A megathrust earthquake cycle model for Northeast Japan: bridging the mismatch between geological uplift and geodetic subsidence
© The Author(s) 2017
Received: 7 September 2016
Accepted: 20 January 2017
Published: 31 January 2017
KeywordsEarthquake cycle Vertical deformation Dislocation theory Viscoelasticity Northeast Japan The 2011 Tohoku earthquake
The Northeast (NE) Japan arc is a typical island arc formed by the subduction of the Pacific plate under the Eurasian plate. It was thought that the maximum magnitude for interplate earthquakes would be M8 based on modern earthquake observation (Yamanaka and Kikuchi 2004), until the M9 2011 Tohoku earthquake occurred. This megathrust rupture reached to the trench with a maximum slip of 50 m (e.g., Yagi and Fukahata 2011) and resulted in a devastating tsunami. Studies of older tsunami deposits suggest a recurrence interval for megathrust earthquakes of 500–800 years (Sawai et al. 2012, 2015). Given that we can now expect the recurrence of an earthquake with magnitude greater than M8, we should explore the tectonic implications in NE Japan of M9-class earthquake cycles.
The mismatch between long-term (geological) and short-term (geodetic) estimates of vertical deformation on the Pacific coast of NE Japan had already been recognized before the M9 earthquake (Ikeda 2003; Tajikara 2004; Matsu’ura et al. 2008, 2009). Marine terraces with the height up to 50 m formed during the last interglacial period (Stage 5e) show average uplift rate of 0.2–0.4 mm/year over NE Japan (Koike and Machida 2001), while leveling observations from the late nineteenth century showed subsidence of 3–6 mm/year (Dambara 1971; Kunimi et al. 2001). Ikeda (2003) pointed out the possibility of occurrence of a megathrust earthquake, which he assumed to cause uplift to cancel out late-interseismic subsidence and restore a long-term balance. In fact, additional subsidence of up to 1.2 m occurred during the 2011 Tohoku earthquake (Nishimura et al. 2011). We now have to reconcile the mismatch between long-term uplift and late-interseismic and coseismic subsidence.
In the 5 years since the earthquake, postseismic vertical rebound of up to ~40 cm has been measured on the Pacific coast which appears to recover the amount of coseismic subsidence in ~100 years, based on prediction of a functional fitting analysis of the time series of postseismic deformation (Nishimura 2014). In order to explain the late-interseismic subsidence using an elastic dislocation model, Ikeda (2014) and Nishimura (2014) had to assume interseismic locking down to a depth of 100 km, where high shear stress is unlikely to be accumulated because of high temperature.
We attempt to reconcile the apparent mismatch by considering the change in vertical movement through an entire megathrust earthquake cycle, with particular attention to the effect of viscoelastic relaxation in the asthenosphere over time given a more than 500-year recurrence interval. Savage and Prescott (1978) first proposed an earthquake cycle model with the concept of dislocation for strike-slip earthquakes. Matsu’ura and Sato (1989) and Sato and Matsu’ura (1988) applied this model to subduction zones, showing that long-term deformation in subduction zones develops over repeated earthquake cycles. An important feature of the model is to prescribe slip motion on the plate interfaces as an input source, which may be accurately determined from modern seismological and geodetic observations. Hashimoto et al. (2004) showed that this method can well reproduce the deformation fields around Japan due to plate subduction. Sato and Matsu’ura (1993) extended the model to include the effect of stress relaxation in the lithosphere for long-lasting subduction (typically longer than 107 years) and the effect of tectonic accretion/erosion. Hashimoto et al. (2008) applied the extended model to long-term deformation in NE Japan. Focusing on late-interseismic and coseismic subsidence in NE Japan, Sagiya (2015) proposed a two-fault system with different recurrence intervals, based on the model of Matsu’ura and Sato (1989). Although the deep part of the fault was incorporated to account for the effect of observed M7-class earthquakes on vertical movement, the modeled fault area was about five times overestimated compared to the historical ~M7 earthquakes. In fact, observed onland displacements for the recent M7-class earthquakes vary spatially (Suito et al. 2011). The Sagiya (2015) result might not represent the regional deformation pattern.
In this study, we apply the earthquake cycle model accounting for the effects of viscoelastic relaxation and tectonic erosion developed by Matsu’ura and Sato (1989), Sato and Matsu’ura (1993), and Hashimoto et al. (2008) to the megathrust earthquake cycle of the NE Japan arc. Our goal is to understand the essential mechanism of the mismatch with a simple model consistent through different periods and not to fit calculation to the observation in detail.
Pacific plate motion for the past 42 My can be determined based on the trajectory of the Hawaiian-Emperor seamount chain (e.g., Sharp and Clague 2006). Around Japan, the current plate configuration was established around 15 Ma, when the opening of the Sea of Japan ended (Otofuji et al. 1985; Baba et al. 2007).
Sato (1994) synthesized the history of tectonic stress in NE Japan based on regional geology and determined that the stress regime was neutral or weakly extensional perpendicular to the trench immediately following the opening of the Sea of Japan. Around 3.5 Ma, the stress regime changed to strong compression. DSDP drilling and seismic reflection studies conducted offshore to the east in the area of the Japan Trench show a widely traceable submarine unconformity which is thought to have formed by subaerial erosion during the Paleogene after which the forearc subsided again (Nasu et al. 1980; von Huene et al. 1982). To explain this broad subsidence, von Huene and Lallemand (1990) proposed basal erosion of the overriding plate and estimated landward retreat of the overriding plate due to tectonic erosion by 3 km/My.
Earthquake cycle model with dislocations
The mechanical effect of tectonic erosion/accretion can be simply expressed by the advective term due to the landward/seaward migration of the plate boundary as the material removed from (or added to) the upper plate (Sato and Matsu’ura 1993; Hashimoto et al. 2008). For simplicity, we assume uniform erosion rate over the base of the upper plate shallower than the lithosphere–asthenosphere boundary. The migration rate v e is assumed to be 3 mm/year (von Huene and Lallemand 1990) and the duration of tectonic erosion T e is set at 3.5 My, considering the duration of the present compressive stress regime (Sato 1994). Assuming the viscosity of the lithosphere and asthenosphere to be 1023–1024 and 1018–1019 Pa s, respectively, the effective stress relaxation time of the lithosphere T L and asthenosphere T A become 107 years and 102 years, respectively (Sato and Matsu’ura 1993). Following Hashimoto et al. (2008), we applied the formulation for tectonic erosion, which assumes T A ≪ T e ≪ T L , and T L ≪ T S , where T S denotes the duration of steady subduction. This assumption corresponds to “moderate-aged subduction” in Hashimoto et al. (2008), where response to the steady tectonic erosion of a two-layered viscoelastic lithosphere–asthenosphere system can be approximated by the response of elastic lithosphere overlying the completely relaxed (t → ∞ limit) asthenosphere. In fact, T e , T L , and T S differ by factors, so the real effect of tectonic erosion may decay to some degree by viscous relaxation in the lithosphere. Still, main features can be expressed in this formulation.
Material parameters used in numerical simulations
We show results of our calculations for two cases, Case 1: d = H = 35 km, where the megathrust earthquake cuts completely through the lithosphere, Case 2: d = 25 km, H = 35 km, where the megathrust rupture stops in the lithosphere, while its unruptured lower end continues to slip steadily. In both cases, η a = 1019 Pa s.
Figure 3e, f shows temporal change in the effects of the viscoelastic response to past great earthquakes compared with the interseismic locking effect. Locking and viscoelastic effects are calculated by separately evaluating the second and third terms of the right-hand side of Eq. (1), respectively. Note that the vertical scale is different between Fig. 3e, f, but the locking effect (dashed line) is the same for both panels. The effect of the viscoelastic response is to compensate for the coseismic gravitational perturbations and to propagate deformation to greater distance (e.g., Fukahata and Matsu’ura 2006). The persistent uplift observed on land over time is due to the viscoelastic effect where the initial uplift offshore caused by rebound of coseismic subsidence migrates landward. In contrast, the locking effect causes strong compression. It creates uplift offshore, but little deformation on land.
Figure 4e, f shows the locking and viscoelastic effects. We see that both effects work differently from their counterparts in Fig. 3. If the rupture stops within lithosphere, stress in the vicinity of the lower edge of the rupture is not relaxed within an earthquake cycle. Deformation related to viscoelastic relaxation is dominantly expressed as downward flexure of the plate in the offshore region, with a related small uplift on land. For Case 2, the magnitude of the viscoelastic effect is around 30 mm/year in the first 100 years, but drops to ~5 mm/year at 500 years. The locking effect on land is constant in time at −10 mm/year (subsidence). Thus, we see that locking and viscoelastic responses are successively dominant effects; viscoelastic uplift dominates at the beginning of the earthquake cycle, and subsidence due to locking becomes more important later. The existence of a steady slip area below Σ P within the lithosphere is important; compared to Case 1 it amplifies both offshore uplift and land subsidence for the locking profile due to compression (dashed line).
Discussion and conclusions
We tackled the problem of a mismatch between long-term uplift versus late-interseismic/coseismic subsidence associated with the 2011 Tohoku earthquake in NE Japan, using a simple and consistent earthquake cycle model accounting for the effects of viscoelastic relaxation and tectonic erosion (Matsu’ura and Sato 1989; Sato and Matsu’ura 1993; Hashimoto et al. 2008). The model behaves differently in the case of a megathrust that ruptures completely through the lithosphere (Case 1) and a rupture that stops within the lithosphere (Case 2). Case 2 can account for the uplift/subsidence mismatch. In this case, the viscoelastic response to the megathrust earthquake compensates for late-interseismic/coseismic subsidence in the early interseismic stage. The locking effect successively governs the late-interseismic stage and causes the late-interseismic subsidence on land assisted by the steady slip below the rupture area. Tectonic erosion partly explains the long-term uplift by landward movement of arc topography. Elastic half-space models (Ikeda 2014; Nishimura 2014) require locking at asthenospheric depths to fit the late-interseismic data, while our viscoelastic model does not.
This study neglects the effect of high viscosity of the Pacific slab. A strong-slab effect was investigated by Miyashita (1983), Pollitz et al. (2008), and Tanaka et al. (2009) for postseismic adjustment and by Shikakura (2008) for relaxed state. Focusing on the onland effect, these strong-slab models show that the addition of a slab does not change the spatial pattern of vertical deformation. Thus, the uplift/subsidence mismatch observed on the land remains the same for models with and without the slab, though it could change the rate of displacement by several tens of a percent (Pollitz et al. 2008).
Among discrepancies between the calculated and observed deformation patterns, the discrepancy in the late-interseismic pattern is the most interesting: The calculated pattern shows overall land subsidence (Fig. 4d), while uplift is observed in the western half of the land area (Fig. 1b). It is difficult to fit this late-interseismic western uplift in the parameter space (H, d, η a , and v e ), keeping consistency with the coseismic and long-term constraints (Fig. 5). One interpretation might be that the western uplift reflects rapid shortening along the western coast (Sato 1989; Okada and Ikeda 2012). Also, lithospheric thinning due to the high temperature beneath volcanoes would be important, which could cause stress concentration and localized deformation (Shibazaki et al. 2008, 2016; Muto et al. 2016).
The calculated permanent uplift rate (~0.08 mm/year for v e = 3 mm/year) is somewhat smaller than the observed (0.2–0.4 mm/year, Fig. 1a). Considering the uncertainty of v e or T e (duration of tectonic erosion), this effect can explain about half of the observed data. As Hashimoto et al. (2008) discussed, this shortfall may be due to indirect effects such as crustal thickening due to horizontal shortening and possible magmatic underplating, which expectedly causes uplift (e.g., Tajikara 2004; Ikeda 2014). Another possibility might be plastic deformation within the lithosphere during the interseismic stage that accumulates over multiple earthquake cycles (van Dinther et al. 2013).
As shown in Fig. 4, evolution of deformation in the offshore is much different from that in the onshore. Offshore observations obtained by both geodetic and geological methods could be important constraints on our earthquake cycle model.
For simplification, this model does not account for afterslip. Since postseismic adjustments that occur in the several years after the megathrust earthquake are governed by both viscoelastic relaxation and afterslip (e.g., Lubis et al. 2013; Yamagiwa et al. 2015; Freed et al. 2017), our analysis cannot accurately model early postseismic deformation.
- NE Japan:
AH performed the computations and prepared the manuscript. TS contributed to the interpretation of the results. All authors contributed to the analysis and writing of the manuscript. All authors read and approved the final manuscript.
We would like to thank Editor Masato Furuya and two anonymous reviewers. We are grateful to Anne D. Van Horne for her constructive comments and grammatical correction. Yumi Amemiya digitized the Quaternary uplift data in NE Japan. Takuya Nishimura kindly provided us the leveling data. We thank the Geospatial Information Authority of Japan for providing GEONET data. This study was supported by the Special Project for Reducing Vulnerability for Urban Mega-earthquake Disasters and the Integrated Research Project on Seismic and Tsunami hazards around the Sea of Japan. Figures were prepared with the use of Generic Mapping Tool (Wessel and Smith 1998).
The authors declare that they have no competing interests.
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