JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, B05311, doi:10.1029/2011JB009124, 2012
Dynamic rupture of the 2011 Mw 9.0 Tohoku-Oki
earthquake: Roles of a possible subducting seamount
Benchun Duan1
Received 23 December 2011; revised 5 April 2012; accepted 5 April 2012; published 22 May 2012.
[1] Using a hybrid MPI/OpenMP parallel finite element method for spontaneous rupture
and seismic wave propagation simulations, we investigate features in rupture propagation,
slip distribution, seismic radiation, and seafloor deformation of the 2011 Mw 9.0
Tohoku-Oki earthquake to gain physical insights into the event. With simplified shallow
dipping (10 ) planar fault geometry, 1D velocity structure, and a slip-weakening friction
law, we primarily investigate initial stress and strength conditions that can produce rupture
and seismic radiation characteristics of the event revealed by kinematic inversions, and
seafloor displacements observed near the epicenter. By a large suite of numerical
experiments aided by parallel computing on modern supercomputers, we find that a
seamount of a dimension of 70 km by 23 km just updip of the hypocenter on the
subducting plane, parameterized by higher static friction, lower pore fluid pressure, and
higher initial stress than surrounding regions, may play a dominant role in the 2011 event.
Its high strength stalls updip rupture for tens of seconds, and its high stress drop generates
large slip. Its failure drives the rupture to propagate into the shallow portion that is likely
velocity-strengthening, resulting in significant slip near the trench within a limited area.
However, the preferred model suggests that the largest slip in the event occurs near the
hypocenter. High-strength patches along the downdip portion of the subducting plane are
most effective among several possible factors in generating high-frequency seismic
radiations, suggesting the initial strength distribution there is very heterogeneous.
Citation: Duan, B. (2012), Dynamic rupture of the 2011 Mw 9.0 Tohoku-Oki earthquake: Roles of a possible subducting
seamount, J. Geophys. Res., 117, B05311, doi:10.1029/2011JB009124.
1. Introduction
[2] The 2011 Mw 9.0 Tohoku-Oki earthquake occurred on
the megathrust fault along the Japan Trench subduction zone
(Figure 1). Its magnitude was much larger than that expected
from historical earthquakes in recent centuries along this part
of the subduction zone. This event was recorded by dense
networks of geophysical instruments. Data from globally
distributed broadband seismic networks, local strong motion
networks, regional geodetic networks, seafloor geodetic stations, and/or tsunami recordings have been inverted for final
slip distribution and kinematic slip history on the megathrust
fault plane by many research groups [e.g., Simons et al.,
2011; Ide et al., 2011; Shao et al., 2011; Lay et al., 2011;
Ammon et al., 2011; Pollitz et al., 2011; Koper et al., 2011;
Koketsu et al., 2011; Roten et al., 2012]. Although the
1
Center for Tectonophysics, Department of Geology and Geophysics,
Texas A&M University, College Station, Texas, USA.
Corresponding author: B. Duan, Center for Tectonophysics, Department
of Geology and Geophysics, Texas A&M University, College Station, TX
77843, USA. ([email protected])
Copyright 2012 by the American Geophysical Union.
0148-0227/12/2011JB009124
inherent non-uniqueness of inversion problems and the
frequency-dependent nature of different types of data result
in large variations among kinematic inversion results, some
important features of the 2011 event have been reported from
these kinematic source models. First, large slip occurred
updip of the hypocenter and relatively concentrated in a
simple patch, while slip downdip of the hypocenter was relatively small [e.g., Simons et al., 2011; Ide et al., 2011; Shao
et al., 2011; Lay et al., 2011; Ammon et al., 2011; Pollitz
et al., 2011; Koper et al., 2011]. Second, the rupture initiated slowly and propagated in the downdip direction in the
early stage of the rupture (i.e., the first 40 s) [e.g., Ide et al.,
2011; Shao et al., 2011; Roten et al., 2012]. In other words,
the ruptured did not propagate upward at the early stage of
the event. Third, high-frequency (HF) radiations predominately came from the deep part of the fault, while they were
relatively weak from the shallow part that produced large slip
[e.g., Simons et al., 2011; Ide et al., 2011; Meng et al., 2011;
Koper et al., 2011; Wang and Mori, 2011].
[3] Although most kinematic inversion studies [e.g., Simons
et al., 2011; Ide et al., 2011; Shao et al., 2011; Lay et al., 2011;
Ammon et al., 2011; Pollitz et al., 2011; Koper et al., 2011]
report that large slip occurred updip of the hypocenter, the
exact location of the maximum slip with respect to the trench
varies among these kinematic models. In some models, the
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Figure 1. ETOPO1 topography [Amante and Eakins, 2009] of the 2011 Tohoku-Oki earthquake region
(color scale), horizontal projection of the fault outline in spontaneous rupture models (maroon rectangular),
five seafloor stations (purple squares) whose displacements from the event are reported [Sato et al., 2011],
and epicenter locations of some supraslab earthquake clusters [Uchida et al., 2010]. A linear seamount
chain, containing a large seamount of 70 km by 25 km, can be clearly seen to the east of the trench. Supraslab earthquake clusters suggest subducted and detached seamounts [Uchida et al., 2010]. Red star denotes
the JMA epicenter of the 2011 main shock and black curve delineates coastline.
maximum slip occurs near the hypocenter [e.g., Simons et al.,
2011; Ammon et al., 2011; Pollitz et al., 2011; Roten et al.,
2012], while it occurs near the trench in some of other models [e.g., Ide et al., 2011; Lay et al., 2011]. Nevertheless,
bathymetric data suggest that significant coseismic slip
reached some portion of the trench in the event [Fujiwara
et al., 2011].
[4] The second feature of the 2011event on rupture propagation revealed by some of kinematic studies [e.g., Ide et al.,
2011; Shao et al., 2011; Roten et al., 2012] provides us with
an important clue about stress and strength distributions just
updip of the hypocenter. Based on our current understanding
of earthquake physics, no updip rupture within the first
40 seconds of the event suggests the frictional strength is
much higher than the initial shear stress just updip of the
hypocenter. It is likely that the initial shear stress is high there
for at least two reasons. First, the portion just updip of the
hypocenter must have experienced strain accumulation over
hundreds to thousands years, during which no significant
earthquakes have occurred. Second, historical earthquakes
over past centuries occurred downdip of the hypocenter and
these previous earthquakes had likely loaded the updip portion of the hypocenter along the fault. Therefore, the
frictional strength just updip of the hypocenter is likely very
high so that the updip rupture was stalled 40 seconds in the
2011 event. In the next section, we will discuss what geological feature most likely acted as the high-strength-patch
(HSP) along the subduction plane in the event.
[5] Theoretical studies demonstrate that HF radiations are
associated with abrupt changes in the rupture speed [e.g.,
Madariaga, 1977], which can happen due to heterogeneous
strength and/or stress distributions on a fault plane, the transition of frictional behavior (e.g., from velocity-weakening to
velocity-strengthening), or roughness of the fault plane. The
third feature of the 2011 event discussed above (i.e., HF
radiation predominantly from the deep part of the fault) suggests a heterogeneous distribution in strength and/or stress on
the deep part of the subducting plane and a relatively smooth
distribution on the shallow part.
[6] Kinematic source models for the 2011 Mw 9.0
Tohoku-Oki earthquake, as those cited above, provide us
with images of how slip was distributed and/or how rupture
propagated on the fault during the earthquake, by fitting
available data collected from a variety of geophysical networks. To further understand why slip and rupture happened
in the way they did in the event, we can resort to dynamic
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source models. In particular, when a failure criterion that
determines whether or not a point on the fault fails and a
friction law that controls the evolution of friction on the fault
plane are introduced in a dynamic rupture model, the rupture
propagation is spontaneous and the dynamic rupture model
is referred to as the spontaneous rupture model [e.g.,
Andrews, 1976; Day, 1982]. By integrating our current
understanding of earthquake physics with characteristics of
recent large earthquakes revealed by kinematic inversions
and near-field observations, spontaneous rupture models can
provide more insights into why these earthquakes happened
in the way they did, which are useful in forecasting future
large earthquake scenarios and mitigating seismic hazards
from them. In current practice, kinematic source models are
widely used in inversion problems of large earthquakes,
while spontaneous rupture models are mainly constructed in
a framework of forwarding modeling because of high
demands in computational resources.
[7] In this study, we construct spontaneous rupture models
of the 2011 Mw 9.0 Tohoku-Oki earthquake to further our
understanding of why the 2011 event happened in the way it
did. We particularly address the first two features of this
event discussed above. The first is that large slip occurred
updip of the hypocenter in a relatively simple, concentrated
patch. The second is that updip rupture was stalled for
40 s. We also examine efficiency of different factors in
generating HF radiations on the deep part of the fault, which
is the third feature discussed above. Although the second
feature was not reported as widely as the first feature, we
believe it is a robust feature of the event because it was
revealed by several different studies independently [e.g., Ide
et al., 2011; Shao et al., 2011; Roten et al., 2012], using
different sets of data and/or different methods. In particular,
in conjunction with the first feature, the second feature
suggests a HSP just updip of the hypocenter acted as a barrier in the early stage of the rupture and became an asperity
(i.e., a patch with large slip) later in the event.
[8] In the following sections, we first examine what geological feature most likely acted as the HSP in the event.
Then we construct spontaneous rupture models to explore
effects of the HSP on rupture propagation and slip distribution. We build a large suite of spontaneous rupture models,
aided by parallel computing on modern cluster systems, to
find appropriate distributions of physical parameters on the
fault plane, including initial fault stresses, static and dynamic
friction coefficients, and pore pressure, to reproduce the
characteristics of the event discussed above and seafloor
displacements observed near the epicenter [Sato et al.,
2011]. We will report results primarily from our preferred
model and discuss insights obtained from our spontaneous
rupture modeling.
2. A Large Subducting Seamount Might Act
as the HSP in the 2011 Event
[9] The geological features that might act as the HSP that
stalled the updip rupture for the first 40 seconds in the 2011
Mw 9.0 Tohoku-Oki earthquake may include non-planar
fault geometry on the megathrust due to bending of the
subducting oceanic plate [e.g., Ito et al., 2004, 2005; Fujie
et al., 2006], and subducting seafloor features [e.g., Bilek,
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2007; Das and Watts, 2009; Carena, 2011]. By analyzing
observations from onshore-offshore wide-angle seismic
experiments in the Japan Trench forearc region, Ito et al.
[2004, 2005] and Fujie et al. [2006] have identified two
bending points of the subducting oceanic plate, at
143.2 E and 142.3 E, respectively. The Japan Meteorological Agency (JMA) epicenter of the 2011 Mw 9.0
Tohoku-Oki earthquake is at 142.861 E. Using a threedimensional seismic velocity model, Zhao et al. [2011]
relocate the epicenter of the 2011 event and obtain an epicenter location (i.e., 142.916 E), which is very close to that
of JMA. Therefore, the epicenter of the 2011 main shock is
relatively far away from the two bending points of the
subducting plate, which unlikely acted as the HSP in the
event.
[10] Bathymetry around the Japan Trench [Amante and
Eakins, 2009] clearly shows a chain of seamounts with
various sizes to the east of the Japan trench (Figure 1). The
largest seamount in this chain that can be seen in Figure 1 is
70 km long by 25 km wide. This seamount will likely be
subducting with the Pacific plate beneath the Japan island in
the future. Furthermore, Uchida et al. [2010] report supraslab earthquake clusters above the subduction plate boundary offshore NE Japan (Figure 1). They interpret that these
clusters represent seismicity in seamounts detached from the
Pacific plate during slab descent. As shown in Figure 1,
these clusters are located to the northwest of the epicenter of
the 2011 event. These detached seamounts to the northwest
of the 2011 epicenter and the existence of seamounts on the
ocean floor to the east of the Japan trench (i.e., to the
southeast of the 2011 epicenter) strongly suggest subducting
seamounts, which may have not been detached from the
subducting plate, may exist on the subducting surface that
ruptured in the 2011 event.
[11] Effects of subducting seafloor topography on some of
previous subduction zone earthquakes have been reported in
literature. Subducting features that may play a role in large
earthquakes include seamounts, ridges, troughs, and fracture
zones. Bilek [2007] reviews examples of subducting features
along some subduction zones and their relations to large
earthquakes, including NE Japan, Java, Alaska-Aleutians,
Tonga, Peru-Chile, Nankai, and Costa Rica. Das and Watts
[2009] discuss rupture characteristics of some great subduction earthquakes in the Indian and Pacific oceans, suggesting a correlation between high slip patches and
subducting seafloor topography, including the1986 Mw 8.0
Andreanof Islands, Alaska, earthquake, the 1996 Mw 8.2
Biak, Indonesia, earthquake, the 2001 Mw 8.4 Peru earthquake, and the 2004 and 2005 great Sumatra earthquakes.
Some characteristics observed in these earthquakes include
(1) large slip concentrated in isolated patches, and (2) rupture was stalled along some directions at the early stage.
Carena [2011] examine the role played by oceanic fracture
zones in controlling the initiation and extent of great earthquakes along the South American trench.
[12] Based on the observations along the Japan subduction
zone and the previous studies just discussed above, we
hypothesize that a large subducting seamount acted as the
HSP in the 2011 Tohoku-Oki main shock. We will show in
the following sections that the subducting seamount may not
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Table 1. 1D Velocity Structure for the Region Used in This Study,
Adapted From Ito et al. [2005]a
Layer
Bottom Depth (km)
Vp (m/s)
Vs (m/s)
Density r (kg/m3)
1
2
3
4
5
12
17
Half-space
5000
6000
7000
8000
2887
3464
4041
4619
2500
2700
3000
3300
a
Poisson solids are assumed.
only have stalled the updip rupture propagation and have
generated large slip in a compact patch, but also have controlled the rupture extent, and thus the size of the 2011 event.
3. Methods and Models
[13] The major ingredients of a spontaneous rupture model
include geological structure, a friction law, and an initial
stress field [e.g., Harris et al., 2009]. In this study, we
assume a shallow-dipping thrust fault with a dip of 10 and a
dimension of 440 km along strike by 220 km along downdip. The fault geometry and dimension are comparable with
those used in kinematic inversion studies [e.g., Simons et al.,
2011; Ide et al., 2011; Shao et al., 2011]. The maroon rectangular in Figure 1 illustrates the horizontal projection of the
fault plane. In this study, we characterize the hypothesized
seamount by frictional and pore fluid parameters. Explicitly
incorporating the seamount geometry on the fault plane will
be the next step for future studies. The fault is embedded in a
half-space with layered geologic structure, i.e., 1D seismic
velocity structure (Table 1). This velocity model is adapted
from Ito et al. [2005, Figure 1c]. We assume a flat free
surface at the top of the model domain. Important physical
parameters on the fault plane in our preferred model are
summarized in Table 2 for different regions illustrated in
Figure 2, and will be discussed in details below.
[14] We use a linear slip-weakening friction law in this
study, which states that frictional coefficient m drops from a
static value ms to a dynamic value md over the critical slip
distance D0. Frictional strength measured on samples from
the Nankai subduction zone is low (i.e., 0.2 ≤ m ≤ 0.46)
[Ikari and Saffer, 2011]. We choose ms = 0.3 and md = 0.2 for
most portions of the fault plane (Figure 2 and Table 2).
Although the Japan trench subduction zone is erosive while
the Nankai subduction zone is accretionary [e.g., Clift and
Vannucchi, 2004], we assume low frictional coefficients
apply to both types of subduction zones. In addition, we
remark that it is the difference in frictional coefficients (see
Section 3.2 for details) that matter in dynamic rupture and
slip distribution. To approximate velocity-strengthening
frictional behavior at shallow depth (Region A in Figure 2)
and bottom (Region C in Figure 2) of the fault plane, we set
md > ms for these regions (Table 2). Tests with various values
of D0 show that dynamic rupture propagation and slip distribution are relatively insensitive to D0 in spontaneous
rupture models for this earthquake. We use a constant D0
value of 1.5 m for the entire fault plane in our preferred
model to ensure a good resolution of the cohesive zone (i.e.,
three or more elements within the zone) at the rupture tip
[e.g., Day et al., 2005; Duan and Day, 2008].
[15] Setup of the initial stresses on the fault plane is based
on our current understanding of the stress state in the crust.
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The shallow fault dipping angle and large fault rupture area
of the giant megathrust event impose challenges in spontaneous rupture modeling in terms of numerical stability and
computational resource requirements. Parameterization of
the seamount needs a large suite of numerical experiments in
order to reproduce the slip and rupture characteristics in the
2011 event discussed above and seafloor displacements
observed near the epicenter. In the following subsections, we
discuss these aspects of our methods and models.
3.1. EQdyna: A Hybrid MPI/OpenMP Parallel Finite
Element Method for Spontaneous Rupture and Seismic
Wave Propagation Simulations
[16] We use an explicit finite element method (FEM) algorithm EQdyna to perform spontaneous rupture and seismic
wave propagation simulations in this study. Sequential versions of EQdyna have been used in rupture dynamics [e.g.,
Duan and Oglesby, 2006; Duan and Day, 2008], ground
motion simulations [Duan and Day, 2010], and fault zone
studies [Duan, 2010a; Duan et al., 2011]. General descriptions
of the method can be found in Duan and Oglesby [2006] and
Duan and Day [2008]. An OpenMP version of the method
[Wu et al., 2009] was used in examining effects of stress
rotations on rupture dynamics and near-field ground motion,
motivated by observations in the 2008 Mw 7.9 Wenchuan
earthquake [Duan, 2010b]. EQdyna adopts the traction-atsplit-node (TSN) scheme to characterize the faulting boundary. Dalguer and Day [2006] show that the accuracy of
spontaneous rupture solutions from the TSN method is the best
among several available schemes in treating the faulting
boundary. The formulation of TSN proposed by Day et al.
[2005] has been implemented in recent versions of EQdyna,
to replace the formulation summarized by Andrews [1999] in
early versions of the algorithm, as the former treats fault
behavior at all times in a concise and robust way. Generalization of the formulation of Day et al. [2005] in which faults
Table 2. Parameters in Different Regions on the Fault Surface
Labeled in Figure 2 for the Preferred Spontaneous Rupture Modela
Region
l
ms
md
m0b
A: V-strengthening
B1: V-weakening
B2: V-weakening
C: V-strengthening
Dc: Seamount
E: Nucleation
F: High strength
G: High stress
0.7
0.7
0.7
0.7
0.4
0.8
0.7
0.7
0.3
0.3
0.3
0.24
0.7
0.26
0.5
0.3
0.42
0.2
0.2
0.27
0.2
0.2
0.2
0.2
0.25
0.25
0.201
0.21
0.4
0.25
0.25
a
Pore pressure ratio l, static frictional coefficient ms, dynamic frictional
coefficient md, and initial stress ratio m0.
b
Values for this parameter (the ratio between initial shear to normal
stresses) are at the x = 10 km (see Figure 2). They taper to 0.2 and 0.21
at the left and right edges of the fault plane, respectively. Values for
Regions F are calculated in this way with m0 = 0.201 at x = 10 km (i.e.,
the value for Region B2), while a value of m0 = 0.25 is assigned for the
entire region of G. In addition, in calculating values for Region B1
outside of the Seamount (Region D), m0 = 0.25 and m0 = 0.31 at
x = 10 km are used for the SSW side and the NNW side, respectively, to
prevent the initial shear stress from being higher than the initial shear
strength.
c
Parameter values given for this region are those at the middle of the
region along the downdip direction. They linearly taper to the values of
the top and bottom regions at the top and bottom edges of the region,
respectively, to mimic gradual changes associated with a seamount.
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Figure 2. Regions on the fault plane in the preferred spontaneous rupture model with different physical
parameters, including pore fluid pressure ratio l, static friction ms, dynamic friction md, and stress ratio
(shear to normal) m0, which are tabulated in Table 2. Regions A and C are velocity-strengthening regions
(approximately by md > ms in the slip-weakening friction law). Regions B1 and B2 are velocity-weakening
regions, within which there are a seamount (Region D), a nucleation patch (Region E), three high-strength
patches (Region F), and a high stress patch (Region G). Black triangles are on-fault stations whose slip
velocity time histories are shown in Figure 5. Red star is the hypocenter.
are parallel to Cartesian coordinate planes in a finite difference
grid to the case in which faults can be arbitrarily oriented in a
finite element mesh can be found in Duan [2010b]. To characterize shallow-dipping fault geometry, we use a degeneration technique to divide a hexahedron element into two wedge
elements along the fault plane in the finite element mesh, in
which most elements are hexahedron for computational
efficiency.
[17] It is challenging to perform spontaneous rupture
modeling for giant megathrust earthquakes, such as the 2011
Tohoku-Oki and the 2004 Sumatra earthquakes. Rupture
areas in these earthquakes are huge, and the requirement of
numerically resolving the cohesive zone at the rupture front
[Andrews, 2004; Day et al., 2005] on fault planes generally
results in a very large model (i.e., very large numbers of
nodes/elements) that is demanding in computer resources,
including CPU time and memory. We have been parallelizing
EQdyna using a hybrid MPI/OpenMP approach [Wu et al.,
2009, 2011a, 2011b; Duan, 2012] to deal with these challenges. The trend in high-performance computing systems
has been shifting toward cluster systems with chip multiprocessors (CMPs). CMPs are usually configured hierarchically to form a compute node of a larger parallel system.
These cluster systems provide a natural programming paradigm for hybrid programs.
[18] In our hybrid MPI/OpenMP implementation, we use
MPI for process-level coarse parallelism and OpenMP for
loop-level fine grain parallelism. As such, we achieve multiple levels of parallelism, with OpenMP at the node level and
MPI between nodes. The hybrid approach can also reduce the
communication overhead of MPI within a CMP node, by
taking advantage of the globally shared address space and
on-chip high inter-core bandwidth and low inter-core
latency. In the hybrid implementation, we separate MPI
regions from OpenMP regions, and OpenMP threads cannot
call MPI subroutines. To facilitate parallelization of EQdyna,
we incorporate 3D mesh subroutines into EQdyna. This also
avoids the need of producing large mesh files and
corresponding I/O expenses. We adopt an element-based
partitioning scheme, in which the entire model domain is
partitioned into subdomains and two adjacent subdomains
share common boundary nodes, whose values need to be
passed to each other by MPI. In the current mesh partitioning
scheme, we partition the entire model domain by the coordinate along fault strike (i.e., x axis in this study) and each
MPI process performs calculations for each sub-mesh.
Shared boundary nodes in mesh between two adjacent MPI
processes are recorded in mesh generation to facilitate message passing in dynamic calculations. Detailed descriptions
of the hybrid implementation and verification of the implementation on a dip-slip faulting benchmark problem are
given in Wu et al. [2011a, 2011b]. The performance analyses
of the hybrid version on several large-scale cluster systems
are reported in Wu et al. [2011a, 2011b] and Duan [2012].
[19] The parallel version of EQdyna and several cluster
systems at local and national supercomputing facilities allow
us to simulate a large suite of spontaneous rupture models to
explore physics of the 2011 Tohoku-Oki main shock rupture. To search for physical parameters that are consistent
with our current understanding of earthquake physics and
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observations from the 2011 event, we perform dynamic
simulations of about 170 experimental models with fault
node spacing of 1 km and a termination time of 200 s. Each
experimental model has about 133 million elements. Using
128 cores on a supercomputer system with 2.8 GHz Nehalem quad-core X5550 processors, each model takes about
156 GB memory and 3.9 h wall-clock time. We select several models to run at a finer element size, i.e., fault node
spacing of 500 m, which results in node spacing of 86.8 m
along the vertical direction within the fault dimension in the
finite element mesh, using the degeneration technique for the
10 dipping fault. The dynamic simulation time step is
0.009 s for these production models to ensure numerical
stability. Each of these production runs has about 580 million elements, and takes about 35 h wall-clock time and
about 640 GB memory with 256 compute cores on the above
supercomputer system. Given velocity structure in Table 1,
the highest frequency in seismic waves accurately simulated
in the production runs is 7 Hz at depth, and 4 Hz near
surface, if we take 8 node intervals per shear wavelength.
3.2. Initial Stress Setup
[20] Initial stress conditions on a fault plane before a large
earthquake may be the most important physical parameters
that determine earthquake rupture scenarios and earthquake
sizes. However, they may also be the least-constrained
parameters that limit our ability in forecasting future earthquakes. By comparing with observations on rupture characteristics and near-field deformation fields, spontaneous
rupture models of recent large earthquakes may provide a
vital means to get some clues of initial stress conditions
before large earthquakes. In this study, we attempt to decipher first-order features in the initial stress distribution on
the fault plane of the 2011 Tohoku-Oki main shock. Thus,
we will largely ignore small-scale stress heterogeneities in
this study that were likely present before the 2011 event.
[21] We assume a pure-thrust faulting stress environment
and the most compressive principle effective stress (horizontal) s1 is perpendicular to the fault strike. We first
determine the two relevant principal effective stresses (i.e.,
the maximum and minimum effective stresses). The minimum principle effective stress s3 (vertical in the thrust
faulting environment) can be calculated by
Z
z
s3 ¼ ð1 lÞg
rðz′Þdz′;
ð1Þ
0
where l is the ratio between pore fluid pressure and lithostatic pressure, r is the rock density, and z is depth (positive
downward). s1 can be calculated as
s1 ¼ Rs3 ;
ð2aÞ
where
R ¼ ½ sinð2b Þ þ m0 ð1 þ cosð2bÞÞ=½ sinð2b Þ m0 ð1 cosð2b ÞÞ:
ð2bÞ
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Equation (2b) is derived under the condition that the shear
stress t 0 on a thrust fault plane of dip b would be in state of
incipient stable sliding, if the frictional resistance were equal
to m0 times the normal stress sn (positive in compression).
Then, the initial normal and shear stresses on the fault plane
can be calculated by
sn ¼ s1 sin2 b þ s3 cos2 b;
ð3aÞ
t 0 ¼ ðs1 s3 Þ sinb cosb:
ð3bÞ
From equations (1)–(3), one can see that the initial stresses at
a point on the fault plane depend on the density profile r(z)
above the point, the dip angle of the fault b, the pore pressure parameter l, and the nominal frictional coefficient m0,
which characterizes the initial shear stress level with respect
to the initial normal stress (i.e., the ratio of the two). Given
the layered material property in Table 1 and the 10 dip
angle, the distribution of the initial shear and normal stresses
on the fault plane is determined by l and m0. The initial fault
strength depends on both the normal stress sn and the static
frictional coefficient ms (i.e., the strength being the product
of the two). For a given sn, dynamic stress drop (i.e., initial
shear stress minus sliding shear stress) is proportional to m0
md, while strength excess (initial shear strength minus
initial shear stress) is proportional to ms m0. We remark
that it is the differences between these frictional coefficients
that matter in controlling dynamic rupture propagation and
slip distribution.
[22] Lab permeability measurements from core samples
suggest that pore fluid pressure along the Nankai subduction
zone is significantly above hydrostatic, with l values in a
range between 0.68 and 0.77 [Skarbek and Saffer, 2009].
We choose l = 0.7 for most portions of the fault plane in our
preferred model. Although the Japan trench subduction zone
is erosive while the Nankai subduction zone is accretionary
[e.g., Clift and Vannucchi, 2004], we assume high pore fluid
pressure is a common feature in both types of subduction
zones.
[23] In setting up m0 on the fault plane, we consider the
following several points. First, the distribution of m0 is as
simple as possible, for our aim is to examine first-order features of the event. Thus, some possible small-scale heterogeneities in m0 are ignored. Second, regions that experienced
significant earthquakes over past centuries (e.g., the downdip
portion relative to the 2011 hypocenter) should have relatively low m0 values, as there had not been enough strain
accumulation since recent events. Third, relatively concentrated slip distributions from kinematic inversions [e.g.,
Simons et al., 2011; Ammon et al., 2011; Shao et al., 2011]
suggest larger m0 values at the middle of the fault plane relative to those at the two lateral edges, particularly updip of
the hypocenter. Based on these considerations, a large number of trial-and-error experiments are performed to obtain
the m0 distribution and the seamount parameters (see below),
for the preferred spontaneous rupture model (Figure 2 and
Table 2). In the preferred model, m0 is both depth- and strikedependent. We first give depth-dependent m0 values at alongstrike distance (x-coordinate) 10 km, with large values at
shallow depth and small values on the deep part. Then small
m0 values are assigned at the two lateral edges of the fault
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plane. The m0 value at each fault node is obtained by linear
interpolations laterally, i.e., along strike.
3.3. Characterizing a Seamount by Friction and Pore
Fluid Pressure Parameters
[24] We characterize the subducting seamount (Region D
in Figure 2) in spontaneous rupture models by higher static
frictional coefficient ms, higher nominal friction coefficient
m0, and lower pore fluid pressure l, relative to surrounding
regions (Table 2). Higher ms values represent the effect
of seamount topography on the fault shear strength, while
lower l values result from less accumulated sediments
associated with the seamount. Higher m0 values associated
with the seamount represent higher initial shear stress from
tectonic loading and previous earthquakes, which were terminated by the seamount. We first set the maximum ms = 0.7
and minimum l = 0.4 at the middle of the seamount along
downdip for the preferred model (Figure 2 and Table 2), via
trial-and-error numerical experiments. Then we obtain their
values within the seamount patch by linear interpolation
between the maximum/minimum values at the middle and
the values at the updip and downdip edges, which are the
values for surrounding regions. We set the maximum m0 =
0.4 at x = 10 km along strike and the middle of the seamount
along downdip. Along dip at x = 10 km, m0 decreases updip
and downdip within the seamount in the same way as ms.
One special treatment in interpolating m0 laterally outside the
x-range of the seamount is that we use a hypothetic value of
m0 = 0.25 for the SSW side and m0 = 0.31 for the NNE side at
x = 10 km within the depth range of the seamount, to prevent
the shear stress from being higher than the shear strength in
the initial stress field. All choices of the parameters,
including the location and dimension of the seamount, are
made by trial-and-error numerical experiments to reproduce
the first and second features of the event discussed in
Section 1 and to fit the seafloor displacement observations
near the epicenter [Sato et al., 2011].
3.4. Initiation of Spontaneous Ruptures
[25] We do not simulate the quasi-static nucleation process. Instead, we adopt the concept of a critical nucleation
patch [Day, 1982] to initiate a spontaneous rupture. Within
the nucleation patch, the rupture is forced to propagate at a
fixed speed. Outside this patch, rupture propagation is
spontaneous. Nucleation is commonly believed to occur in a
region with low strength and/or high shear stress on the fault
plane. Low strength may result from high pore fluid pressure
and/or inherently weak material. We set higher pore pressure
(l = 0.8) and lower static friction (ms = 0.26) for the nucleation patch (Region E in Figure 2) in the preferred model
(Table 2). Motivated by the second feature in the 2011 event
discussed in Section 1, we set the nucleation patch in the
preferred model to downdip of the hypocenter only. Thus,
the hypocenter separates the seamount (Region D) and the
nucleation patch (Region E) in the preferred model
(Figure 2). The minimum size of the nucleation patch
depends on the initial stress state and frictional parameters
[Day, 1982]. An analysis based on parameter values below
the hypocenter suggests a semi-circle area with a minimum
radius of 30 km is needed to initiate the rupture. With
some numerical experiments, we assign the nucleation
values of l and ms (i.e., l = 0.8 and ms = 0.26) within a
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rectangular patch of 60 km by 30 km in the preferred
model for numerical convenience.
4. The Preferred Spontaneous Rupture Model
for the 2011 Mw 9.0 Tohoku-Oki Earthquake
[26] In this section, we report the preferred spontaneous
rupture model for the 2011 Mw 9.0 main shock, which is
obtained through a large suite of numerical experiments. We
will discuss physical parameters, rupture propagation characteristics, slip distribution, HF seismic radiations, and seafloor displacements from the model, aiming to gain some
physical insights into the 2011 earthquake rupture.
4.1. The Model
[27] Distributions of important physical parameters on the
fault plane in the preferred spontaneous rupture model of the
2011 Mw 9.0 Tohoku-Oki earthquake are summarized in
Figure 2 and Table 2. Essentially, the fault plane is first
divided into three regions along the downdip direction, with
velocity-strengthening behavior (approximated by md > ms in
the slip-weakening friction law) on the top (Region A) and
bottom (Region C) parts of the fault plane, and velocityweakening behavior (i.e., seismogenic, with md < ms in the
slip-weakening friction law) in between (all other regions).
Within the seismogenic region, there is one patch (Region
D) of 70 km along strike by 23 km along downdip just updip
of the hypocenter (red star). This patch has lower l, higher
ms, and higher m0 than surrounding regions and corresponds
to a seamount. There is another patch (Region E) of 60 km
by 30 km with higher l and lower ms just downdip of the
hypocenter. The rupture initiates in the region E. In the
preferred model, we arbitrary introduce three small highstrength patches (Regions F) with higher ms and a small
high-stress patch (Region G) with higher m0 relative to surrounding areas, to examine effectiveness of these patches in
generating HF seismic radiations.
[28] Figures 3a and 3b show initial shear and normal
stresses, respectively, on the fault plane in the preferred
model, calculated from equations (1)–(3) with the density
profile in Table 1 and physical parameters on the fault plane
in Figure 2 and Table 2. Overall, both shear and normal
stresses are depth-dependent and generally increase with
depth. The seamount results in a distinguished patch in the
initial stress field with both higher shear and normal stresses
than surrounding areas, while the normal stress within the
nucleation patch is relatively low. The small high-stress
patch is visible in the initial shear stress field (Figure 3a),
while there is no expression of the three high-strength patches. Although the initial shear stress largely increases with
depth, fault slip will be controlled by stress drop, which is
small on the downdip region (i.e., Region B2 with small
difference between m0 and md, Table 2). Initial stress/strength
conditions on the fault plane and effects of the seamount/
nucleation patches on them may be more clearly seen from
two profiles in Figures 3c and 3d. Figure 3c shows a profile
along the downdip direction (see the black line in Figure 3a
for the location). Figure 3d shows another profile along
strike (see the black line in Figure 3b for the location). Final
shear stress at the end of the dynamic simulation (i.e., 200 s)
is also plotted here. The seamount results in both high
strength excess (initial shear strength minus initial shear
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Figure 3. (a) Initial shear stress and (b) initial normal stress on the fault plane in the preferred spontaneous rupture model for the 2011 Mw 9.0 Tohoku-Oki earthquake. Both stresses largely increase with depth.
Star is the hypocenter. (c) Initial shear strength and stress and final shear stress along a downdip profile
denoted by the dashed, black line in Figure 3a, and (d) those along a strike profile denoted by the dashed,
black line in Figure 3b. Initial shear strength is the product of static frictional coefficient and normal stress.
Seamount, nucleation patch, and a high-strength patch can be clearly seen in these profiles.
stress) and high stress drop (initial shear stress minus final
shear stress), while the strength excess over the nucleation
patch is very small. Outside the rectangular patches in
Figure 2, initial shear strength does not change along strike,
while initial shear stress and stress drop decreases toward the
two lateral fault edges (e.g., Figure 3d).
4.2. The Rupture Propagation
[29] A fixed speed of 1.5 km/s within a semi-circle
nucleation patch with a radius of 30 km (i.e., downdip only)
is used to initiate the rupture. Outside the nucleation patch,
the rupture propagates spontaneously, which can be examined by slip velocity snapshots (Figure 4). At 30 s, the rupture has already spontaneously propagated for 10 s and slip
velocity is still very small. At 50 s, the seamount partially
fails from bottom and the two lateral edges, and large slip
velocity starts to emerge. The rupture primarily propagates
bilaterally along strike between 30 and 50 s. The seamount
completely breaks at 55 s, resulting in large slip velocity.
Several strong slip pulses originated from failure of the seamount propagate upward at 60 s, and they coalesce to form a
large strong-slip-rate belt at 65 s. These strong slip pulses
drive the rupture to penetrate into the shallow velocitystrengthening region (i.e., above the top white line). Failure
of the seamount also drives the rupture to resume the downdip propagation, which has stalled for a while due to low
stress drop and high strength excess there (Figure 3c). Broken of seafloor updip of the seamount can be clearly seen at
70, 75, and 80 s, with some strong slip velocity pulses near
the top edge of the fault (i.e., the trench). Broken of seafloor
facilitates downward rupture propagation. The rupture also
steadily propagates laterally to the SSW and NNE sides
during the entire process in the model.
[30] The above rupture propagation process results in long
risetime on large portions of the fault plane, as shown by
time histories of slip velocity at selected on-fault stations in
Figure 5, whose locations can be found in Figure 2. At depth
of the hypocenter (e.g., Stations S2 and S5), the risetime
is 40 s. It is 30 s at Stations S1 and S4, and 35 s
at Station 6. The risetime is relatively shorter (10 s) at
Station 3, which is near the downdip edge of the fault plane.
Time histories of slip velocity at stations above the seamount
(e.g., Stations S1 and S4) are relatively complex, due to
multiple strong slip pulses from broken of the seamount
and seafloor. The two stations (S1 and S4) also experience
reactivation of rupture (e.g., after a short period of zero slip
velocity), which is likely caused by broken of seafloor.
[31] The rupture propagation process discussed above is
further illustrated by the rupture time contour and image
(Figure 6c). The model reproduces well several first-order
rupture propagation characteristics revealed by kinematic
inversions [e.g., Ide et al., 2011; Shao et al., 2011], including
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Figure 4. Snapshots of slip velocity on the fault plane from the preferred spontaneous rupture model for
the 2011 Mw 9.0 Tohoku-Oki earthquake. Broken of the seamount just updip the hypocenter (red star) and
seafloor in the region updip of the seamount plays critical roles in the rupture propagation. Two white
dashed lines denote boundaries between velocity strengthening behavior at top and bottom and velocity
weakening behavior in between on the fault plane. White rectangle denotes the seamount outline.
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weak initial phase of the rupture before 45 s, and a strong
burst of energy release that lasts 50 s with a peak at 73 s.
The peak moment rate in the spontaneous rupture model
appears to be associated with strong slip pulses near the
trench and a large slipping fault area (see 70 s and 75 s panels
in Figure 4). Because of simplicity in the initial stress distribution toward two lateral edges of the fault, the spontaneous rupture model does not capture the long tail after 120 s
in the moment rate function reported from kinematic inversions [e.g., Shao et al., 2011; Ide et al., 2011].
Figure 5. Time histories of slip velocity at six on-fault stations (see Figure 2 for location) from the preferred spontaneous rupture model. Long risetimes are observed.
(1) no updip rupture before 40 s, (2) seafloor failure at
70 s, and (3) downdip edge failure at 90 s. The moment
rate function from the preferred model (Figure 7) exhibits an
energy release pattern similar to that reported from kinematic
inversions [e.g., Shao et al., 2011; Ide et al., 2011]: a very
4.3. The Slip Distribution and Seismic Moment
[32] The slip distribution from the preferred spontaneous
rupture model are consistent with those from several kinematic inversions in terms of first-order features (Figure 6a).
It is comparable in shape to one of kinematic slip distributions [Shao et al., 2011] (i.e., their Model II) that fits teleseismic body and surface waves well, and in the location
of the maximum slip to the static slip distribution based on
GPS and tsunami observations [Simons et al., 2011]. The
largest slip in the model concentrates on the seamount, with
the peak value of 45 m, where significantly large stress
drop (up to 50 MPa) occurs (Figures 3c, 3d, and 6b).
[33] Significant shallow slip (i.e., >25 m) near the trench
just updip of the seamount occurs in the preferred model
(Figure 6a). This suggests that it is not necessary for the
shallow part of the subduction zone to accumulate elastic
Figure 6. Distributions of (a) slip distribution, (b) stress drop, (c) rupture time, and (d) peaks slip velocity
on the fault plane from the preferred spontaneous rupture model for the 2011 Mw 9.0 Tohoku-Oki earthquake. White star denotes the hypocenter. Two white dashed lines denote boundaries between velocity
strengthening behavior at top and bottom and velocity weakening behavior in between on the fault plane.
White rectangle denotes the seamount outline.
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Figure 7. The moment rate function from the preferred
spontaneous rupture model of the 2011 Mw 9.0 TohokuOki earthquake.
strain before the 2011 event, even though large fault slip and
seafloor displacements may have occurred there during the
event. In the model, md is set to be larger than ms on the
shallow part of the fault plane (Region A in Figure 2 and
Table 2), and thus primarily negative stress drop (thus
energy sink) is associated with this portion (Figures 3c
and 6b). Large slip there observed in the model is primarily
driven from below by strong slip pulses from broken of the
seamount, and is further aided by broken of seafloor and free
surface effects [Oglesby et al., 1998]. The shallow large slip
is associated with a small positive stress-drop patch within
the largely negative stress drop region (Figures 3c and 6b).
The positive stress drop near the free surface in Region A
in the model is likely a manifestation of dynamic overshoot
(e.g., final shear stress being below sliding shear stress)
[Oglesby and Day, 2001]. Our numerical experiments (not
shown) suggest the amplitude of shallow slip is sensitive to
the difference between md and ms in Region A, which represents how strong velocity-strengthening is: larger difference (i.e., stronger velocity-strengthening) results in smaller
shallow slip. For example, when we increase md from 0.42
to 0.5 for Region A without changes in other aspects of
the model (not shown), the maximum slip in Region A is
below 15 m.
[34] The preferred spontaneous rupture model suggests the
seamount, which might act as a barrier at the early stage and
an asperity with large slip later in the 2011 event, has a
dimension of 70 km along strike by 23 km along dip.
The total seismic moment from the preferred model is
4.6 1022N ⋅ m and Mw is 9.08, comparable with those
reported from kinematic inversions [e.g., Simons et al.,
2011; Ide et al., 2011; Shao et al., 2011].
4.4. High-Frequency Radiations
[35] HF radiations during an earthquake are mostly generated by sudden changes of rupture velocity [Madariaga,
1977]. Spatial variations of rupture velocity are strongly
coupled to spatial variations of peak slip velocity [Day,
1982]. Thus, we examine the distribution of peak slip
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velocity on the fault plane from the preferred model
(Figure 6d) to gain some physical insights into HF radiations
in the 2011 event. We remark that there are other ways
of quantifying the high-frequency versus low-frequency
slip (e.g., Y. Huang et al., A dynamic model of the frequency-dependent rupture process of the 2011 Tohoku-Oki
earthquake, submitted to Earth, Planets and Space, 2012).
Nevertheless, our purpose in this study on this issue is to
examine effectiveness of several factors in generating highfrequency radiations. We do not attempt to reproduce details
of the HF radiation feature observed in the event. Therefore,
in the preferred model, we arbitrarily introduce three highstrength patches (Region F) and one high-stress patch
(Region G) (see Figure 2 and Table 2) on the downdip portion of the fault plane for our purpose. Together with the
bottom boundary between velocity-weakening and velocitystrengthening frictional behaviors (i.e., the brittle-ductile
transition zone), they are expected to be the sources of HF
radiations from the deep part of the fault in the model. Notice
that large variations, not large values themselves, in peak slip
velocity indicate good sources of HF radiations. Figure 6d
demonstrates that high-strength patches are very effective
in generating HF radiations. The brittle-ductile transition
zone is less effective, while high-stress patches are least
effective. Thus, strong HF radiations from the downdip portion reported from kinematic studies [e.g., Simons et al.,
2011; Ide et al., 2011; Meng et al., 2011; Koper et al.,
2011; Wang and Mori, 2011] may suggest a very heterogeneous strength distribution on this portion of the subducting
plane before the 2011 event. Some candidates for highstrength patches there may be fragments of subducting seamounts and bending of the subducting plate.
[36] Failure of the seamount results in large variations in
peak slip velocity in the preferred model (Figure 6d), which
could be a source of strong HF radiations. Although dominantly from the downdip portion in the 2011 event, HF
radiations from the region near the hypocenter are also
reported [e.g., Simons et al., 2011]. Broken of the seafloor
may also radiate HF seismic waves (Figure 6d). However,
this source of HF radiations near the trench may be limited
to a narrow region, i.e., just updip of the seamount. Furthermore, when we increase md from 0.42 to 0.5 in Region A
(i.e., stronger velocity strengthening), variations in peak slip
velocity (thus HF radiations) near the trench are significantly
reduced (not shown).
4.5. Seafloor Deformation
[37] The preferred spontaneous rupture model produces
seafloor displacements that match the observations [Sato
et al., 2011] at two near-epicenter stations (MYGI and
MYGW, see Figure 1 for location) extremely well (Table 3).
Displacements at these two stations should be most sensitive
to slip distribution near the hypocenter. Thus, this suggests
that concentrated slip with a peak value of 45 m near
the hypocenter in the preferred spontaneous rupture model
may be robust. Matches in both the horizontal and vertical
displacements at the two stations suggest the 10 fault dip
in the model characterizes the fault geometry near the
hypocenter well. The hypocenter depth in the model is
18.58 km, which is between a relocated hypocenter depth
(i.e., 14.50 1.21 km) using a 3D velocity structure [Zhao
et al., 2011] and the JMA hypocenter depth (i.e., 24.0 km)
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Table 3. Comparison of Seafloor Displacements Between the
Observed and the Simulated From the Preferred Spontaneous
Rupture Model at Five Stationsa
Horizontal
Displacement (m)
Vertical
Displacement (m)
Station
Observed
Simulated
Observed
Simulated
MYGI
MYGW
KAMS
KAMN
FUKU
24
15
23
15
5
23.8
15.0
20.0
15.1
5.5
3
0.8
1.5
1.6
0.9
2.5
0.7
5.2
4.3
1.3
a
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due to simplifications in the model, in particular in fault
geometry. Larger vertical displacements from the model
than the observed at the two stations (KAMS, KAMN) to the
north of the epicenter suggest the subduction plane may
have an shallower dip (i.e., <10 ) to the north. The reversed
sense of the vertical displacement at FUKU to the south may
be attributed to a large mismatch between the fault surface
trace in the model and the actual location of the trench
(Figure 1). Nevertheless, both the matches and mismatches
between the outputs from the preferred model and the
observations allow us to gain insights into slip distribution
on the source fault and fault geometry.
Observations are from Sato et al. [2011]. See Figure 1.
for the 2011 main shock. Time histories of seafloor velocity
and displacement at the two stations from the model exhibit
how seafloor near the epicenter might have shaken during
the 2011 main shock (Figure 8). Horizontal peak velocity
normal to the fault strike at the epicenter (MYGI) reaches
2 m/s (negative meaning toward the trench). MYGI exhibits
more high-frequency contents than MYGW.
[38] Horizontal displacements from the model at the other
three stations (KAMS, KAMN, FUKU, Figure 1) also fit
well with the observations (Table 3). Large misfits in the
vertical displacement at the three stations (Table 3) may be
5. Discussion
[39] In this section, we first report a companion spontaneous rupture model, and then discuss applications of
spontaneous rupture models in improving our understanding
of megathrust earthquakes in subduction zones.
5.1. A Companion Spontaneous Rupture Model
[40] The critical role a subducting seamount may have
played in the 2011 main shock demonstrated by the preferred
spontaneous rupture model above can be further corroborated
by a companion spontaneous rupture model. In the
Figure 8. Time histories of seafloor velocity and displacement from the preferred spontaneous rupture
model at two seafloor stations where seafloor displacements are reported [Sato et al., 2011]. Positive
values in this plot mean NNE motion along strike, NWW motion normal to strike, and upward motion
vertically.
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Figure 9. (a) Slip distribution and (b) rupture time on the fault plane of a companion spontaneous rupture
model, in which the seamount is longer and stronger than that in the preferred model. White rectangle
denotes the seamount outline. White star denotes the hypocenter. Without failure of this longer and stronger seamount, the rupture is confined within a much smaller area, resulting in a much smaller earthquake
(i.e., Mw = 7.8).
companion model, we extend the lateral dimension of the
seamount to be x ∈ [60 km, 70 km] and increase the static
friction at the middle of the seamount to be ms = 0.8. These
two quantities in the preferred model are x ∈ [30 km,
40 km] and ms = 0.7, respectively. All other aspects of the
companion model are same as those in the preferred model.
In the companion model, the seamount does not break
(Figure 9). Although the initial stress condition on other parts
of the fault plane are the same between the two models,
without failure of this larger seamount, the rupture in the
companion model is confined within a much smaller area,
resulting in a much smaller earthquake (i.e., Mw = 7.8),
which is the size of typical historical earthquakes in this
region. This suggests that the 2011 Mw 9.0 Tohoku-Oki
earthquake may be primarily failure of a seamount with a
dimension of 70 km by 23 km. One would imagine that a
larger megathrust earthquake (i.e., Mw > 9.1) may result
from failure of the larger seamount in the companion model.
[41] As discussed earlier, subducting seafloor topographic
features, including seamounts, have been reported to play
important roles in previous great subduction zone earthquakes [e.g., Bilek, 2007; Das and Watts, 2009], primarily
based on kinematic source models. To our knowledge, this
work may be the first from a dynamic point of view to
demonstrate critical roles subducting seamounts may play in
megathrust earthquakes. Spontaneous rupture models in this
study reveal physical conditions that allow a subducting
seamount to act as a barrier at the early stage and to eventually become an asperity with high slip later in an event, as
reported previously [e.g., Bilek, 2007; Das and Watts, 2009].
They also demonstrate that failure of a large seamount can
drive a rupture to penetrate into the velocity-strengthening
shallow portion near a trench and low-stress-drop surrounding areas on a subduction plane, resulting in a giant
megathrust earthquake. Whether or not a large subducting
seafloor feature fails in an earthquake may determine the
final size of the event. Therefore, mapping subducting seafloor features in a subduction zone may provide some
important clues about the maximum size of future megathrust earthquakes, which appears to be critical in hazards
mitigation, as demonstrated by the 2011 earthquake and its
catastrophic consequences.
5.2. Investigations of Megathrust Earthquakes Using
Spontaneous Rupture Models
[42] Advance in geophysical networks over the past
decades has led to capturing geophysical signals associated
with earthquake rupture with increasing fidelity. Kinematic
source inversions have been playing important and dominant
roles in utilizing these signals to constrain earthquake rupture processes and slip distributions in large earthquakes.
Further studies using spontaneous rupture models are needed
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to gain physical insights into dynamic rupture propagation,
seismic radiations, and ground motion excitation. 3D spontaneous rupture modeling studies have been conducted for
some of recent large earthquakes, such as the 1992 Landers
[e.g., Olsen et al., 1997; Aochi and Fukuyama, 2002], the
1999 Hector Mine [e.g., Oglesby et al., 2003], the 1999
Izmit, Turkey [e.g., Harris et al., 2002], the 1999 Chi-Chi
[e.g., Oglesby and Day, 2001], the 2002 Denali fault, Alaska
[e.g., Aagaard et al., 2004; Oglesby et al., 2004], and the
2008 Wenchuan, China [e.g., Duan, 2010b] earthquakes.
These studies have gained physical insights into some
rupture and/or ground motion characteristics of these earthquakes. However, these earthquakes primarily occurred on
continents, with the moment magnitude ranging from 7 to 8.
Very few spontaneous rupture modeling studies have been
performed for megathrust earthquakes along subduction
zones, probably because of challenges imposed by shallowdipping fault geometry and huge rupture areas in these Mw 9
or above earthquakes.
[43] Initial stress and strength conditions may be least
constrained input parameters for spontaneous rupture models, while they may also be the most critical physical quantities that control dynamic earthquake rupture and seismic
radiations, including the rupture extent and thus the final size
of an earthquake. Their distributions on the fault plane can
be very heterogeneous, or relatively smooth. For example,
the fact that high-frequency seismic radiations were dominantly from the downdip portion in the 2011 Tohoku-Oki
main shock [e.g., Simons et al., 2011; Ide et al., 2011; Meng
et al., 2011; Koper et al., 2011; Wang and Mori, 2011]
suggests that the initial strength and/or stress distributions
(particularly the strength distribution) on the downdip portion may be very heterogeneous, while they may be relatively smooth on the updip portion. As demonstrated in this
study, we may be able to infer initial stress and strength
conditions for megathrust earthquakes through spontaneous
rupture modeling, by integrating what we understand about
the stress and strength state in the crust and upper mantle
with rupture propagation and slip distribution characteristics
revealed by kinematic studies, and near-field seismic and
geodetic recordings. More spontaneous rupture modeling
studies on recent megathrust earthquakes, such as the 2004
Sumatra earthquake, may allow us to gain some insights into
characteristics of initial stress and strength distributions
before giant megathrust earthquakes.
[44] From a physical point of view, spontaneous rupture
models can unify a variety of characteristics of earthquake
rupture propagation and seismic radiations revealed by
kinematic inversions and near-field recordings. As such, they
are able to not only provide physical insights into these
characteristics, but also help resolve discrepancies among
different kinematic studies. For example, our preferred
spontaneous rupture model for the 2011 earthquake demonstrates that significant slip (e.g., >25 m in the model) can
occur near the Japan trench, even if the shallow portion of the
subducting plane is velocity-strengthening (approximated by
md > ms in the slip-weakening law). However, the model
suggests that the largest slip patch is near the hypocenter (i.e.,
just updip of the hypocenter), not near the trench, though
kinematic inversions suggest both views can fit available
data. As discussed in the model setup, the feature that the
rupture did not propagate upward before 40 s suggests a
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high-strength patch just updip of the hypocenter. No significant historical earthquakes there suggests the patch had
accumulated large elastic strain before the 2011 rupture,
which should result in large stress drop and thus large slip in
the 2011 event. Furthermore, relatively weak HF radiations
from the shallow portion of the fault [e.g., Simons et al.,
2011; Ide et al., 2011; Meng et al., 2011; Koper et al.,
2011; Wang and Mori, 2011] strongly suggests that the
shallow portion may be indeed velocity-strengthening. By
unifying these rupture propagation and seismic radiation
characteristics and near-field recordings, our preferred spontaneous rupture model suggests that the largest slip occur
near the hypocenter, with significant slip near the trench
confined in a limited region in the 2011 event.
[45] Spontaneous rupture modeling of giant megathrust
earthquakes is challenging. In this study, we assume planar
fault geometry and 1D velocity structure and parameterize
the seamount to simplify finite element mesh generation.
These approximations are justified as we aim to gain physical insights into some of first-order features of the 2011
event in this study. The subducting plane is likely non-planar
along both downdip and strike directions. 3D velocity
structure may be important in high-frequency seismic wave
propagation. The seamount geometry (i.e., a large bump on
the fault plane) can induce additional normal stress variations on the fault plane during dynamic rupture. More heterogeneous strength/stress conditions on the deep portion
of the subducting plane are needed to reproduce deep HF
radiations. These factors need to be taken into account in
future spontaneous rupture models of the 2011 earthquake to
fully capture features observed in the event and to fit available near-field seismic and geodetic recordings.
6. Conclusions
[46] 3D spontaneous rupture modeling of the 2011 Mw
9.0 Tohoku-Oki earthquake, based on rupture propagation
and seismic radiation features revealed by kinematic inversions and seafloor displacements observed near the epicenter, suggests that the event may be primarily failure of
a subducting seamount just updip of the hypocenter. High
strength of the seamount stalls the updip rupture propagation
for tens of seconds, and high stress drop associated with it
results in the large slip patch. Failure of the seamount drives
the rupture to penetrate into likely the velocity-strengthening
shallow portion and to propagate into low stress-drop deep
parts of the subducting plane. Without failure of the seamount, the rupture would be limited in a small area, resulting
in a much smaller earthquake. The preferred spontaneous
rupture model of the event suggests the seamount has a
dimension of 70 km by 23 km on the subducting plane.
[47] 3D spontaneous rupture models also demonstrate that
significant slip can occur near the trench, even if the shallow
portion of the subducting plane is velocity strengthening and
experiences stable sliding without strain accumulation before
the event. Strong slip pulses from failure of the seamount and
free surface effects associated with shallow dipping fault
geometry play key roles in this phenomenon. However, significant slip near the trench may be confined in a limited area,
i.e., just updip of the hypocenter.
[48] Unifying a variety of features revealed by kinematic inversions and near-field observations from a physical
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point of view, spontaneous rupture modeling of the 2011
Tohoku-Oki event provides physical insights into rupture
propagation, slip distribution, seismic radiations, and nearfield deformation fields of the event. Parallel computing,
which allows a large suite of spontaneous rupture models to
be simulated on modern supercomputers effectively, facilitates this investigation. It will play more and more important
roles in future investigations of large earthquakes, in particular, giant megathrust earthquakes at subduction zones.
[49] Acknowledgments. This work is supported by NSF grant
EAR-1015597. Comments from the Associate Editor and two anonymous
reviewers improved the manuscript significantly. The author acknowledges
the Texas A&M supercomputing facility (http://sc.tamu.edu/) and the
Extreme Science and Engineering Discovery Environment (XSEDE)
(https://www.xsede.org/) for providing computing resources used in this
work. XSEDE is supported by NSF grant OCI-1053575.
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