Dynamic Source Model for the 2011 Tohoku Earthquake in a Wide Period Range Combining Slip Reactivation with the Short-Period Ground Motion Generation Process


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.


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 teleseismic, 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 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).

Fig. 1

a 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)

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 backprojection 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 teleseismic 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 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 radiation is most efficiently generated by abrupt changes of rupture speed (e.g., Madariaga 1977; Pulido and Dalguer 2009) induced by the residual stress concentrations left by previous slip events, or by sharp spatial contrasts of fracture energy due to heterogeneities 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 Δσ. The effectiveness of this model for the Tohoku 2011 earthquake was demonstrated by Galvez et al. (2014, Fig. 12). Yoshida et al. (2012) estimated distributions of peak slip rate, Δσ, 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 Δσ and short Dc, as well as with areas of small Se.

Galvez et al. (2014) presented a conceptual minimalistic 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 (backprojection 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 reactivation 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.

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 timing: 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 earthquake 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.

Fig. 2

Distribution 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

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 agreement 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 (consistent 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 reactivation, of Meng et al. (2011) for the backprojection, and of Kurahashi and Irikura (2013) for the EGF simulation.

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 capabilities into a spectral element solver on unstructured meshes, the 3D code SPECFEM3D (Peter et al. 2011). This tool provides high flexibility in representing fault systems with complex geometries, including nonplanar faults and sharp wedges. The 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 earthquake, including large shallow slip, rupture reactivation, and large rupture extent. They presented evidence supporting this friction model, obtained from seismological observations, laboratory experiments, 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 powerful 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.

Fig. 3

a 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)

To create more slip in the shallow regions, the main asperity is moved closer to the trench in comparison 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 inversion (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).

Fig. 4

a 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

In deeper regions between 30 and 50 km depth, short-period radiation has been detected by EGF techniques (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 investigated in total. Among them, the strength excess (= static friction coefficient × normal stress − initial stress) and the nominal stress drop (= initial stress − dynamic friction coefficient × normal stress) are systematically tuned to reproduce the rupture 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 nominal stress drop, and Fig. 5 shows the frictional parameter settings, Dc and the static friction coefficient, 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 coefficient = 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.

Fig. 5

Slip critical distance Dca 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

Friction Model Settings for Asperity A: Slip Reactivation

Following Galvez et al. (2016), reactivation by the double-slip-weakening friction model is considered in this study. Evidence of a slip reactivation 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 relevance of the experimental material to the fault material is unclear. According to this experiment, during faulting, the fault surfaces reach high temperature 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 constant, 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 during 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.

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 techniques 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 spatiotemporal distribution of slip velocity as a boundary condition along the fault in a spectral element seismic-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 fitting 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.

Fig. 6

a 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

Distribution of SMGA’s and Smaller Asperities: Rupture Bridge of Small Asperities

Based on the observations of Kurahashi and Irikura (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).

Fig. 7

Source 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

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 complex 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 between 30 and 40 s a down-dip rupture front breaks the SMGA1 asperity.

Fig. 8

Slip-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

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. Subsequently 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.

Fig. 9

Dynamic simulation results: Rupture time showing the time when the SMGA asperities were activated

Supplementary animation of seismic wave propagation 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 reproduces 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 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.

Fig. 10

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

Fig. 11

Dynamic simulation results: final stress drop (MPa) distribution

Table 2 Stress drop (MPa)
Table 3 Rupture sequence (s)

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 waveforms 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 SPECFEM. 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 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 subsources at all target sites can be calculated in one FDM run, whereas DWM requires a separate calculation 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 environment 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 propagation 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 difference, 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.

Fig. 12

Comparison 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

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 earthquake. However, arrival time of the wave packets, their durations and envelopes, i.e., variation of amplitudes, are valuable information for model validation too (e.g,. Kakehi and Irikura 1997; Nakahara 2013). For this reason, instead of waveform comparison, for the short-period range we compare envelopes of velocity records; see Fig. 13. The simulated 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 amplitudes are overestimated (Fig. 13).

Fig. 13

Comparison 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

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.


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 × dynamic friction 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 observational data. One of these is the duration of the 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 persists 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 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 earthquake 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 asymmetric 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.

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 parameterization of the previous model. All the models are rather conceptual, in that the authors tried to reproduce 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:

Fig. 14

Comparison 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

Table 4 Comparison of conceptual dynamic rupture models for the 2011 Tohoku earthquake
  1. 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 earthquake, 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 Δσ 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. 2.

    Galvez et al. (2016) noticed evidence for reactivation of slip weakening in the moment-rate functions of the kinematic source inversion of Lee et al. (2011). They employed rupture reactivation for the large asperity and improved the fit both for the total slip pattern and for the LP waveforms in this way.

  3. 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 alternating 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.


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 reproduce 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.


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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.

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Galvez, P., Petukhin, A., Irikura, K. et al. Dynamic Source Model for the 2011 Tohoku Earthquake in a Wide Period Range Combining Slip Reactivation with the Short-Period Ground Motion Generation Process. Pure Appl. Geophys. 177, 2143–2161 (2020). https://doi.org/10.1007/s00024-019-02210-7

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  • 2011 Tohoku earthquake
  • dynamic simulation
  • rupture propagation
  • slip reactivation