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Official Journal of the Asia Oceania Geosciences Society (AOGS)

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  • Original article
  • Open Access

Testing the Coulomb stress triggering hypothesis for three recent megathrust earthquakes

  • 1Email author,
  • 2, 3,
  • 2 and
  • 2
Geoscience LettersOfficial Journal of the Asia Oceania Geosciences Society (AOGS)20174:5

  • Received: 26 October 2016
  • Accepted: 10 February 2017
  • Published:


We test the static Coulomb stress triggering hypothesis for three recent megathrust earthquakes (the 2004 Sumatra–Andaman earthquake, the 2010 Maule earthquake, and the 2011 Tohoku-Oki earthquake) using focal mechanism solutions for actual earthquakes as receiver faults to calculate Coulomb stress changes. For the 2004 Sumatra–Andaman and 2011 Tohoku-Oki earthquakes, the median values of the Coulomb stress changes for 100 consecutive earthquakes revealed temporal changes from approximately zero before the megathrust earthquake to significant positive values following the mainshock, followed by decay over time. Furthermore, the ratio of the number of positively to negatively stressed receiver faults increased after the megathrust. These results support the triggering hypothesis that the static stress changes imparted by megathrust earthquakes cause seismicity changes. This is in contrast to the results of a previous study that used optimally orientated receiver faults to calculate Coulomb stress changes, and this difference indicates the importance of considering the spatial and temporal heterogeneities of receiver fault distributions. For the 2010 Maule earthquake, however, the results are strongly dependent on fault-slip models. Since most receiver faults are concentrated in the mainshock source region, slip models significantly affect the computed Coulomb stress changes and sometimes cause anomalous stress concentrations along the edge of each sub-fault.


  • Coulomb stress changes
  • 2004 Sumatra–Andaman earthquake
  • 2010 Maule earthquake
  • 2011 Tohoku-Oki earthquake
  • Heterogeneity of receiver fault mechanisms


Earthquake triggering and seismicity rate changes following large or great earthquakes have been discussed in terms of static (and/or dynamic) changes in the Coulomb failure function (ΔCFF) (Harris and Simpson 1992; Stein et al. 1992, 1994; Reasenberg and Simpson 1992; Hill et al. 1993; Anderson et al. 1994; Toda et al. 1998; Ogata 2007; Chan and Stein 2009; Chan et al. 2016). The ΔCFF is defined as ΔCFF = Δτ − μΔσ, where Δτ is the shear stress change on a given failure plane (assumed to be positive in the fault-slip direction), Δσ is the normal stress change (assumed to be positive in the compressive direction), and μ′ is the apparent coefficient of friction. Positive ΔCFF values enhance failures, whereas negative values suppress failures.

Three megathrust earthquakes, the 2004 Sumatra–Andaman earthquake (Mw 9.1; U. S. Geological Survey), the 2010 Maule earthquake (Mw 8.8), and the 2011 Tohoku-Oki earthquake (Mw 9.0), provided us a great opportunity to investigate the triggering hypothesis that co-seismic stress changes transferred from large earthquakes cause seismicity changes (Fig. 1). For the Tohoku-Oki earthquake, Toda et al. (2011) showed that there is a mean 47% gain in positively stressed aftershock mechanisms over background (1997–2011 March 10) earthquakes. Furthermore, Ishibe et al. (2015) showed that the ΔCFF values following the Tohoku-Oki earthquake have a statistically higher ratio of positively stressed receiver faults compared to those before the Tohoku-Oki earthquake.
Fig. 1
Fig. 1

a Three megathrust earthquakes investigated in the present study (the 2004 Sumatra–Andaman earthquake (Mw 9.1; orange), the 2010 Maule earthquake (Mw 8.8; dark green), and the 2011 Tohoku-Oki earthquake (Mw 9.0; purple). bd The fault-slip model for each earthquake as well as the distribution of 1-day aftershocks (open circles) according to the U.S. Geological Survey. The focal mechanism solutions for major earthquakes are from the Global Centroid Moment Tensor catalog. The plate boundary data from Bird (2003) are modified

Recently, Miao and Zhu (2012) compared the spatial distribution of the ΔCFF imparted by the above three megathrust earthquakes with their aftershock distributions by assuming optimally orientated faults to be receiver faults, and concluded that there is no clear evidence that the Coulomb stress changes enhanced the aftershock activity. The ratios of aftershocks that occurred in the positively stressed regions following the Sumatra–Andaman, Maule, and Tohoku-Oki earthquakes were 47.6, 49.8, and 47.0%, respectively. They reported that the static triggering hypothesis worked well, with more than 85% of aftershocks having positive ΔCFF values, for the two large intraplate earthquakes (the 1999 Chi–Chi and 2008 Wenchuan earthquakes).

Assumption of the receiver fault mechanism sometimes greatly affects estimation of the ΔCFF. The simplest way to assume the specified receiver fault is to fix the strike, dip angle, and rake angle, but this method is valid either for major source faults with well-known fault geometries or a region with a spatially and temporally homogeneous stress field. Another way is to assume optimally oriented receiver faults, which are determined so as to maximize the ΔCFF under the specified local/regional stress field (King et al. 1994). This can also produce large errors in a complex regional stress field in which earthquakes with various focal mechanisms occur, unless the heterogeneity of the local/regional stress field is properly considered.

In the present study, we calculate the ΔCFF for nodal planes of focal mechanism solutions for actual earthquakes. This method has been proven to be effective in reducing the uncertainty of receiver faults in heterogeneous stress fields (Hardebeck et al. 1998; Imanishi et al. 2006; Toda 2008; Ishibe et al. 2011a, b, 2015; Enescu et al. 2012; Heidarzadeh et al. 2016). Following the recent occurrence of megathrust earthquakes, drastic changes in focal mechanism solutions from dominant thrust-type to a variety of types have been observed (e.g. Lay et al. 2005; Asano et al. 2011; Nettles et al. 2011). We investigate the correlation between the Coulomb stress changes transferred from three megathrust earthquakes and seismicity changes before and after the megathrust earthquakes in the neighboring regions.

Data and methodology

We use variable-slip models obtained from tsunami waveforms for the three megathrust earthquakes [the 2004 Sumatra–Andaman earthquake (Fujii and Satake 2007), the 2010 Maule earthquake (Fujii and Satake 2013), and the 2011 Tohoku-Oki earthquake (Satake et al. 2013)] (Fig. 1). In order to examine the sensitivity of ΔCFF computation to slip models, we also use the variable-slip models proposed by Rhie et al. (2007) and Ammon et al. (2005) for the Sumatra–Andaman earthquake, by Delouis et al. (2010) and Luttrell et al. (2011) for the Maule earthquake, and by Yokota et al. (2011) and Gusman et al. (2012) for the Tohoku-Oki earthquake (Additional file 1: Figure S1). For the case of the Sumatra–Andaman earthquake, we include the ΔCFF due to the Mw 8.5 Nias earthquake that occurred in March 2005 southeast of the 2004 source region using the fault-slip model obtained from teleseismic body-wave inversion (Konca et al. 2007).

For receiver faults on which stress changes are calculated, we use the focal mechanism solutions of earthquakes between January 1, 1976 and September 31, 2015 obtained from the Global Centroid Moment Tensor (GCMT) catalog (e.g. Ekström et al. 2012) (Additional file 2: Figure S2). For the case of the Tohoku-Oki earthquake, we also use the F-net focal mechanisms provided by the National Research Institute for Earth Science and Disaster Resilience (Fukuyama et al. 1998). We grouped these mechanisms into pre-seismic and post-seismic periods, before and after the occurrence of the megathrust earthquakes. The number of earthquakes we used to compute the ΔCFF values was 1374 for the Sumatra–Andaman earthquake, 436 for the Maule earthquake, and 1537 for the Tohoku-Oki earthquake. Even if a majority of aftershock nodal planes were positively stressed by the mainshock rupture, this would not necessarily prove the stress triggering hypothesis because the distribution of receiver faults is controlled primarily by predominant stress fields. Thus, we evaluate the triggering hypothesis by comparing the calculated Coulomb stress changes after the megathrusts to those during pre-seismic periods as background.

We calculate the ΔCFF values for two nodal planes of each focal mechanism solution. We assume an elastic half-space with a shear modulus of 40 GPa and a Poisson’s ratio of 0.25. For the apparent friction coefficient (μ′), we adopt an empirically introduced value, μ′ = 0.4, but we also repeat our analyses for two other values (= 0.1 and 0.8). Laboratory rock experiments on frictional slip indicate higher values, e.g., 0.5 ≤ μ′ ≤ 0.8 (e.g., Byerlee and Brace 1968), whereas fluid injection decreases the apparent friction coefficient when the pore–fluid pressure increases (Skempton 1954).

We calculate the median ΔCFF value for receiver faults for 100 consecutive earthquakes by moving the time window for 50 earthquakes. The ΔCFF values for the two nodal planes differ because the unclamping stresses are not the same, but we do not know which of these is the actual receiver fault. In order to consider the arbitrariness of nodal plane selection, we conduct a Monte Carlo simulation in which either the first or the second nodal plane of each focal mechanism solution is randomly selected as a receiver fault. In each time-window, we create 1000 datasets and calculate the average and standard deviation of the median ΔCFF values. We also calculate the ratios of three cases in which (1) both nodal planes are positively stressed; (2) one nodal plane is positively stressed, while the other is negatively stressed; and (3) both nodal planes are negatively stressed. We then evaluate the Coulomb index, which is the ratio of the number of receiver faults with stress increases for at least one nodal plane (e.g., Hardebeck et al. 1998) during both the pre-seismic and post-seismic periods.

Results and discussion

Figure 2 shows the distribution of the ΔCFF values and the focal mechanism solutions during the pre-seismic and post-seismic periods. One of the characteristics of the focal mechanism distribution during the post-seismic period is activation of normal-faulting earthquakes in the shallow crustal region of the overriding plate and the outer-rise region. For the case of the Tohoku-Oki earthquake, shallow normal-faulting earthquakes abruptly began to occur in the Ibaraki/Fukushima prefectural boundary area (coastal region around 37 °N) (e.g., Kato et al. 2011) and the outer-rise region along the Japan Trench. Similar normal-faulting earthquake sequences were also reported for the other two megathrust earthquakes: the Pichilemu region (around 34.5 °S) along the Chilean coast after the Maule earthquake (e.g., Farías et al. 2011) and East offshore of the Nicobar Islands (around 8 °N) after the Sumatra–Andaman earthquake (e.g., Lay et al. 2005; Dewey et al. 2007). Most of these normal-faulting earthquakes were positively stressed due to the occurrence of the megathrust earthquakes.
Fig. 2
Fig. 2

a Distribution of focal mechanism solutions and their ΔCFF values during the pre-seismic periods before the 2004 Sumatra–Andaman earthquake (left), the 2010 Maule earthquake (center), and the 2011 Tohoku-Oki earthquake (right); and b those during the post-seismic periods

The temporal changes in the median ΔCFF values for the three megathrust earthquakes are shown in Fig. 3. Here, we focused on the temporal changes since 2000, because the temporal changes during the pre-seismic periods are negligibly small. (See Additional file 3: Figure S3, Additional file 4: Figure S4 for temporal changes in the median Coulomb stress change after January 1976.) The median values of ΔCFF are several bars during post-seismic periods, whereas they are approximately zero during pre-seismic periods for the Sumatra–Andaman and Tohoku-Oki earthquakes (Fig. 3). The rapidly increased median ΔCFF values gradually decayed to background levels for the Sumatra–Andaman earthquake. However, these were still elevated 4 years after the Tohoku-Oki earthquake. The decay rate became smaller approximately 3 years after the mainshock, suggesting that factors other than Coulomb stress changes, which will be discussed later, also contributed to keep the median ΔCFF elevated (e.g., Toda and Stein 2013).
Fig. 3
Fig. 3

Temporal changes in median Coulomb stress changes after 2000 for a the 2004 Sumatra–Andaman earthquake (orange) b the 2010 Maule earthquake (dark green), and c the 2011 Tohoku-Oki earthquake (purple). Vertical dashed lines indicate the occurrence times of mainshocks. Vertical error bars indicate the standard deviations obtained by Monte Carlo simulation, which randomly selects either the first or the second nodal plane as a receiver fault. See Additional file 3: Figures S3 and Additional file 4: Figure S4 in the electronic supplement for the temporal changes of median Coulomb stress changes after January 1976

The Coulomb index during the post-seismic period was greater than 50%, with the exception of one of the 27 cases (Table 1). These results are inconsistent with those of a previous study, in which the seismicity was determined to be less than 50% in the positively stressed region by assuming an optimally oriented receiver fault. For 19 cases out of 27 cases, the Coulomb index was higher during the post-seismic period than that during the pre-seismic period. For example, using the fault model of Yokota et al. (2011) with an apparent coefficient friction of 0.4, 79.3% of receiver faults were positively stressed for at least one nodal plane following the Tohoku-Oki earthquake, whereas 64.2% of receiver faults were positive during the pre-seismic period. This is consistent with the findings of previous studies (e.g., Toda et al. 2011; Ishibe et al. 2015).
Table 1

Ratios of receiver faults during the pre-seismic and post-seismic periods with different apparent coefficients of friction and fault-slip models




Pre-seismic period

Post-seismic period

Both positive


One positive


Both negative


Coulomb index


Both positive


One positive


Both negative


Coulomb index


2004 Sumatra–Andaman

Fujii and Satake (2007)




























Rhie et al. (2007)




























Ammon et al. (2005)




























2010 Maule

Fujii and Satake (2013)




























Delouis et al. (2010)




























Luttrell et al. (2011)




























2011 Tohoku-Oki

Satake et al. (2013)




























Yokota et al. (2011))




























Gusman et al. (2012)




























The underlined/italic numbers indicate that the Coulomb index during the post-seismic period increased/decreased compared to that during the pre-seismic period

For the Maule earthquake, however, temporal changes in the median ΔCFF exhibit various patterns depending on the slip model: an abrupt increase in median ΔCFF value for the slip model of Delouis et al. (2010), an abrupt decrease for that of Fujii and Satake (2013), and almost no change for that of Luttrell et al. (2011). Most of the receiver faults used to compute the ΔCFF for the 2010 Maule earthquake were interplate aftershocks with a thrust mechanism and were concentrated in the mainshock source region (see Additional file 5: Figure S5). The evaluated ΔCFF for these receiver faults may include large uncertainties because slip models using rectangular sub-faults artificially cause anomalous stress concentrations along the edge of each sub-fault (e.g., Woessner et al. 2012), and hence the computed median values are strongly affected by these anomalous values near the source. Another possible reason is the smaller number of available receiver faults compared with the other two megathrust earthquakes.

In order to examine the sensitivity of the ΔCFF calculation to the slip model and the assumed value of the apparent friction coefficient, we repeated our analyses for other slip models (see Additional files 6, 7, 8, 9, 10, 11, 12: Figures S6 through S12) and two other apparent friction coefficients (μ′ = 0.1 and 0.8). The computed ΔCFF value is insensitive to the slip model for the Tohoku-Oki and Sumatra–Andaman earthquakes. The temporal change in the ΔCFF is similar for different values of the friction coefficient, i.e., the abrupt increase in the median value following the occurrence of a megathrust earthquake and the gradual decay toward the background level.

The catalog dependency of our results was also tested for the case of the Tohoku-Oki earthquake by using F-net focal mechanisms as receiver faults. Figure 4 shows the distribution of the receiver faults with the calculated ΔCFF and the temporal changes in the median ΔCFF value using the fault-slip model of Yokota et al. (2011) with μ′ = 0.4. (see Additional file 13: Figure S13, Additional file 14: Figure S14 for different apparent coefficients of friction). The median ΔCFF exhibited similar temporal changes associated with the Tohoku-Oki earthquake: a sudden increase followed by a gradual decrease toward the background level. The median ΔCFF fluctuates more for the F-net catalog than for the GCMT catalog. This may reflect the characteristics of earthquake clustering, because the F-net data include a much larger number of focal mechanism solutions than the GCMT catalog.
Fig. 4
Fig. 4

a Distribution of focal mechanism solutions and their ΔCFF values calculated for the F-net catalog during the pre-seismic (left) and post-seismic (right) periods of the 2011 Tohoku-Oki earthquake. The slip model of Yokota et al. (2011) was used. b Temporal changes of the median Coulomb stress change. The histograms for receiver faults during the pre-seismic and post-seismic periods are also shown

Concluding remarks and future developments

We investigated the correlation between static Coulomb stress changes imparted by three megathrust earthquakes and changes in focal mechanism solutions by means of abundant focal mechanism solutions of earthquake catalogs as receiver faults. The median Coulomb stress was approximately zero during the pre-seismic period before the megathrust earthquake, abruptly increased as a result of the earthquake, and then gradually decreased, at least for the Sumatra–Andaman and Tohoku-Oki earthquakes. The ratio of positively to negatively stressed receiver faults increased following these megathrust earthquakes for almost all slip models and apparent friction coefficient values. Changes in the focal mechanism distribution that can be correlated with static Coulomb stress changes due to megathrust earthquakes support the static stress triggering hypothesis. The conclusion of the present study is opposite that of a previous study using optimally orientated receiver faults, and this difference indicates the importance of considering the spatial and temporal heterogeneities of receiver faults.

In the present study, we considered only the static stress changes transferred from co-seismic fault slips of the mainshocks. However, other possible factors for triggering seismicity changes, such as dynamic stress change due to the passage of seismic waves (e.g., Hill et al. 1993; Miyazawa 2011), a decrease in failure strength due to an increase in pore–fluid pressure (e.g., Hubbert and Rubey 1959), post-seismic slip, static stress change from indirectly triggered earthquakes by numerous aftershocks, acceleration of relative plate motion (e.g., Heki and Mitsui 2013; Uchida et al. 2016), and/or viscoelastic relaxation (e.g., Pollitz and Sacks 1995), have been suggested by various studies. These might disturb or mask the correlation between Coulomb stress changes co-seismically transferred from the mainshocks and changes in seismicity following the occurrence of mainshocks.



static change in the Coulomb failure function


global centroid moment tensor


Authors’ contributions

TI conceived the original concept of the present paper, performed the computations and analysis, and wrote the final manuscript. YO, HT, and KS provided suggestions to improve the research, supervised the writing of the manuscript, and approved the final version. All authors read and approved the final manuscript.


The authors would like to thank Jian Wang and the anonymous reviewers for their helpful comments. The authors would also like to thank all of the organizations and individuals mentioned in the “Availability of data and materials” section, who provided the data and information used in the present study.

Competing interests

The authors declare that they have no competing interests.

Availability of data and materials

We used the Global Centroid Moment Tensor (GCMT) catalog (, last accessed October 2015) and F-net focal mechanism solutions provided by the National Research Institute for Earth Science and Disaster Resilience (NIED) (, last accessed November 2015) for receiver faults in calculating Coulomb stress changes. We also used Generic Mapping Tools (Wessel and Smith 1998) for drawing figures (, last accessed January 2012), the TSEIS visualization package (Tsuruoka 1998) for the study of hypocenter data (, last accessed October 2015), and a subroutine program developed by Okada (1992) for calculating ΔCFF (, last accessed October 2015). Several fault-slip models for the 2004 Sumatra–Andaman, 2010 Maule, and 2011 Tohoku-Oki earthquakes are available from the online database of finite-fault rupture models (SRCMOD) (Mai and Thingbaijam 2014) (, last accessed August 2016).


The present study was supported by the Ministry of Education, Culture, Sports, Science, and Technology of Japan under its Earthquake and Volcano Hazards Observation and Research Program and the Special Project for Reducing Vulnerability for Urban Mega-earthquake Disasters.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors’ Affiliations

Association for the Development of Earthquake Prediction, 1-5-18, Sarugaku-cho, Chiyoda-ku, Tokyo 101-0064, Japan
Earthquake Research Institute, the University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan
The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa Tokyo, 190-8562, Japan


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