Dynamic Overshoot Near Trench Caused by Large Asperity Break at Depth
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In an attempt to explain the large shallow slip that occurred near the trench during the 2011 Tohoku-Oki earthquake, numerical simulations of earthquake dynamic rupture were carried out using a fault model with a subduction interface containing a bump-shaped asperity, which might result from subduction of an old submarine volcano or seamount. It was assumed that during the interseismic period, slip only occurs outside the bump area and that stress accumulates inside the bump, creating a seismogenic asperity. We roughly evaluated the amount of slip outside the bump during the interseismic period, assuming a constant long-term subduction rate. Then we could estimate the accumulated stress inside the bump. We constructed the initial stress distribution based on the stress change caused by the slip-deficit distribution. A constitutive relation was constructed based on a slip-weakening friction law and was used to compute spontaneous ruptures. The results indicate that a large slip can occur between the trench and the bump, even though a very small amount of stress is accumulated there before the rupture. This is due to an interaction between the free surface and the fault that causes slip overshoot. On the region of the fault below the bump, such overshoot cannot occur because the fault is pinned by the deeper un-slipped zone. However, on the shallower side, the edge of the fault becomes free when the rupture approaches the free surface. In this region, such a large slip can occur without releasing a large amount of stress.
Key wordsEarthquake rupture dynamics non-planar fault subduction earthquake 2011 Tohoku-Oki earthquake
The 2011 Tohoku-Oki earthquake is one of the most important earthquakes for seismologists in many senses. From the viewpoint of earthquake source physics, this earthquake posed several as of yet unresolved questions. One such question concerns the slip distribution. A large number of slip models have been proposed based on many kinds of observations (e.g. Ozawa et al. 2011; Simons et al. 2011; Miyazaki et al. 2011; Hashimoto et al. 2012; Ide et al. 2011; Yagi and Fukahata 2011; Suzuki et al. 2011; Lee et al. 2011; Shao et al. 2011; Yoshida et al. 2011; Ishii 2011; Wan and Mori 2011; Fujii et al. 2011; Maeda et al. 2011; Saito et al. 2011; Satake et al. 2013). These slip models seem to vary depending on the data used in the analysis (e.g. Koketsu et al. 2011; Koper et al. 2011; Yao et al. 2011; Lay et al. 2012).
Although this earthquake occurred close to one of the best seismic and geodetic networks in the world (Kinoshita et al. 1998; Fukuyama et al. 1996; Obara et al. 2005; Sagiya et al. 2000), the slip model does not seem well constrained by the observations because of the station coverage; near-distance stations are located on land, and the trench where the rupture occurred is far from the coast. In addition, the velocity structure in the source region is reported to be very heterogeneous due to the low temperature of the subducting slab (Zhao et al. 2011). These factors make reliable estimation of the slip distribution difficult, despite the huge amount of available observations.
During the 2011 Tohoku-Oki earthquake, a large slip near the trench was reported to have occurred (e.g. Ito et al. 2011; Lee et al. 2011; Suzuki et al. 2011; Yagi and Fukahata 2011; Satake et al. 2013). Sato et al. (2011) and Kido et al. (2011) reported a large degree of seafloor deformation above the hypocentral region, and Fujiwara et al. (2011) reported significant deformation in the trench. These independent observations strongly suggest a large shallow slip, which supports the kinematic slip models with shallow slip near the trench. In the present study, a large slip that occurred at shallow depth is considered in addition to the large slip near the hypocenter.
In general, at shallow depths near the trench, stress accumulation would be expected to be small because of the low lithostatic stress. In such a situation, a large slip would not be expected, which contradicts the Tohoku-Oki earthquake observations. In fact, based on the focal mechanisms of aftershocks that occurred just after the mainshock, a very low level of total stress is expected to have been present close to the trench. Many intraplate normal-fault aftershocks occurred, which was not the case in this region before the mainshock (Asano et al. 2011; Ide et al. 2011; Hasegawa et al. 2011). Apparently, these unusual phenomena are associated with the occurrence of a large slip in this region where stress accumulation was low, which led to a drastic change in the stress field.
Noda and Lapusta (2013) proposed a scenario in which thermal pressurization can promote the complete stress release at shallow depths during a rupture. Yoshida and Kato ( 2011) proposed a depth dependent pore pressure distribution that forced a large slip to occur at shallow depths. These mechanisms might provide a possible explanation for the occurrence of a huge earthquake with a large slip at shallow depths.
In the present study, another possible scenario that can produce a large slip at shallow depths is considered. Numerical simulations are carried out using a spontaneous rupture model in which a bump at seismogenic depths releases a large amount of strain, in order to study how the rupture propagates and produces large slips between the bump and the trench.
1.1 Fault Model and Initial Conditions
A boundary integral equation method (Hok and Fukuyama 2011) was used for the computation of a spontaneous rupture along a subduction interface with a bump in a homogeneous half-space elastic medium. This method enables spontaneous rupture propagation to be simulated for a model of a non-planar fault system with a free surface, which is composed of arbitrary triangle elements.
It should be noted that the present computations can be scaled to a different model size, as long as the parameter κ = (Δσ/μ)(L/D c) is kept the same, where Δσ, μ, L, D c are dynamic stress drop, rigidity, characteristic length scale, and slip-weakening distance, respectively (e.g. Aochi et al. 2000; Fukuyama and Madariaga 1998; Madariaga and Olsen 2000). For example, to make the bump two times larger, the amount of slip and D c should be multiplied by two.
As the constitutive relation for the fault, a linear slip-weakening relation (Ida 1972) was used, which is defined by three parameters: static friction coefficient (μ s), dynamic friction coefficient (μ d) and D c. The value of D c is assumed to be 1 m for the entire fault, and μ s is assumed as 0.6. The strength excess (i.e. the peak shear strength minus the initial shear stress) is taken to be 0.5 and 2 MPa for inside and outside the bump, respectively. The normal stress is then computed using the static shear strength and μ s. A dynamic shear strength of 7 MPa is also assumed, and μ d is determined by the normal stress and the dynamic shear strength (7 MPa). It should be noted that following Hok and Fukuyama (2011), both shear and normal stress changes are taken into account during spontaneous rupture propagation, i.e. as the rupture propagates, the stress ratio (the shear stress divided by the normal stress) follows the slip-weakening curve.
The rupture was initiated in a circular zone with a radius of 7.5 km, whose center was located at the edge of the bump. Inside the initiation zone, the static shear strength was set equal to the initial stress. When the computation begins, the fracture condition is immediately satisfied inside the initiation zone and the rupture starts to propagate outwards. Finally, to satisfy the Courant–Friedrich–Lewy condition (e.g. Fukuyama and Madariaga 1998), a time step of 0.05 s was used for this computation.
1.2 Computation Result
Because of the numerical instability at the trench, it was not possible to compute the entire rupture process, and the simulation does not fully extend to the final stage. This is the reason why the stress does not drop close to the trench in Fig. 5. Since this numerical instability is intrinsic (independent of the numerical parameters) and cannot be solved without introducing artificial damping such as Laplacian smoothing, which might alter the computation result, the computation was stopped just before the numerical instability occurred at the trench.
As mentioned in the introduction, the slip model for the 2011 Tohoku earthquake includes some uncertainties in the slip distribution at the shallow depth near the trench. In the present study, although the slip becomes large between the bump and the trench, it cannot exceed the amount of slip inside the bump. It should be noted, however, that heterogeneity in the velocity structure was not considered, but instead a homogeneous elastic medium was assumed. Mikumo et al. (1987) pointed out that due to a heterogeneous velocity structure, slip at a shallow part of the fault can be magnified. If a heterogeneous structure was taken into account to achieve a more realistic condition, the slip near the trench could be explained by the proposed model.
It is worth noting that according to the numerical simulation results, a high stress drop region is required at the bottom of the large slip region to generate a large shallow slip near the trench. In the present simulation, the high stress drop patch is modeled as a subducting bump on the plate interface. A similar situation could occur if there was an equivalent structure that could store the strain at the bottom of the high slip region (e.g. Duan 2012). If a high stress region does not exist at the bottom of the high slip region, the interface could not sustain high stress concentration at deep parts of the fault, and aseismic slip would instead occur during the interseismic period.
Simulations using a model of a plate interface containing a bump were found to be capable of reproducing a region of large slip near the trench, which has been reported for the 2011 Tohoku-Oki earthquake. This indicates that subduction of such an interface could be one possible mechanism producing this earthquake. Since this mechanism is rather general, in any subduction zone where a locked region exists due to subduction of a bump, slip overshoot can occur during coseismic slip, leading to enhanced generation of tsunamis by magnifying deformation near the trench.
We are grateful for the comments by two anonymous reviewers that helped improve the manuscript. This work was supported by the NIED project “Development of Monitoring and Forecasting Technology for Crustal Activity”, the NIED-JAMSTEC joint project “High Frequency Source Modeling” and the JST J-Rapid/ANR Flash Japan DYNTOHOKU project (ANR-11-JAPN-0009).
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