Dynamic Source Model for the 2011 Tohoku Earthquake in a Wide Period Range Combining

Slip Reactivation with the Short-Period Ground Motion Generation Process

PERCY GALVEZ,1,4 ANATOLY PETUKHIN,2 KOJIRO IRIKURA,3 and PAUL SOMERVILLE4

Abstract—This paper describes a validated dynamic rupture

model of the 2011 Tohoku earthquake that reproduces both long-

period (20–100 s) and short-period (3–20 s) ground motions. In

order to reproduce the observed large slip area (slip asperity), we

assign a large Dc (slip critical distance) area following kinematic

source inversion results. Sufficiently large slip is achieved through

rupture reactivation by the double-slip-weakening friction model.

In order to reproduce the strong-motion generation areas (SMGAs),

we assign short Dc and large stress-drop areas following empirical

Green’s function (EGF) simulation results, which indicate that,

although more distant from the hypocenter, SMGA1 ruptured

earlier than SMGA2 or SMGA3, which are closer to the

hypocenter. This observation is confirmed by the backprojection

method. In order to reproduce this important feature in dynamic

simulation results, we introduce a chain of small high stress-drop

patches between the hypocenter and SMGA1. By systematic

adjustment of stress drops and Dc, the rupture reproduces the

observed sequence and timing of SMGA ruptures and the final slip

derived by kinematic models. This model also reproduces the

multiseismic wavefront observed from strong ground motion data

recorded along the Pacific coast of the Tohoku region. We compare

the velocity waveforms recorded at rock sites along the coastline

with one-dimensional (1D) synthetic seismograms for periods of

20–100 s. The fit is very good at stations in the northern and central

areas of Tohoku. We also perform finite-difference method (FDM)

simulations for periods of 3–20 s, and confirm that our dynamic

model also reproduces wave envelopes. Overall, we are able to

validate the rupture process of the Tohoku earthquake.

Key words: 2011 Tohoku earthquake, dynamic simulation,

rupture propagation, slip reactivation.

1. Introduction

The 11 March 2011, Mw 9 Tohoku earthquake

occurred in the subduction zone between the Pacific

and North American Plates in northeastern Honshu,

Japan. This giant event was recorded by a vast Global

Positioning System (GPS) and seismic network. The

Tohoku earthquake featured complex rupture patterns

involving multiple rupture fronts. Numerous source

models have been generated using extensive tele-

seismic, GPS, strong ground motion, and tsunami

data (see reviews by Tajima et al. 2013; and Lay

2017 for the most recent results).

Visual inspection of the short-period strong

ground motion recorded by the K-NET and KiK-net

networks and the high-rate 1-Hz GPS long-period

displacements recorded by the GEONET network

along the Japanese coast clearly show several groups

of waves. Two long-period groups of waves (S1 and

S2 in Fig. 1) arrived about 40–50 s apart in both the

Miyagi and Iwate regions. A third group of waves (S3

in Fig. 1) was observed further south in the Ibaraki

and Chiba regions. The short-period ground motions

had a more complicated pattern: five wave packets

(WP1–WP5 in Fig. 1) were identified by Kurahashi

and Irikura (2013). These observations indicate that

the Tohoku earthquake featured complex rupture

patterns involving multiple rupture fronts. Using the

empirical Green’s function (EGF) method (Hartzell

1978; Irikura 1986), Kurahashi and Irikura

(2011, 2013) found that these multiple wavefronts

were generated by strong ground motion areas

(SMGAs) located in the deep region of the plate

interface. SMGAs were introduced by Miyake et al.

(2001, 2003) as extended areas of relatively large slip

velocity (slip rate) that reproduce the observed

1 King Abdullah University of Science and Technology

(KAUST), Thuwal, Saudi Arabia. E-mail: percy.galvez.barron@

gmail.com2 Geo-Research Institute, Osaka, Japan. E-mail: anatolyp

@geor.or.jp3 Aichi Institute of Technology, Toyota, Japan.4 AECOM, Los Angeles, USA.

Pure Appl. Geophys. 177 (2020), 2143–2161

� 2019 Springer Nature Switzerland AG

https://doi.org/10.1007/s00024-019-02210-7 Pure and Applied Geophysics

ground motions in the relatively high frequency range

of 0.2–10 Hz. In this frequency range, SMGAs have

been identified by the EGF method. They also found

that the stress drop in SMGAs is high, on the order of

10–20 MPa for crustal earthquakes, and due to larger

depth can be even higher for subduction earthquakes

(e.g., 20–25 MPa for the Tohoku earthquake, see

Kurahashi and Irikura 2013).

There is strong evidence that the fault regions that

generate short-period and long-period wave radiation

during a given earthquake are spatially distinct. The

most direct observations of this phenomenon have

been obtained for large subduction earthquakes, for

which the combination of geodetic, tsunami, strong

motion, and teleseismic data [including backprojec-

tion of short-period (SP) teleseismic data from large

arrays] provides adequate spatial resolution on the

location of slip at different frequencies (examples for

the Tohoku 2011 earthquake include Kubo et al.

2013; Yoshida et al. 2011; Kurahashi and Irikura

2013 among others). Other related observations

include a lack of coincidence between the timing of

long- and short-period wave amplitudes in teleseis-

mic data (e.g,. Gusev et al. 2006). Statistical analysis

of kinematic finite source models inferred from

geophysical data reveals that areas of large final slip

(long-period generation areas) and areas of large peak

slip rate (short-period generation areas or SMGAs)

are spatially distinct (Simons et al. 2011; Meng et al.

2011; Huang et al. 2012, 2014; Galvez et al.

2014, 2016; Avouac et al. 2015). This feature has

important implications for procedures adopted for the

Figure 1a Green and red squares show seismic and GPS stations, respectively. Red arrows indicate coseismic displacements generated during the

Tohoku earthquake. b High-rate continuous GPS records sampled at 1 Hz from the GEONET network. Transparent red lines delineate the first

(S1) and second seismic wavefronts (S2) observed in the records. The green line (S3) highlights the third pulse observed in the southern part.

c The strong ground motion recorded from (Kik-net and K-NET) networks between 0 and 3 Hz. Colored lines denote wave packets WP1–

WP5 identified by Kurahashi and Irikura (2013)

2144 P. Galvez et al. Pure Appl. Geophys.

prediction of strong ground motion. In particular, it is

not incorporated into many kinematic/stochastic

source models developed for engineering applications

that assume that short-period radiation is uniformly

distributed over the rupture area or correlated with

the spatial distribution of final slip (e.g., Somerville

et al. 1999; Irikura and Miyake 2001).

One plausible explanation for the discrepancy

between short-period and long-period generation

areas is based on the spatial heterogeneity of stress

and strength (frictional parameters) along the fault. In

fundamental models of earthquake dynamics based

on classical fracture mechanics, short-period radia-

tion is most efficiently generated by abrupt changes

of rupture speed (e.g., Madariaga 1977; Pulido and

Dalguer 2009) induced by the residual stress con-

centrations left by previous slip events, or by sharp

spatial contrasts of fracture energy due to hetero-

geneities of friction properties or effective normal

stress (Huang et al. 2012, 2014; Galvez et al.

2014, 2016). Short-period radiation is also enhanced

by short rise time (the duration of slip at a given point

on the fault, e.g., Nakamura and Miyatake 2000;

Hisada 2000, 2001; Guatteri et al. 2003) which can

be controlled by a number of processes, such as

frictional velocity-weakening parameters (short Dc),

characteristic width of asperities, and thickness of a

damaged fault zone (Heaton 1990; Perrin et al. 1995;

Beroza and Mikumo 1996; Huang and Ampuero

2011).

We conclude that the rupture dynamics of an

SMGA can be modeled as an asperity (short Dc area)

with a high stress drop Dr. The effectiveness of this

model for the Tohoku 2011 earthquake was demon-

strated by Galvez et al. (2014, Fig. 12). Yoshida

et al. (2012) estimated distributions of peak slip rate,

Dr, Dc and strength excess Se from the kinematic

source inversion (Yoshida et al. 2011) of the Tohoku

2011 earthquake. They confirmed that areas of high

slip rate (SMGAs) are associated with areas of high

Dr and short Dc, as well as with areas of small Se.

Galvez et al. (2014) presented a conceptual min-

imalistic dynamic rupture model of the 2011 Mw 9.0

Tohoku earthquake, including a nonplanar plate

interface with heterogeneous frictional properties and

initial stresses. The model is consistent with depth-

dependent frequency content of slip, where the

shallow part radiates coherent energy at long periods

(LP; kinematic source inversions, tsunami models)

while the deep part radiates at short periods (back-

projection of SP radiation). The deep SP radiation is

interpreted as the rupture of high stress drop patches

in the bottom part of the seismogenic zone of the

megathrust (e.g,. Huang et al. 2012; Lay et al. 2012).

The model parameters are assigned by systematic

trials, taking as a starting point the two-dimensional

(2D) dynamic rupture models developed by Huang

et al. (2014). The simulation results of Galvez et al.

(2014) qualitatively reproduce the depth-dependent

frequency content of the source and the large slip

close to the trench observed in the Tohoku

earthquake.

At the next step, Galvez et al. (2016) developed a

new rupture reactivation model based on a double-

slip-weakening friction law similar to that introduced

by Kanamori and Heaton (2000). These authors

proposed that melting or fluid pressurization induced

by frictional heating can reduce fault strength for a

second time once slip exceeds a certain critical slip

distance (Dr). They argued that, when superimposed

onto the conventional (isothermal) slip-weakening

process with shorter critical slip distance (Dc), these

thermally activated weakening mechanisms lead to a

slip-dependent friction model with two sequential

strength drops. They showed that this model produces

(1) a rupture pattern consistent with a kinematic

source inversion model that features rupture reacti-

vation and (2) ground motion patterns along the

Japanese coast consistent with the observations,

namely two groups of long-period seismic waves (S1

and S2 in Fig. 1).

In order to reproduce the large rupture extent and

the depth-dependent frequency content qualitatively,

Galvez et al. (2014, 2016) used cloudy distributions

of high stress drop patches in the deep part of the

megathrust, following the backprojection results of

Meng et al. (2011). In contrast, Kurahashi and Irikura

(2011, 2013), as well as Asano and Iwata (2012),

Satoh (2012), and Kawabe and Kamae (2013), used

empirical Green’s function (EGF) simulations and

demonstrated that strong ground motions can be

reproduced by a model having only five compact

SMGAs, numbered SMGA1–SMGA5 in accordance

with their rupture time.

Vol. 177, (2020) Dynamic Source Model for the 2011 Tohoku Earthquake in a Wide Period Range 2145

From the rupture dynamics point of view, a

paradox in the EGF results is that the hypocenter,

SMGA1, and SMGA3 are located approximately on

the same east–west line but in reverse order of tim-

ing: SMGA1, which ruptured first, is far from the

hypocenter, while SMGA3, which is between the

hypocenter and SMGA1, ruptured after SMGA1, as

shown in Fig. 2. This kind of reverse rupturing of

SMGAs was also observed during other earthquakes,

including the 2007 Niigata-ken Chuetsu-oki earth-

quake in Japan (Kamae and Kawabe 2008). It has a

strong influence on rupture directivity effects, which

strongly increase strong ground motions; so it is

important to find a physical explanation for this

dangerous phenomenon.

In this study, we enhance the dynamic model of

the 2011 Tohoku earthquake developed earlier by

Galvez et al. (2014, 2016) in order to obtain agree-

ment between the EGF modeled and the dynamically

modeled SMGA rupture time, especially the reverse

rupturing of SMGA1 and SMGA3. We also seek

agreement between dynamically modeled slip and the

slip distribution estimated by kinematic source

inversion [so that the short-period (SMGAs) and

long-period (slip asperity) content of the source is

reproduced], and agreement between simulated and

recorded strong motion waveforms, which could

validate the dynamic rupture model that we develop.

The improved dynamic model of the 2011 Tohoku

earthquake has five SMGAs in the deeper part (con-

sistent with Kurahashi and Irikura 2013) and one

large slip area in the shallower part of the fault

adjacent to the trench (consistent with kinematic

source inversion results that are validated by the

tsunami simulations).

Our goal is to understand the mechanical origin of

the phenomenon at a sufficient level to provide a

physical basis for the formulation of simplified

methods to account for distinct short- and long-period

slip in kinematic or pseudodynamic earthquake

source generation algorithms for engineering ground

motion prediction. This study employs results of

studies of Galvez et al. (2016) for the slip reactiva-

tion, of Meng et al. (2011) for the backprojection,

and of Kurahashi and Irikura (2013) for the EGF

simulation.

2. Dynamic Model Settings

The tool used to simulate the rupture process of

the 2011 Tohoku earthquake is SPECFEM3D with

the recent dynamic rupture module implemented by

Galvez et al. (2014). In order to simulate dynamic

earthquake rupture and strong ground motion in

realistic models that include crustal heterogeneities

and complex fault geometries, which is an important

goal of computational seismology, Galvez et al.

(2014) incorporate dynamic rupture modeling capa-

bilities into a spectral element solver on unstructured

meshes, the 3D code SPECFEM3D (Peter et al.

2011). This tool provides high flexibility in repre-

senting fault systems with complex geometries,

including nonplanar faults and sharp wedges. The

139 140 141 142 143 144 14535

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37

38

39

40

41

Figure 2Distribution of SMGA areas of the 2011 Tohoku earthquake.

Rectangular areas are SMGAs according to the EGF analysis of

Kurahashi and Irikura (2013, red), Asano and Iwata (2012, green),

Kawabe and Kamae (2013, blue), and Satoh (2012, light blue). The

numbers assigned to the SMGAs correspond to their rupture

sequence. Arrows indicate reverse sequence from SMGA1 to

subsequent SMGA2 or SMGA3. The star marks the earthquake

epicenter

2146 P. Galvez et al. Pure Appl. Geophys.

domain size is extended with progressive mesh

coarsening to maintain an accurate resolution of the

static field.

Following the asperity model presented by Galvez

et al. (2016), we present a minimalistic dynamic

rupture model with slip reactivation. The main goal

of Galvez et al. (2016) was to show that the double

slip-weakening friction in the form proposed by

Kanamori and Heaton (2000) offers a plausible model

for the rupture process of the 2011 Tohoku earth-

quake, including large shallow slip, rupture

reactivation, and large rupture extent. They presented

evidence supporting this friction model, obtained

from seismological observations, laboratory experi-

ments, and theoretical considerations. Then, they

extended the dynamic rupture model developed by

Galvez et al. (2014) by modifying the slip-weakening

friction model to account for rupture reactivation.

The intraslab fault geometry is adapted from

Simons et al. (2011), taking into account the folded

slab interface including the small dip angles of the

wedge close to the trench. The state-of-the-art

unstructured mesh software CUBIT provides a pow-

erful tool to deal with geometrical complexities. We

use these capabilities to perform dynamic rupture

simulation for the Tohoku earthquake including the

nonplanar slab interface and small dip angles (\ 5�)found in the trench wedge; see Fig. 3. The velocity

structure is a 1D layered medium taken from

Fukuyama et al. (1998); see Table 1. Based on this

nonplanar fault geometry, we assign asperities and

SMGAs following the source inversion results and

gradually modify the asperity distribution.

To create more slip in the shallow regions, the

main asperity is moved closer to the trench in com-

parison with Galvez et al. (2016). Many kinematic

models have been generated by seismic inversion for

the 2011 Tohoku earthquake, and most of them

unequivocally reveal a shallow region (\ 20 km) of

large slip ([ 40 m) close to the trench (e.g., Lee et al.

2011; Yue and Lay 2011; Suzuki et al. 2011; Yagi and

Fukahata 2011; Yoshida et al. 2011; Wei et al. 2012).

Models of this type are supported by tsunami inver-

sion (e.g., Satake et al. 2013; Gusman et al. 2012) or

are able to reproduce the tsunami by themselves (e.g.,

Yamazaki et al. 2013; Petukhin et al. 2017). Here, we

follow the final slip model of Lee et al. (2011) (see

Fig. 7) and place a semielliptical asperity closer to the

trench, delimiting the region of large slip (Fig. 4).

In deeper regions between 30 and 50 km depth,

short-period radiation has been detected by EGF tech-

niques (e.g., Kurahashi and Irikura 2011, 2013; Asano

and Iwata 2012) and also backprojection techniques

(e.g., Meng et al. 2011; Ishii 2011; Yagi et al. 2012),

possibly explained by the presence of prior small

asperities from historical earthquakes (Ide and Aochi

2013) that broke again during the Tohoku earthquake.

We place deep asperities on the detected SMGAs, close

to the positions identified by Kurahashi and Irikura

(2013) and other researchers; see Fig. 4.

The slip weakening friction law is assumed. By the

systematic adjustment of stress drops and slip critical

distance (Dc) values, the rupture reproduces the final

slip derived by kinematic models (e.g., Suzuki et al.

2011; Lee et al. 2011). Around 20 models are inves-

tigated in total. Among them, the strength excess

(= static friction coefficient 9 normal stress - initial

stress) and the nominal stress drop (= initial

stress - dynamic friction coefficient 9 normal

stress) are systematically tuned to reproduce the rup-

ture sequence of SMGAs in the down dip region and

the kinematic source models in the shallow region.

Figure 4 shows the strength excess and the nom-

inal stress drop, and Fig. 5 shows the frictional

parameter settings, Dc and the static friction coeffi-

cient, used in this study. Other friction parameters are

the normal stress and the dynamic friction coefficient.

Their distributions are mostly uniform: normal

stress = 100 MPa and dynamic friction coeffi-

cient = 0.2, except in the (shallow) trench wedge area

(see Fig. 3). Inside the trench wedge area close to the

trench, normal stress increases linearly from 46 MPa

near the surface to 100 MPa at depth of 10 km, and

remains constant bellow 10 km depth. The dynamic

friction coefficient decreases linearly from 0.26 near

the surface to 0.2 at depth of 10 km, and remains

constant below 10 km depth.

3. Friction Model Settings for Asperity A: Slip

Reactivation

Following Galvez et al. (2016), reactivation by

the double-slip-weakening friction model is

Vol. 177, (2020) Dynamic Source Model for the 2011 Tohoku Earthquake in a Wide Period Range 2147

considered in this study. Evidence of a slip reacti-

vation process, first proposed by Kanamori and

Heaton (2000), has been reported by Lee et al. (2011)

for the Tohoku earthquake, and by laboratory rock

experiments (O’Hara et al. 2006), although the rele-

vance of the experimental material to the fault

material is unclear. According to this experiment,

during faulting, the fault surfaces reach high tem-

perature and decay, emanating CO2 (by thermal

decomposition). This thermal decomposition process

generates nanolayers of soft material, weakening the

fault once again. The experiment recorded four stages

of friction. In stage I and II, the friction coefficient

decreases (first weakening) during the first 2–5 m of

slip. In stage III, the friction initially remains con-

stant, but after 20–25 m of slip, a second reduction in

friction occurs. This second drop of friction may have

produced the slip reactivation process that evidently

occurred during the Tohoku earthquake. The slip

associated with the second reduction of friction dur-

ing stage III leads to a reliable estimate of Dr.

Experiments on a more relevant granitic rock were

carried out recently by Chen et al. (2017). These

experiments also reveal a second friction drop due to

melting at large slip.

Figure 3a The blue nonplanar interface adapted from Simons et al. (2011) is the fault geometry used in our model. The vertical brown plane is the

vertical section of the volume meshed by CUBIT. b ‘‘PQ’’ is a profile cutting the mesh. The rectangle ‘‘R’’ is a zoom in of the shallow wedge

region close to the trench. Tiny angles (\ 5�) could be meshed

Table 1

One-dimensional velocity structure used in dynamic simulation

(Fukuyama et al. 1998)

Thickness

(m)

P velocity (m/s) S velocity (m/s) Density (kg/

m3)

3000 5500 3140 2300

15,000 6000 3550 2400

15,000 6700 3830 2800

67,000 7800 4460 3200

Inf 8000 4570 3300

2148 P. Galvez et al. Pure Appl. Geophys.

Figure 4a The nominal stress drop distribution. The ellipses labeled ‘‘SMGA1’’ to ‘‘SMGA5’’ are located on the SMGA regions found by Kurahashi

and Irikura (2013). Asperity A is placed on a region of large slip revealed by the kinematic models. The chain of two high stress drop spots

(rupture bridge) between the rupture initiation area (orange-colored spot inside asperity A) and SMGA1 is introduced in order to drive rupture

to SMGA1 first in accordance with the rupture sequence in Figs. 1 and 2. b The strength excess distribution

Figure 5Slip critical distance Dc a and friction law b used in the model. The asperity (A) follows a slip weakening distance friction with two stress

drop steps. In this constitutive friction law, the stress drops a second time once the slip reaches a critical distance (Dr). Dr = 20 m is prescribed

on the main asperity A and not on the other asperities. In the deeper asperities, a slip weakening friction law is prescribed with only one stress

drop step. c Static friction coefficient. For other frictional parameters see text

Vol. 177, (2020) Dynamic Source Model for the 2011 Tohoku Earthquake in a Wide Period Range 2149

The kinematic model of Lee et al. (2011) shows a

predominant repeating slip patch close to the

hypocenter. This model inverted teleseismic, local

dense strong ground motion, and near-field coseismic

geodetic data covering a broad frequency range that

allowed the details of the megathrust earthquake

rupture to be resolved. The inversion method made

use of multiple time windows and took advantage of

robust data and powerful parallel computing tech-

niques to achieve a high-resolution source inversion.

Lee’s model shows a slip reactivation on the largest

asperity close to the trench. To illustrate the rupture

reactivation, Galvez et al. (2016) took a sequence of

slip-velocity snapshots and stacked the slip velocity

on the fault at locations crossing the hypocenter. The

stacking of slip velocities along these locations

reveals two ruptures, both initiating close to the

hypocenter, separated by about 40–50 s. The first

rupture propagates mainly towards the trench and the

second rupture propagates bilaterally, with one front

moving towards the trench and the other front moving

down-dip.

Galvez et al. (2016) also computed the dynamic

fault stress changes implied by the Lee et al. (2011)

kinematic source model by applying its spatiotem-

poral distribution of slip velocity as a boundary

condition along the fault in a spectral element seis-

mic-wave propagation simulation done with the

SPECFEM3D code. The stress change features two

sequential drops, correlated in time with two peaks of

slip velocity. In particular, it shows that the critical

slip for the onset of the second weakening is Dr &20 m in the hypocentral region (Fig. 6a). The second

stress drop starts at 40 s when the slip reaches 20 m

and the slip rates increases again. This second stress

drop causes the slip rupture reactivation. There is a

step in the stress versus slip function. This stress-slip

step function has been adapted to a simple linear slip-

weakening friction law, where the friction decays

linearly to a critical slip weakening distance Dc and

after reaching a threshold slip Dr, the friction

decreases again (Fig. 6b, see also Fig. 5b). This

model qualitatively reproduces the multiseismic

wavefront observed in the strong ground motion and

GPS data along the Japanese coast (Fig. 1). The fit-

ting of the recorded velocity waveform with 1D

synthetic seismograms between 20 and 100 s period

is very good at station MYGH08 and neighboring

stations, but requires improvement at other stations.

4. Distribution of SMGA’s and Smaller Asperities:

Rupture Bridge of Small Asperities

Based on the observations of Kurahashi and Iri-

kura (2013), we place small SMGAs (smaller than

asperity A) at a depth of about 30 km along the

intraslab interface, denoted by SMGA1 to SMGA5

according to their rupture sequence, as shown in

Fig. 5a. In the dynamic rupture model, SMGAs are

modeled as intermediate-size asperities (small Dc

patches) having high nominal stress drop. In order to

promote rupture propagation between SMGAs, a

swarm of small asperities surround SMGAs.

Using EGF simulations, Kurahashi and Irikura

(2013) (see also Kawabe and Kamae 2013; Asano

and Iwata 2012) observed a reverse rupture sequence

of SMGAs: Hypocenter–SMGA1–SMGA2–SMGA3;

see Fig. 2. In order to reproduce this anomalous

SMGA strong motion radiation sequence, we need to

try specific SMGA settings, like the example in

Fig. 4, where a bridge of small asperities, having high

nominal stress drop, drive rupture to SMGA1 first,

and then let rupture propagate to SMGA2 and

SMGA3 in the order found by Kurahashi and Irikura

(2013).

Figure 7 demonstrates observational evidence for

the bridge in the backprojection result of Meng et al.

(2011), which indicates a chain of bursts of short-

period radiation from the hypocenter to the west

(chain of blue dots marked by the first arrow).

5. Dynamic Simulation Results

For efficiency, SPEC3FDM requires large meshes

for regions outside the rupture zones. As a result,

waveforms produced by dynamic simulation are valid

in the long-period range: 20–100 s. The dynamic

model including the SMGA regions radiates a com-

plex seismic wave field. Figure 8 shows snapshots of

rupture propagation. In the first 20 s, the rupture

initially propagates up-dip towards the trench, and

2150 P. Galvez et al. Pure Appl. Geophys.

between 30 and 40 s a down-dip rupture front breaks

the SMGA1 asperity.

During up-dip propagation, the slip on asperity A

increases and rupture reactivates, strongly breaking

the trench and generating a second rupture front with

enough energy to rupture SMGA3 at 68.2 s. Subse-

quently the rupture propagates northwest, activating

SMGA2 between 75 and 80 s. In the southward

propagation, the rupture breaks SMGA4 at 100 s and

travels further to finally activate SMGA5 at 120 s.

The rupture time is shown in Fig. 9.

Supplementary animation of seismic wave prop-

agation shows the multiseismic wavefronts that arrive

at the seismic stations along the Japanese coast. In the

first 30 s the up-dip rupture radiates an energetic

seismic wave field towards the trench but radiates

weak seismic waves toward the land. In fact the

waves die out before arriving at the Japanese coast.

The first strong seismic waves onshore appear once

the down-dip rupture starts breaking the SMGAs.

These SMGA asperities have enough stress drop to

radiate seismic waves that are detected by the seismic

stations along the Japanese coast. This model repro-

duces qualitatively the multiseismic wavefront

observed from the strong ground motion and GPS

data along the Japanese coast; see Fig. 1.

The rupture time is shown in Fig. 9. This sketch

reflects the time when the rupture broke the SMGA

regions. Additionally we show the final slip and peak

slip rate distributions in Fig. 10, and for reference we

Stress

Slip

Stress drop1Sd

Stress drop2Sd

Dc Dr D +Dr c)

s

0

d

(b)(a)

Reactivation

Figure 6a Step stress-slip distribution at a point close to the hypocenter computed from the slip-rate snapshots of Lee et al. (2011); dashed ellipse

indicates stress drop related to the rupture reactivation. b Sketch of the stress-slip relation used in the dynamic model

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40

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0 50 100 150Time (sec)

50403020

10

Figure 7Source area of the 2011 Tohoku earthquake. Contours represent the

slip distribution according to a kinematic source inversion (Lee

et al. 2011). Dots are high-frequency radiators according to the

backprojection analysis of Meng et al. (2011) slightly shifted to the

east–southeast due to change from the USGS to the JMA epicenter

location in this study. Color of dots denotes timing with respect to

the source time; size of dots denotes radiation amplitudes. Arrows

indicate propagation of high-frequency radiator. The reverse

character of the propagation is similar to the rupture sequence of

SMGAs in Fig. 1

Vol. 177, (2020) Dynamic Source Model for the 2011 Tohoku Earthquake in a Wide Period Range 2151

show the final stress drop distribution in Fig. 11 (see

also Table 2). Comparison of the rupture time with

the EGF model of Kurahashi and Irikura (2013) in

Table 3 demonstrates that our improved model

reproduces the rupture time of the EGF model.

6. FDM Simulations of Waveforms in Wide (3–100 s)

Period Range

The objective of this work is to develop a

dynamic model that qualitatively reproduces wave-

forms both at long periods and in the strong-motion

short-period range. To check if the model that we

developed can reproduce these waveforms, we run

simulations in the 3–100 s period range using the

staggered grid three-dimensional (3D) FDM (Graves

1996; Pitarka 1999). For the same computation cost,

FDM allows much smaller mesh size than SPEC-

FEM. The velocity structure is the 1D velocity model

of Fukuyama et al. (1998) shown in Table 1, the

same as was used for dynamic rupture simulation.

Waveforms are simulated for the dynamic source

model without making any modifications to their

source characteristics. We extract the dynamic source

parameters, slip velocity or moment rate function, at

each grid point on the fault and use them to calculate

the strong ground motions of the Tohoku earthquake

Figure 8Slip-rate snapshots showing the rupture sequence. Initially the rupture propagates to the trench and a down-dip rupture front appears at 22.8 s

and then starts to break the SMGA1 asperity at between 40 and 45.5 s. During this time the up-dip rupture reactivates close to the trench and

generates a second rupture front strong enough to break SMGA3 at 68.2 s. At 100.8 s the southward rupture propagation breaks SMGA4 and

finally activates SMGA5 at 120.2 s

2152 P. Galvez et al. Pure Appl. Geophys.

Figure 9Dynamic simulation results: Rupture time showing the time when

the SMGA asperities were activated

Figure 10Dynamic simulation results: a final slip (m), and b peak slip rate (m/s) distributions. Light-grey area is not ruptured

Figure 11Dynamic simulation results: final stress drop (MPa) distribution

Vol. 177, (2020) Dynamic Source Model for the 2011 Tohoku Earthquake in a Wide Period Range 2153

using 3D FDM. We consider only the slip rate

functions in cells of the dynamic source that have slip

rate larger than 0.02 m/s. Due to the large number of

cells and time steps (up to 5 million for a Mw 9.0

event), we used the staggered grid 3D FDM method

of Graves (1996) instead of the discrete wavenumber

method (DWM, Bouchon 1981) widely used for 1D

velocity structures, because the effect of all sub-

sources at all target sites can be calculated in one

FDM run, whereas DWM requires a separate calcu-

lation for each subsource–site pair.

Usually, the 3D velocity structure model [e.g.,

Japan Integrated Velocity Structure Model by

Koketsu et al. (2012)] is required for simulation of

waveforms in a complex wave propagation environ-

ment that includes subduction slab, accretionary

wedge sediments, and sedimentary basins. However,

due to large wavelength in the long-period range, the

effects of the accretionary prism and basins are

negligible. Short-period radiators (SMGAs) are

located in the deeper part of the subduction plate

upper interface close to the shoreline, so their prop-

agation path is approximately vertical, coming under

and aside the accretion wedge. The effect of basins

can be neglected for rock sites. For these reasons, 1D

velocity structure may also be valid for waveform

simulation in our case. Actually we tried both

models, 3D and 1D, but did not find a large differ-

ence, except for smaller amplitudes and longer

duration in the 3D case. Smaller amplitudes are the

result of accretion wedge (e.g., Guo et al. 2016),

while the longer duration is the result of surface

waves scattering in sedimentary accretion wedge and

in the near-surface low-velocity layers (e.g., Petukhin

et al. 2012).

Figure 12 compares the recorded and synthetic

waveforms for the long-period range of 20–100 s at

Japanese seismic stations (Kik-net and K-NET). It

demonstrates that the waveform fit is good or very

good in the central part of the region (Iwate and

Miyagi Prefectures, stations IWT* and MYG*). In

the northern (Aomori Prefecture, stations AOM*) and

southern (Fukushima, Ibaraki, and Chiba Prefectures,

stations FKS*, IBR*, and CHI*, respectively) parts,

the amplitude fit is good, but the delay time of the

synthetic waveforms is slightly different from that

observed.

For the short-period range of 3–20 s, we are not

able to fit simulated and observed waveforms,

including phase information. This would require

formal waveform inversion, which is impossible in

case of full dynamic simulation of the Mw 9 earth-

quake. However, arrival time of the wave packets,

their durations and envelopes, i.e., variation of

amplitudes, are valuable information for model vali-

dation too (e.g,. Kakehi and Irikura 1997; Nakahara

2013). For this reason, instead of waveform com-

parison, for the short-period range we compare

envelopes of velocity records; see Fig. 13. The sim-

ulated envelopes generally reproduce the observed

envelopes, both in amplitude and arrival time

(marked by dots in Fig. 13) of the most intense wave

packets WP1, WP3, and WP5. Wave packets WP2

and WP4 are unclear in the 3– 20 s period range. In

the southern part of the region, the simulated ampli-

tudes are overestimated (Fig. 13).

Overall, we are able to reproduce the rupture

process of the Tohoku earthquake and qualitatively

reproduce the recorded multiseismic wavefront

detected by the K-NET and KiK-net networks, and in

this way validate the dynamic rupture model.

Table 2

Stress drop (MPa)

Model SMGA1 SMGA2 SMGA3 SMGA4 SMGA5

Dyn 14.5 20.5 14.7 25 29

K and I 16 20 20 25.2 26

Dyn dynamic model (this study), K and I Kurahashi and Irikura

(2013)

Table 3

Rupture sequence (s)

Model SMGA1 SMGA2 SMGA3 SMGA4 SMGA5

Dyn 38.0 72.0 67.3 106.0 120.0

K and I 24.5 66.5 66.5 117.5 127.5

Dyn dynamic model (this study), K and I Kurahashi and Irikura

(2013)

2154 P. Galvez et al. Pure Appl. Geophys.

7. Discussion

An important contribution of the SMGAs is that

they allow the continuous increase in total slip as the

rupture keeps growing down-dip. As shown in

Fig. 13 of Galvez et al. (2016), in the absence of the

SMGA asperities, the down-dip rupture arrests once

when it leaves the shallow slip and ends with lower

total slip. Therefore the existence of the SMGAs

contributes not only to the ground motions but also to

the final earthquake magnitude.

In the southern regions, there is an overestimation

of peak ground motions due to the values of stress

drop prescribed in the SMGAs. Even though the

values of the nominal stress drop (defined here as:

initial shear stress - normal stress 9 dynamic fric-

tion coefficient) at the SMGAs are taken from

Kurahashi and Irikura (2013), the dynamic overshoot

of slip in dynamic rupture modeling results in larger

final stress drop (initial shear stress - final shear

stress, computed once the rupture stops). Therefore

decreasing the stress drops in the SMGAs will lead to

better fitting of short-period (3–20 s) ground motions

in the southern region.

Among the main targets of dynamic modeling like

this is the ‘‘indirect measurement’’ of parameters that

are important for strong ground motion simulation

but cannot be estimated or are poorly estimated by

direct measurement or kinematic inversion of obser-

vational data. One of these is the duration of the

0 50 100 150 200 25035

36

37

38

39

40

41

42

t origin (s)

Vel.(cm

/s)

138 139 140 141 142 14335

36

37

38

39

40

41

42

144

A

20 - 100s

AOM004AOM007

AOM011

AOM013

CHB011

CHB016

FKS001

FKS011FKS012IBR002

IBR018

IWT010

IWT014

MYG004MYG006MYG009

AOMH06

FKSH19

IBRH18

IWTH11

IWTH20IWTH24

MYGH08MYGH10

S1 S2

Figure 12Comparison of synthetic (red) and recorded (black) seismograms at seismic stations along the Japanese coast shown in Fig. 1. The

seismograms are bandpass-filtered from 20 to 100 s. Pink lines denote waves S1 and S2 from Fig. 1. Synthetic seismograms from Galvez

et al. (2016) are also shown by thin lines for comparison

Vol. 177, (2020) Dynamic Source Model for the 2011 Tohoku Earthquake in a Wide Period Range 2155

source time function (STF): short pulse-like STFs

effectively generate short-period strong ground

motions, while long smooth STFs only generate long-

period ground motions. In previous companion

studies (Galvez et al. 2014, 2015), we found that the

duration of STFs may correlate well with Dc values.

The STFs in high-Dc asperity A are long and smooth,

while the STFs in low-Dc SMGA areas are short and

impulsive. Dc is an internal property of the fault and,

in contrast to stress distribution for example, it per-

sists through earthquake cycles. This finding (if

confirmed) will be invaluable for strong motion

prediction (Irikura and Miyake 2011), because it

limits the location of SMGAs of future earthquakes to

the location of SMGAs of past earthquakes on the

same fault. However, if this is not the case, it may be

necessary to vary the location of SMGAs.

Somewhat similar reverse rupture propagation

was observed by EGF analysis and ray concentration

analysis for the 2007 Niigata-ken Chuetsu-oki

earthquake. Kamae and Kawabe (2008) and Petukhin

et al. (2009) (see also Irikura et al. 2009) found that

large ground motions recorded at the Kashiwazaki

Kariwa NPP (KKNPP) could be explained better

138 139 140 141 142 14335

36

37

38

39

40

41

42

0 50 100 150 200 25035

36

37

38

39

40

41

42

t origin, (s)

WP1 WP3

WP2

WP4

WP5

AOM004AOM007

AOM013

FKS001FKS004

FKS009

IBR003

IWT014

IWT021

IWT024

AOMH06

CHBH10

CHBH17

FKSH19

IBRH13

IBRH18

IWTH04

IWTH11

IWTH15

IWTH20

MYGH04

MYGH08

MYGH12

3 - 20s

Figure 13Comparison of synthetic (red) and recorded (black) short-period (3–20 s) envelopes for the line of rock sites along the Japanese coast. Dots are

manual picks of arrivals of wave packets: black for observed and red for synthetic envelopes. Colored circles on the left plot correspond to

SMGA1–SMGA5 in Fig. 4. Colored lines on the right plot denotes wave packets WP1-WP5 identified by Kurahashi and Irikura (2013);

dashed segments are our extension to the lines shown in Fig. 1; their colors correspond to the colors of SMGAs

2156 P. Galvez et al. Pure Appl. Geophys.

using a source model with three SMGAs and rupture

of SMGA3 toward KKNPP, opposite to that of the

main rupture. In addition to the 2011 Tohoku earth-

quake example, the 2007 Chuetsu-oki example shows

that reverse rupture propagation may be not rare on

heterogeneous faults.

As is revealed by the backprojection of Meng

et al. (2011) and reproduced by our dynamic rupture

model, the down-dip propagation is mainly bilateral

during the first 100 s. Then a predominantly down-

dip rupture propagates in mode III towards the

southwest, as shown in Fig. 7. This rupture directivity

toward the southwest produces a stress drop/nominal

stress drop ratio at SMGA4 (which has a circular

shape) close to one and a stress drop/nominal stress

drop ratio at SMGA5 (which has a pseudoelliptical

shape) that is large than one. The stress drop/nominal

stress drop ratio is larger on the side of the asperity

farther away from the rupture initiation. This asym-

metric stress drop/nominal stress drop ratio due to

rupture directivity has been reported in dynamic

rupture simulations by Kaneko and Shearer (2015) on

circular and elliptical asperities; see Figs. 5 and 9 in

Kaneko and Shearer’s study. The directivity effect

and stress drop/nominal stress drop ratio are more

predominant in elliptical asymmetric ruptures

(Kaneko and Shearer 2015), therefore the SMGAs

present a larger dynamically simulated stress drop

(29 MPa) than the initially prescribed nominal stress

drop (25 MPa). At the circular SMGA4, where the

rupture is asymmetric, the overshooting process is

attenuated by the incoherent propagation of the

stopping phases generated at the periphery of the

circular asperity (Kaneko and Shearer 2015, Sect. 4).

Therefore, the values of dynamically simulated stress

drop are much closer to the nominal stress drop at

SMGA4 and the northern asperities, which are

circular.

7.1. Comparison of the Rupture Dynamic Models

Here we compare the rupture dynamic model

from this study with those of two previous studies by

Galvez et al. (2014) and Galvez et al. (2016).

Figure 14 shows size and location of asperities in

all three studies. Key features, parameter settings, and

results are compiled in Table 4. In order to preserve

the advantages of the previous model, for each

subsequent model we tried to preserve the parame-

terization of the previous model. All the models are

Stress

Slip

Stress drop 1Sd

Stress drop 2Sd

Dc Dr D +Dr c)

s

0

d

Stress

Slip

Stress dropSd

Dc

s

0

d

(c) slip reactivationmodel

(d) slip weakeningmodel

139 140 141 142 143 144 14535

36

37

38

39

40

41

SMGA1

SMGA2

SMGA3

SMGA4

SMGA5

A

(b) This study

Large asperity

SMGA

Rupture bridge

Smallasperities

(a) Galvez et al.(2014, 2016)

139 140 141 142 143 144 14535

36

37

38

39

40

41

A2

A1

Figure 14Comparison of conceptual dynamic rupture models for 2011 Tohoku earthquake: a models of Galvez et al. (2014, 2016), b model used in this

study, c slip reactivation model for asperities A1 in (Galvez et al. 2016) and asperity A in this study, d slip weakening model for all other

asperities

Vol. 177, (2020) Dynamic Source Model for the 2011 Tohoku Earthquake in a Wide Period Range 2157

rather conceptual, in that the authors tried to repro-

duce the key features of observations without trying

to perfect the fit to observations, as in source

inversions. The features of each model are as follows:

1. The main goal of the dynamic rupture modeling of

Galvez et al. (2014) was to find a model that

reproduces the spatially separated sources of the

SP and LP radiation for the 2011 Tohoku earth-

quake, as identified in the kinematic source

inversion results for the LP area (Lee et al.

2011) and backprojection result for the SP area

(Meng et al. 2011), as well as 2D dynamic rupture

modeling of Huang et al. (2012). The large

asperity in the shallow area is intended to

reproduce the large slip area, the main source of

LP radiation. The cloud of small asperities in the

deeper part of source, having increased Dr and

decreased Dc, is intended to reproduce the SP

radiation (see Table 4). Galvez et al. (2014)

demonstrated that, under such settings, small

asperities generate large and very short slip-rate

(moment-rate) pulses, the source of SP radiation,

while the large asperity has a long moment-rate

function, the source of LP radiation.

2. Galvez et al. (2016) noticed evidence for reacti-

vation of slip weakening in the moment-rate

functions of the kinematic source inversion of

Lee et al. (2011). They employed rupture reacti-

vation for the large asperity and improved the fit

both for the total slip pattern and for the LP

waveforms in this way.

3. This study makes improvements for the SP part of

the model. Instead of a chaotic cloud of small

asperities, we employ compact SMGAs. The exact

location of SMGAs is retrieved by a semblance

analysis of Kurahashi and Irikura (2013). SMGAs

are modeled as intermediate-size asperities alter-

nating with small asperities. Small asperities are

necessary to promote rupture propagation (Galvez

et al. 2016). The key paradox in the SMGA

locations of Kurahashi and Irikura (2013), as well

as other EGF studies mentioned above, is the

reverse rupturing of SMGA2 and SMGA3 relative

to SMGA1. In this study we use evidence of a

rupture bridge from the hypocenter to SMGA1,

traced by the SP bursts. This bridge is modeled by

a chain of small asperities too. In this way we

obtain a model that reproduces the timing of

SMGAs, as well as a quantitative fit to the SP

radiation, while retaining the features of LP

radiation.

Table 4

Comparison of conceptual dynamic rupture models for the 2011 Tohoku earthquake

Galvez et al. (2014) Galvez et al. (2016) This study

Target

phenomena

Separated SP and LP generation areas Large total slip Reverse rupturing of SMGAs

Enhancements Separation of small and large asperities Slip reactivation after slip increases

to a certain value (Dr = 20 m)

Rupture bridge (chain of small asperities

from hypocenter to the first ruptured

SMGA1)

Dr (small/

large), MPa

12.0/9.0 12.0/4.5 and 4.5a 12.0b/4.5 and 4.5a

Dc (small/

large), m

1.0/3.0 1.0/3.0 and 20.0a 1.0/3.0 and 20.0a

Se (small/

large)

12.0/9.0 12.0/9.0 12.0/9.0

Result Many short pulses from small asperities

generate SP. Long pulse from large

asperity generates LP

50 m large slip in accordance with

kinematic inversion results (e.g.,

Lee et al. 2011)

Rupture sequence of SMGAs in

accordance with EGF results (e.g.

Kurahashi and Irikura 2013)

Dyn dynamic model (this study), K and I Kurahashi and Irikura (2013)aThe two values shown are for the slip-weakening and rupture reactivation stagesbFor SMGAs (medium size asperities) Dr values are presented in Table 2. For small asperities of the rupture bridge Dr = 6 MPa

2158 P. Galvez et al. Pure Appl. Geophys.

8. Conclusions

We perform dynamic rupture simulation of the

Tohoku earthquake using the spectral element code

SPECFEM3D. This tool allows for complex ruptures in

subduction zones. Using these capabilities, a bridge of

small high stress drop patches is introduced to repro-

duce the observed rupture sequence of the SMGAs:

Hypocenter–SMGA1–SMGA2&3–SMGA4–SMGA5.

The resulting dynamic model successfully reproduces

the recorded waveforms in the 20–100 s period range.

For short-period waveform simulation (3–20 s), 3D

FDM is used with a detailed 3D JIVSM velocity model.

The peak amplitudes of the simulated short-period

waveforms generally reproduce the peak amplitudes of

the recorded waveforms. However, in southern areas

they are overestimated due to the larger final stress drop

of the SMGA.

Acknowledgements

We deeply appreciate comments provided by two

anonymous reviewers and Guest Editor Dr. Changjiang

Wu. Discussions with Dr. Ken Miyakoshi were helpful

to improve the paper. This study was based on the 2014

research project ‘‘Improvement for uncertainty of strong

ground motion prediction’’ by the Secretariat of the

Nuclear Regulation Authority (NRA), Japan. The Super

Computer Shaheen II at KAUST University was used to

run the models presented in this study. Shaheen II is a

Cray XC40 delivering over 7.2 Pflop/s of theoretical

peak performance. Overall the system has a total of

197,568 processor cores and 790 TB of aggregate

memory.

Publisher’s Note Springer Nature remains neutral

with regard to jurisdictional claims in published maps

and institutional affiliations.

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(Received October 1, 2018, revised April 25, 2019, accepted May 2, 2019, Published online May 17, 2019)

Vol. 177, (2020) Dynamic Source Model for the 2011 Tohoku Earthquake in a Wide Period Range 2161