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Ground motions characterized by a multi-scale heterogeneous earthquake model
- Hideo Aochi^{1}Email author and
- Satoshi Ide^{2}
https://doi.org/10.1186/1880-5981-66-42
© Aochi and Ide; licensee Springer. 2014
Received: 22 January 2014
Accepted: 30 April 2014
Published: 29 May 2014
Abstract
We have carried out numerical simulations of seismic ground motion radiating from a mega-earthquake whose rupture process is governed by a multi-scale heterogeneous distribution of fracture energy. The observed complexity of the Mw 9.0 2011 Tohoku-Oki earthquake can be explained by such heterogeneities with fractal patches (size and number), even without introducing any heterogeneity in the stress state. In our model, scale dependency in fracture energy (i.e., the slip-weakening distance D_{c}) on patch size is essential. Our results indicate that wave radiation is generally governed by the largest patch at each moment and that the contribution from small patches is minor. We then conducted parametric studies on the frictional parameters of peak (τ_{p}) and residual (τ_{r}) friction to produce the case where the effect of the small patches is evident during the progress of the main rupture. We found that heterogeneity in τ_{r} has a greater influence on the ground motions than does heterogeneity in τ_{p}. As such, local heterogeneity in the static stress drop (Δτ) influences the rupture process more than that in the stress excess (Δτ^{excess}). The effect of small patches is particularly evident when these are almost geometrically isolated and not simultaneously involved in the rupture of larger patches. In other cases, the wave radiation from small patches is probably hidden by the major contributions from large patches. Small patches may play a role in strong motion generation areas with low τ_{r} (high Δτ), particularly during slow average rupture propagation. This effect can be identified from the differences in the spatial distributions of peak ground velocities for different frequency ranges.
Keywords
- Ground Motion
- Fracture Energy
- Stress Drop
- Small Patch
- Large Patch
Background
Near-field ground motion is strongly affected by the heterogeneity of earthquake rupture processes, such as multiple ruptures, rupture directivity, and the acceleration and deceleration of the rupture front. To quantitatively estimate the ground motion for seismic hazard assessment, characterization of this heterogeneity is essential. In kinematic earthquake models, an assumed target fault plane is usually decomposed by many rectangular sub-faults on which the spatio-temporal slip distribution is determined by a waveform inversion of seismic data (e.g., Hartzell and Heaton 1983). Numerous slip models have been presented for the Mw 9.0 2011 Tohoku-Oki earthquake (e.g., Ide et al. 2011; Koketsu et al. 2011; Simons et al. 2011; Suzuki et al. 2011). In these slip models, model parameters (e.g., total slip, rupture time, and rise time) have been attributed to each sub-fault.
The seismic waves inverted for slip models are usually displacements or velocities filtered in a low-frequency band, which is typically <1 Hz. There has been debate over whether the source of high-frequency waves is identical to the large slip areas in slip models (Hartzell et al. 1996; Kakehi et al. 1996; Nakahara et al. 1999). Although a general consensus has not yet been reached (e.g., Nakahara 2008), for many subduction earthquakes, high-frequency sources tend to be located deeper than the large slip areas (e.g., Lay et al. 2012). High-frequency sources are typically identified as several small isolated regions referred to as 'strong motion generation areas’ (SMGAs) (e.g., Kamae et al. 1998; Irikura and Miyake 2011). Some SMGA models have also been presented for the Tohoku-Oki earthquake (Kurahashi and Irikura 2011; Asano and Iwata 2012; Satoh 2012). Given that the number of parameters is much smaller when characterizing the kinematic earthquake rupture process in terms of SMGAs than when using a finely discretized finite-fault rupture model, the approach using SMGAs may be a more robust approach for ground motion simulations.
From a dynamic point of view, Ide and Aochi (2005) proposed that the heterogeneity in earthquake faults can be expressed as a superposition of different scales of heterogeneity. This is termed 'multi-scale heterogeneity’ and a seismic source can be represented as cascading ruptures of many circular patches of different sizes on a crack plane. In terms of kinematic finite source description, such heterogeneity may correspond to a class of composite models developed by Frankel (1991) and Zeng et al. (1994), and similar to those of Bernard et al. (1996). Aochi and Ide (2011) and Ide and Aochi (2013) attempted to characterize the Mw 9.0 2011 Tohoku-Oki earthquake based on this source expression and were able to dynamically simulate the growth of the rupture process from a small rupture through to the Mw 9 event. In these studies, a large elliptical patch corresponding to the large slip area of a Mw 9 event, which was unknown prior to this earthquake, was key in explaining the gross seismic moment release, whereas the distributed small circular patches governed the rupture growth before triggering the large elliptical patch. These small patches were introduced to reflect moderate earthquakes that had occurred previously in this region.
The apparent similarity in both the timing and locations of SMGAs (Kurahashi and Irikura 2011; Asano and Iwata 2012) and the circular patches of Ide and Aochi (2013) suggest that such small-scale heterogeneity corresponds to SMGAs. The dynamic models explored by Aochi and Ide (2011) and Ide and Aochi (2013) were neither constrained nor calibrated directly using observed data. Moreover, the radiation of ground motion based on this multi-scale heterogeneity has not yet been discussed. The purposes of this study are to show the characteristics of ground motions from the simulated fractal patch model for the 2011 Tohoku-Oki earthquake and to discuss the similarities (or differences) with respect to other synthetic heterogeneity models of the earthquake.
Methods
Model and method - reference model
Crustal structure used in the ground motion simulations
Upper depth of layer [km] | P wave velocity [m/s] | S wave velocity [m/s] | Density [kg/m^{3}] | Quality factor Q |
---|---|---|---|---|
0 | 5,500 | 3,140 | 2,300 | 600 |
3 | 6,000 | 3,550 | 2,400 | 600 |
18 | 6,700 | 3,830 | 2,800 | 600 |
33 | 7,800 | 4,460 | 3,200 | 600 |
However, according to the SMGAs reported for the 2011 Tohoku-Oki earthquake (Kurahashi and Irikura 2011; Asano and Iwata 2012; Satoh 2012), it is expected that it should be possible to identify certain phases with different frequency contexts. One possible explanation for this is that the difference is due to heterogeneity in stress conditions as our dynamic concept varies fracture energy (keeping stress conditions uniform), whereas the SMGA includes stress heterogeneity. From the point of view of the slip-weakening relationship for fault friction, both approaches imply that small patches may 'locally’ radiate more seismic energy compared with large patches. This study further explores this through parametric studies.
Parametric studies
Model parameters of the parametric studies
Large patch (all cases) | Small patches (case 1) | Small patches (case 2) | Small patches (case 3) | |
---|---|---|---|---|
Dimension of ellipse (a, b) or circle (r) [km] | a = 57.1, b = 175 | r = 25 | r = 25 | r = 25 |
Slip-weakening distance D_{c} [m] | 3.2 | 0.8 | 0.8 | 0.8 |
Initial shear stress τ_{0} [MPa] | 0 | 0 | 0 | 0 |
Dynamic strength drop Δσ [MPa] | 10 | 20, 20.5, 21, 22.5 | 20 | 20 |
Stress excess Δτ^{excess} [MPa] | 5 | 15, 15.5, 16, 17.5 | 5 | 10 |
Stress drop Δτ [MPa] | 5 | 5 | 15 | 10 |
where the dynamic strength drop Δσ is defined as Δσ ≡ τ_{p} - τ_{r}. The fracture energy G_{c} is defined as G_{c} ≡ Δσ × D_{c}/2. We assumed that D_{c} is proportional to the patch dimension (e.g., Ide and Aochi 2005). In this case, D_{c} is 3.2 and 0.8 m for a large and small patch, respectively. To initiate rupture on the large ellipse having a large D_{c}, we assumed that D_{c} also scales with the distance from the hypocenter around the initiation point and produces a small (but large enough with respect to the simulation element size of 2 km) finite initial crack (radius of 10 km) located at the coordinate origin in Figure 4. This helps to minimize an artificial initial phase of the dynamic rupture process (e.g., Aochi and Ide 2004; Ide and Aochi 2005; Aochi and Douglas 2006).
Given that we did not aim to discuss the effect of the ground surface on the rupture process, all the simulations were carried out in a 3D infinite, homogeneous elastic medium (P and S wave velocities of 6,000 and 3,464 m/s, respectively, and material density = 2,500 kg/m^{3}) using a BIEM (Fukuyama and Madariaga 1995, 1998). In fact, as observed in Figures 2 and 3, the seismic wave radiation originating from the rupture arrival on the ground surface is obvious since the dynamic rupture significantly interacts with the ground surface. This masks the other radiation effects and may be exaggerated, as no shallow, slow layer was included (e.g., Goto et al. 2012; Ide and Aochi 2013). To better identify the radiation from the deep part of the fault as proposed in SMGA models, we ignored the interaction of the dynamic rupture with the ground surface.
We described the derivative stress with respect to the initial stress level (assumed to be zero, i.e., τ_{0} = 0) rather than to the absolute stress level. Therefore, instead of the two parameters τ_{p} and τ_{r} we refer to the stress excess Δτ^{excess}(≡τ_{p} - τ_{0}) and the static stress drop Δτ(≡τ_{0} - τ_{r}). A large Δτ^{excess} may lead to a delay in the rupture onset. A large Δτ may produce a large fault slip. We firstly kept Δτ constant and changed Δτ^{excess} (case 1 in Table 2). We then varied Δτ^{excess} (case 2), and finally, we changed both parameters simultaneously (case 3). The ground motions were compared at several stations along the fault strike (the same locations as in Figure 1), assuming the same hypocenter location and fault geometry as for the 2011 Tohoku-Oki earthquake. As the focus of this study is the wave radiation from the causal source, we used the simple 1D structure given in Table 1.
Results
Therefore, we gleaned from these simulations that heterogeneity in the static stress drop Δτ (i.e., residual stress level τ_{r}) leads to more significant differences in ground motion than those produced by heterogeneity in the stress excess Δτ^{excess} (or peak strength τ_{p}). Small patches are visible when they are isolated from a large patch, such that the small patches are in some way separated from the nearby ongoing rupture. Therefore, the locally identified SMGAs may be different from the main rupture front or characterized by a larger stress drop. A more complicated 'inhomogeneous’ fault model (e.g., Ripperger et al. 2008) might be more appropriate in such cases. Stochastically heterogeneous models (e.g., Ide and Aochi 2005) should be used in future ground motion estimation studies.
Discussion
Our parametric study confirms the observations of Ide and Aochi (2005). We have determined that the role of small patches during rupture propagation makes the rupture front heterogeneous, not by delaying it, but through advancing it according to the low fracture energy given that the rupture propagation is governed by the energy balance. In our model, the rupture propagation velocity is close to the S wave speed, and it is difficult to identify the effect of further advancing the rupture front on the seismic wave radiation. Nevertheless, such an effect would be evident if the rupture velocity were slower, and in fact, we observed a slight difference between case 1 of Figure 5 and case (a) of Figure 9. However, the influence on the ground motion is limited (Figure 10). Ulrich and Aochi (2014) attempted to identify different sizes of patch by inversion, but any secondary small patches were difficult to identify whereas a large patch was able to be easily characterized. This is because the radiation from the small patches tends to be hidden by the waves from the greater area of a large patch. This effect should be important when the main rupture triggers remote small patches. In other cases, the rupture of small patches should be significantly delayed. However, we cannot rule out the possibility of delayed rupture of small patches for more realistic friction laws. For example, in the case when fault strength τ_{p} is time-dependent, the rupture may be delayed according to the accumulation of strain and some relaxation process. This is in effect the same mechanism as aftershock occurrence (e.g., Dieterich 1994; Helmstetter and Shaw 2009).
However, the differences in Δτ demonstrate the influence of small patches on ground motions. The mechanical features dynamically investigated in this study should be consistent with kinematic interpretations. In the original concept of SMGAs, Irikura and Miyake (2011) proposed a high stress drop on the SMGAs to distinguish it from background rupture propagation. This appears to make sense, given that Aochi and Dupros (2011) reconstructed a fault constitutive relationship from the SMGA source model (Irikura 2008) for the 2007 Mw 6.6 Niigata-Chuetsu-Oki earthquake in Japan and obtained a difference in Δτ (and Δτ^{excess}) that was about double between SMGA area and the rest of the fault plane. The studies of Das and Aki (1977) and Mikumo and Miyatake (1978) have shown that the rupture process is very sensitive to stress parameters such as Δτ and Δτ^{excess} (e.g., Madariaga and Olsen 2000; Gabriel et al. 2012). Even if our study were to take into account differences in fracture energy, the sensitivity to these parameters remains valid and coherent.
Conclusions
We have simulated the wave radiation process from multi-scale heterogeneous models of fracture energy for a mega-earthquake such as the 2011 Tohoku-Oki earthquake. Based on our previous research, we started by assuming heterogeneity only in the slip-weakening distance D_{c} under uniform stress conditions and frictional levels τ_{p} and τ_{r} (i.e., uniform stress excess Δτ^{excess} and stress drop Δτ). However, in this case, once a rupture is initiated on a large patch, the influence of nearby small patches on the ground motions is insignificant and hidden by the dominant wave radiation from the large patch, which has a rupture propagation velocity similar to the S wave speed. We then introduced additional heterogeneity in Δτ^{excess} and/or Δτ. Finally, we showed that heterogeneity in Δτ has a greater influence on ground motions than the same level of heterogeneity just in Δτ^{excess}. In fact, small patches can be easily ruptured by the use of the multi-scale concept in fracture energy, but these are difficult to rupture behind a large patch even if high Δτ^{excess} is assumed. Small patches exert an influence on SMGAs with low τ_{r} (i.e., those with a higher static stress drop Δτ). This effect can be identified from differences in the spatial distribution of peak ground velocities at different frequency ranges. Our models indicate that the distribution of large patches may be inferred from past seismicity when earthquakes recur frequently. However, uncertainties on the stress heterogeneity need to be treated stochastically. Our multi-scale heterogeneity earthquake model is consistent with inferred earthquake models, such as SMGA models, and may be a useful approach for probabilistically introducing stress state heterogeneity when predicting ground motion for quantitative seismic hazard studies.
Declarations
Acknowledgements
We thank Hiroe Miyake and Nobuki Kame for inviting us to the working group on 'Dynamic Source Models for the Next Generation Ground Motion Prediction’ in 2013-2014, which was funded by the Earthquake Research Institute of the University of Tokyo. We also thank John Douglas for offering comments that improved this paper. The comments from Martin Mai and an anonymous reviewer were very helpful. This research began under the framework of the French-Japanese ANR-JST joint program DYNTOHOKU (2011-2013) and was then funded by the French national project S4 (Subduction: Slow and Standard Seismology, 2012-2014, ANR-2011-BS56-017) of the Agence National de la Recherche. Most of the calculations were made at the French national supercomputing center GENCI-CINES (grant 2013/2014-c46700). This work was also partially supported by JSPS KAKENHI (23244090) and MEXT KAKENHI (21107007) grants.
Authors’ Affiliations
References
- Andrews DJ: Rupture dynamics with energy loss outside the slip zone. J Geophys Res 2005., 110: B01307, doi:10.1029/2004JB003191 B01307Google Scholar
- Aochi H, Douglas J: Testing the validity of simulated strong ground motion from the dynamic rupture of a fault system, by using empirical equations. Bull Earthq Eng 2006, 4: 211–229. 10.1007/s10518-006-0001-3View ArticleGoogle Scholar
- Aochi H, Dupros F: MPI-OpenMP hybrid simulations using boundary integral equation and finite difference methods for earthquake dynamics and wave propagation: application to the 2007 Niigata Chuetsu-Oki earthquake (Mw6.6). Procedia Comput Sci 2011, 4: 1496–1505. doi:10.1016/j.procs.2011.04.162, 2011View ArticleGoogle Scholar
- Aochi H, Ide S: Numerical study on multi-scaling earthquake rupture. Geophys Res Lett 2004. doi:10.1029/2003GL018708Google Scholar
- Aochi H, Ide S: Complexity in earthquake sequences controlled by multi-scale heterogeneity in fault fracture energy. J Geophys Res 2009. doi:10.1029/2008JB006034Google Scholar
- Aochi H, Ide S: Conceptual multi-scale dynamic rupture model for the 2011 Tohoku earthquake. Earth Planets Space 2011, 63: 761–765. doi:10.5047/eps2011.05.008View ArticleGoogle Scholar
- Aochi H, Madariaga R: The 1999 Izmit, Turkey, earthquake: Non-planar fault structure, dynamic rupture process and strong ground motion. Bull Seism Soc Am 2003, 93: 1249–1266. doi:10.1785/0120020167View ArticleGoogle Scholar
- Asano K, Iwata T: Source model for strong ground motion generation in the frequency range 0.1–10 Hz during the 2011 Tohoku earthquake. Earth Planets Space 2012, 64: 1111–1123.View ArticleGoogle Scholar
- Bernard P, Herrero A, Berge C: Modeling directivity of heterogeneous earthquake ruptures. Bull Seism Soc Am 1996, 86: 1149–1160.Google Scholar
- Campillo M, Favreau P, Ionescu IR, Voisin C: On the effective friction law of a heterogeneous fault. J Geophys Res 2001, 106: 16307–16322. 10.1029/2000JB900467View ArticleGoogle Scholar
- Das S, Aki K: A numerical study of two-dimensional spontaneous rupture propagation. Geophys J R Astron Soc 1977, 50: 643–668. 10.1111/j.1365-246X.1977.tb01339.xView ArticleGoogle Scholar
- Dieterich JH: A constitutive law for the rate of earthquake production and its application to earthquake clustering. J Geophys Res 1994, 99: 2601–2618. 10.1029/93JB02581View ArticleGoogle Scholar
- Dupros F, Aochi H, Ducellier A, Komatitsch D, Roman J: Exploiting intensive multithreading for efficient simulation of seismic wave propagation. 11th International conference on computational science and engineering, Sao Paulo, 16–18 July 2008 2008. doi:10.1109/CSE.2008.51Google Scholar
- Frankel A: High-frequency spectral falloff of earthquakes, fractal dimension of complex rupture, b value, and the scaling of strength on faults. J Geophys Res 1991, 96: 6291–6302. 10.1029/91JB00237View ArticleGoogle Scholar
- Fukuyama E, Madariaga R: Integral equation method for a plane crack with arbitrary shape in 3D elastic media. Bull Seismol Soc Am 1995, 85: 614–628.Google Scholar
- Fukuyama E, Madariaga R: Rupture dynamics of a planar fault in a 3D elastic medium: rate- and slip-weakening friction. Bull Seisim Soc Am 1998, 88: 1–17.Google Scholar
- Gabriel AA, Ampuero J-P, Dalguer LA, Mai PM: The transition of dynamic rupture styles in elastic media under velocity-weakening friction. J Geophys Res 2012., 117: B09311, doi:10.1029/2012JB009468 B09311Google Scholar
- Goto H, Yamamoto Y, Kita S: Dynamic rupture simulation of the 2011 off the Pacific coast of Tohoku earthquake: multi-event generation within dozens of seconds. Earth Planets Space 2012, 64: 1167–1175.View ArticleGoogle Scholar
- Hartzell SH, Heaton TH: Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake. Bull Seism Soc Am 1983, 73: 1153–1184.Google Scholar
- Hartzell S, Liu P, Mendoza C: The 1994 Northridge, California, earthquake: investigation of rupture velocity, risetime, and high-frequency radiation. J Geophys Res 1996, 101: 20091–20108. 10.1029/96JB01883View ArticleGoogle Scholar
- Helmstetter A, Shaw BE: Afterslip and aftershocks in the rate-and-state friction law. J Geophys Res 2009., 114: B01308, doi:1029/2007JB005077 B01308Google Scholar
- Ide S, Aochi H: Earthquakes as multiscale dynamic rupture with heterogeneous fracture surface energy. J Geophys Res 2005., 110: B11303, doi:10.1029/2004JB003591 B11303Google Scholar
- Ide S, Aochi H: Historical seismicity and dynamic rupture process of the 2011 Tohoku-Oki earthquake. Tectonophysics 2013, 600: 1–13.View ArticleGoogle Scholar
- Ide S, Baltay A, Beroza GC: Shallow dynamic overshoot and energetic deep rupture in the 2011 Mw 9.0 Tohoku-Oki earthquake. Science 2011, 332: 1426–1429. doi:10.1126/science.1207020View ArticleGoogle Scholar
- Irikura K: Lesson from the 2007 Niigata-ken Chuetsu-oki earthquake on seismic safety for nuclear power plant. Bull Jap Asso Earthq Eng 2008, 7: 25–29. (in Japanese) (in Japanese)Google Scholar
- Irikura K, Miyake H: Recipe for predicting strong ground motion from crustal earthquake scenarios. Pure Appl Geophys 2011, 168: 85–104. doi:10.1007/s00024–010–0150–9View ArticleGoogle Scholar
- Kakehi Y, Irikura K, Hoshiba M: Estimation of high-frequency wave radiation areas on the fault plane of the 1995 Hyogo-ken Nanbu earthquake by the envelope inversion of acceleration seismograms. J Phys Earth 1996, 44: 505–517. 10.4294/jpe1952.44.505View ArticleGoogle Scholar
- Kamae K, Irikura K, Pitarka A: A technique for simulating strong ground motion using hybrid Green’s function. Bull Seism Soc Am 1998, 88: 357–367.Google Scholar
- Koketsu K, Yokota Y, Nishimura N, Yagi Y, Miyazaki S, Satake K, Fujii Y, Miyake H, Sakai S, Yamanaka Y, Okada T: A unified source model for the 2011 Tohoku earthquake. Earth Planet Sci Lett 2011, 310: 480–487. doi:10.1016/j.epsl.2011.09.009View ArticleGoogle Scholar
- Kurahashi S, Irikura K: Source model for generating strong ground motions during the 2011 off the Pacific coast of Tohoku Earthquake. Earth Planets Space 2011, 63: 571–576. 10.5047/eps.2011.06.044View ArticleGoogle Scholar
- Lay T, Kanamori H, Ammon CJ, Koper KD, Hutko AR, Ye L, Yue H, Rushing TM: Depth-varying rupture properties of subduction zone megathrust faults. J Geophys Res 2012., 117: B04311, doi:10.1029/2011JB009133 B04311Google Scholar
- Madariaga R, Olsen KB: Criticality of rupture dynamics in 3-D. Pageoph 2000, 157: 1981–2001. 10.1007/PL00001071View ArticleGoogle Scholar
- Matsu’ura M, Kataoka H, Shibazaki B: Slip-dependent friction law and nucleation process in earthquake rupture. Tectonophys 1992, 211: 135–148. 10.1016/0040-1951(92)90056-CView ArticleGoogle Scholar
- Mikumo T, Miyatake T: Dynamical rupture process on a 3-dimensional fault with non-uniform frictions and near-field seismic-waves. Geophys J Royal Astro Soc 1978, 54: 417–438. 10.1111/j.1365-246X.1978.tb04267.xView ArticleGoogle Scholar
- Nakahara H: Chapter 15 Seismogram envelope inversion for high-frequency seismic energy radiation from moderate-to-large earthquakes. Adv Geophys 2008, 50: 401–426. doi:10.1016/S0065–2687(08)00015–0View ArticleGoogle Scholar
- Nakahara H, Sato H, Ohtake M, Nishimura T: Spatial distribution of high-frequency energy radiation on the fault of the 1995 Hyogo-Ken Nanbu, Japan, earthquake (Mw 6.9) on the basis of the seismogram envelope inversion. Bull Seism Soc Am 1999, 89: 22–35.Google Scholar
- Ohnaka M: A constitutive scaling law and a unified comprehension for frictional slip failure, shear fracture of intact rock, and earthquake rupture. J Geophys Res 2003, 108(B2):2080. doi:10.1029/2000JB000123 View ArticleGoogle Scholar
- Ripperger J, Mai PM, Ampuero J-P: Variability of near-field ground motion from dynamic earthquake rupture simulations. Bull Seism Soc Am 2008, 98(3):1207–1228. doi:10.1785/0120070076View ArticleGoogle Scholar
- Satoh T: Source modeling of the 2011 off the Pacific coast of Tohoku earthquake using empirical Green’s function method. J Struct Const Eng 2012, 77: 695–704. (in Japanese) (in Japanese) 10.3130/aijs.77.695View ArticleGoogle Scholar
- Simons M, Minson SE, Sladen A, Ortega F, Jiang J, Owen SE, Meng L, Ampuero JP, Wei S, Chu R, Helmberger DV, Kanamori H, Hetland E, Moore AW, Webb FH: The 2011 magnitude 9.0 Tohoku-Oki earthquake: mosaicking the megathrust from seconds to centuries. Science 2011, 332: 1421. doi:10.1126/science.1206731View ArticleGoogle Scholar
- Suzuki W, Aoi S, Sekiguchi H, Kunugi T: Rupture process of the 2011 Tohoku-Oki mega-thrust earthquake (M9.0) inverted from strong-motion data. Geophys Res Lett 2011, 38: L00G16. doi: 10.1029/2011GL049136Google Scholar
- Ulrich T, Aochi H: Rapidness and robustness of finite-source inversion of the 2011 M_{w}9.0 Tohoku earthquake by an elliptical-patches method using continuous GPS and acceleration data. Pageoph 2014. doi:10.1007/s00024–014–0857–0Google Scholar
- Wibberley CAJ, Shimamoto T: Earthquake slip weakening and asperities explained by thermal pressurization. Nature 2005, 436: 689–692. 10.1038/nature03901View ArticleGoogle Scholar
- Zeng Y, Anderson JG, Guang Y: A composite source model for computing realistic synthetic strong ground motions. Geophys Res Lett 1994, 21: 725–728. 10.1029/94GL00367View ArticleGoogle Scholar
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