition, these two media contribute differently to the surface deformation, as mentioned in the previous subsection. Moreover, DeMets et al. (2014) recently reported that the viscosity of the asthenosphere below the oceanic plate is greater than 1 × 1019 Pa s. Since we considered that the viscosity of the oceanic mantle is higher than that of the mantle wedge, we used a viscosity value for the oceanic mantle of at least 1 × 1019 Pa s. On the basis of Model 1 and the results of the previous studies, we next designed Model 2, which assumes different viscosities between the mantle wedge, set at 2 × 1018 Pa s, and the oceanic mantle, set at 1 × 1019 Pa s.
In the case of different viscosities between the mantle wedge and the oceanic mantle (Model 2), the mantle wedge relaxation dominates in both the horizontal and vertical displacements (Fig. 5b). This medium controls the dominantly onshore eastward motion and uplift of the Pacific coast and seafloor (Fig. 4b). This model can explain the onshore observations, but it fails to explain the seafloor observations, which is the most inadequate feature of the model. In order to address this problem, we incorporated a thin weak layer (LAB) below the subducting Pacific plate. The LAB is a mechanical decoupling of the oceanic lithosphere from the underlying mantle material, as reported in previous seismic velocity studies (e.g., Kawakatsu et al. 2009; Fischer et al. 2010). The origin of the LAB remains uncertain and may be due to the presence of either partial melt (Kawakatsu et al. 2009; Hirschmann 2010) or fluids (Karato and Jung 1998). A thin weak layer with low viscosity was introduced below the elastic plate to approximate this effect. Recent viscoelastic modeling studies have also incorporated this weak layer (Sun et al. 2014; Hu et al. 2016a). Our third tentative model consists of three viscoelastic media: the mantle wedge, with a viscosity of 2 × 1018 Pa s; the oceanic mantle, with a viscosity of 1 × 1019 Pa s; and the LAB, with a viscosity of 1 × 1018 Pa s.
To complement the previous three models, we next considered the depth-dependent viscosity model. We conducted the computation using differential viscosities with a depth interval of 40 km. The viscosities ranged from 1 × 1018–1 × 1019 Pa s in the mantle wedge, 5 × 1017–1 × 1019 Pa s for the LAB, and 1 × 1019–1 × 1020 Pa s in the oceanic mantle. We then determined the optimum depth-dependent viscosity model (Model 4), which was constrained by the observed deformation characteristics summarized in “Characteristics of postseismic deformation” section. Of these, the key observations are the far-field displacement direction in the Chubu district, and the uplift on Sado Island and in the northern Tohoku district. Figure 5d shows the results of Model 4. The general features are similar to Model 3; however, the horizontal displacement direction in the Chubu district was somewhat improved (Fig. 6a, b). We consider that this model best fits the observed data, reproducing the key characteristics of the cumulative 5-year horizontal and vertical displacements and strain field (Fig. 1). In the following subsection, we compare this model to the data and discuss its varied results upon changing the viscosity, as well as the reasons for selecting Model 4 as the optimal model.
Viscoelastic relaxation according to the optimal model
Viscoelastic uplift was predicted over most of the coseismic subsidence area (Fig. 7a). The predicted area of subsidence is focused at the large slip zones on the seafloor and is also found in the Japan Sea coastal region. In northern Iwate prefecture, the predicted deformation resulting from viscoelastic relaxation alone is uplift, although the observed cumulative deformation is subsidence (Fig. 1a). Temporal variation occurs in this area. The area first subsided 1 year after the earthquake and subsequently began to uplift (Fig. 1c), as described in “Characteristics of postseismic deformation” section. Therefore, the uplift observed in this area is controlled by viscoelastic relaxation (Fig. 1c), whereas the subsidence first observed after 1 year was likely controlled by afterslip. It should be noted that the spatial pattern of the predicted vertical deformation is more sensitive than that of the horizontal deformation. In particular, the uplift or subsidence pattern in the Japan Sea coastal region and offshore area changed dramatically with viscosity. The predicted subsidence of the offshore area decreased as the viscosity of the oceanic mantle increased. In this case, the uplift on Sado Island and in the northern Tohoku district along the Japan Sea coast also decreased. In contrast, when the viscosity in the mantle wedge was reduced, the predicted subsidence in the offshore area increased, and the uplift along the Japan Sea coast also increased. Therefore, the ratio of the viscosity between the mantle wedge and the oceanic mantle has an important influence on the uplift and subsidence patterns.
Viscoelastic relaxation produces extension across the entire Tohoku district, except for the Pacific coastal region (Fig. 7b). Contraction is produced along the Pacific coast and offshore. The dominant principal strain axes are E‒W extension in the extensional area and E‒W contraction in the contractional area. N‒S contraction is also produced within the extensional area in the central Tohoku district. The large area of extension is produced mainly by mantle wedge relaxation (Fig. 4c). In contrast, the area of contraction along the Pacific coast and offshore is produced by a combination of mantle wedge and oceanic mantle relaxation (Fig. 4c, f). The viscoelastic-only model generally explained the essential characteristics of the observed strain field. However, the extensional strain was somewhat small in the north Tohoku and Kanto districts; as similarly observed for the horizontal displacement field. Therefore, large residual extensional strain is concentrated in the northern and southern areas of the Tohoku and Kanto districts (Fig. 7d).
Clearly, viscoelastic relaxation alone cannot completely explain the observations, particularly in the northern and southern areas of the Tohoku and Kanto districts. The amounts of predicted displacement and extensional strain in these areas were small compared to the observations. Changing the viscosity can explain the residuals in these areas. In such a case, however, the predicted deformation is overestimated in other areas. Substantial viscoelastic flow was produced in the zones of high coseismic slip, which resulted in viscoelastic relaxation becoming the dominant mechanism in the neighboring areas. In contrast, viscoelastic relaxation was small in the zones of relatively low coseismic slip, which corresponds to the northern and southern Tohoku and Kanto districts. Afterslip is likely generated and plays an important role in this area.
Assessment of viscoelastic structure
The viscosity of the upper mantle wedge in northeast Japan was estimated from geodetic data obtained several years to decades after the occurrence of inland earthquakes such as the 1896 Riku-u earthquake (Suito and Hirahara 1999) and the 2008 Iwate–Miyagi Nairiku earthquake (Ohzono et al. 2012), as well as the 1993 Hokkaido–Nansei–Oki thrust earthquake on the eastern margin of the Japan Sea (Ueda et al. 2003). The postseismic signals following these events were explained using Maxwell rheology with a viscosity range of 2.4‒9.3 × 1018 Pa s. Recent viscoelastic modeling studies of the 2011 Tohoku-Oki earthquake use Burgers rheology (Sun et al. 2014; Hu et al. 2016a); therefore, direct comparison may be difficult. The estimated viscosities of the Maxwell part are 1.8 × 1018 Pa s (Sun et al. 2014) and 3 × 1019 Pa s (Hu et al. 2016a). The mantle wedge viscosity of 2 × 1018 Pa s in this study is consistent with these previous estimates, except for that of Hu et al. (2016a). However, a lower viscosity zone, with a viscosity of 1 × 1018 Pa s, is assumed at a depth of 25–100 km in the mantle wedge in the total effects model of Hu et al. (2016a). The viscosity of the oceanic mantle is generally found to be an order of magnitude higher than that of the mantle wedge (e.g., Hirth and Kohlstedt 2003). The oceanic mantle viscosity of 1 × 1019 Pa s in this study, which is higher than that of the mantle wedge, is consistent with these rock rheological studies. We introduced a thin weak layer with low viscosity below the subducting plate to approximate the LAB. Hu et al. (2016a) suggested that the viscosity of this weak layer, at least 1 × 1018 Pa s, is sufficient to produce landward motion, although they assumed the thickness of the weak zone to be 80 km. Our estimated viscosity is consistent with their results, although our model assumed the thickness of the weak layer to be 20 km.
Depth-dependent viscosity typically originates from the temperature, pressure, and water content dependences of rock rheology (e.g., Hirth and Kohlstedt 2003). Considering this dependences, the minimum viscosity value may occur at a depth of around 100–200 km in the mantle wedge under hot and wet conditions (e.g., Karato and Jung 2003). The depth-dependent viscosity structure in this study contained the lowest viscosity at a depth of 150–300 km, which is consistent with these rock rheological estimates. Although we also attempted to estimate the depth-dependent viscosity in the oceanic mantle, the depth dependence was not resolvable. Therefore, the optimum viscosity of 1 × 1019 Pa s for the oceanic mantle was selected as the result. One of the best locations for studying oceanic mantle rheology is the Indian Ocean, where a large Mw8.6 earthquake occurred in 2012 (e.g., Meng et al. 2012). Two recently published papers regarding oceanic mantle rheology analyze the postseismic deformation following the 2012 Indian Ocean earthquake (Hu et al. 2016b; Masuti et al. 2016).
Small-scale rheological heterogeneities across the arc, such as a weak volcanic front and a strong forearc, contribute to local deformation, as reported by Muto et al. (2016); however, their modeling is based on a 2D profile. On close examination of the residuals of displacement in our model (Fig. 7c), the subsidence along the volcanic front in the central Tohoku district may reflect this effect. This type of small-scale heterogeneity should be incorporated into a more precise estimate of the viscoelastic effect in future modeling studies.
In order to complement previous modeling efforts and to understand the postseismic deformation following the 2011 Tohoku-Oki earthquake, we implemented a 3D viscoelastic model using FEM. The question of which elements of the viscoelastic media affect the surface deformation is of particular importance.
We first examined the individual effects of two viscoelastic media: the mantle wedge and the oceanic mantle including the LAB. These two media produced almost opposite deformation patterns. Mantle wedge relaxation controls dominantly onshore eastward (seaward) motion, uplift offshore and along the Pacific coast, and extension across a broad area. We noted that N‒S contraction observed in the central Tohoku district is produced only by mantle wedge relaxation. In contrast, oceanic mantle relaxation controls dominantly offshore westward (landward) motion, as well as subsidence across a broad area, minor uplift in the Kanto, Chubu, and Hokkaido districts, and contraction offshore and along the Pacific coast. The difference between the viscoelastic effects resulting from these two media is the most important issue for understanding viscoelastic relaxation caused by subduction earthquakes.
Next, we used four typical models to clarify which elements of the viscoelastic media affect the observed surface deformation. Of particular importance was the consideration of different viscosities between the mantle wedge and the oceanic mantle, and the inclusion of a thin weak layer (LAB), which has a dramatic impact on seafloor deformation. The simplest model, with uniform viscosity for all viscoelastic media (Model 1), was able to explain the observed horizontal deformation but not the vertical deformation. The second model, with different viscosities between the mantle wedge and oceanic mantle (Model 2), explained the observations onshore but not those on the seafloor. In order to improve the modeled seafloor deformation, we incorporated a thin weak layer (LAB) below the subducting Pacific plate. This third model, with different viscosities for the three viscoelastic media (Model 3), was able to essentially explain the important characteristics observed in the near-field data. However, for the far-field data (~500 km), the direction of the computed horizontal displacement was somewhat different from the observations. Finally, we developed a depth-dependent model, which explained the far-field data as well as the near-field data. This optimal model reproduced the horizontal displacement and strain field fairly well in the central part of the Tohoku district, and to some degree in the northern and southern areas of the district. Therefore, large residuals of eastward displacement are concentrated in these areas.
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. In order to construct a complete postseismic deformation model of the 2011 Tohoku-Oki earthquake, it is necessary to estimate the afterslip distribution after removing the viscoelastic effect and to consider the temporal changes in the deformation in future studies.
Global Navigation Satellite System
seafloor geodetic observation
finite element method
We used Generic Mapping Tools (Wessel and Smith 1998) to create the figures. Careful reviews and constructive comments from two reviewers, Dr. Jun Muto and Dr. Sylvain Barbot, were very helpful in revising the manuscript.
The author declares that he has no competing interests.
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