UTRIP Final Report
Tidal Triggering of Earthquakes --Case Study of 2011 Tohoku Earthquake
Ta-‐Wei, Chang1, 2, 3 Supervisor: Dr. Satoshi Ide1 1) Dept. Earth and Planetary Sciences, School of Science, Univ. Tokyo, Tokyo, Japan 2) Dept. Earth Sciences, School of Earth Sciences, National Central University, Taoyuan, Taiwan 3) Dept. Geophysics, School of Earth and Space Sciences, Peking University, Beijing, China
Abstract:
Following the study of Tanaka (2012), by looking at the earthquake sequence for 10-‐year time span prior to the 2011 Tohoku earthquake, we find that there is strong correlation between tidal stress fluctuation and earthquake occurrence in several regions close to the epicenter of the Tohoku earthquake. In addition to this, we also did declustering, and found out that the declustered catalog showed far less correlation; which indicates that aftershock sequences might be the most sensitive to the tidal stress fluctuation prior to very large earthquakes. Keywords: Tidal triggering of earthquakes, declustering, Tohoku earthquake
1. Introduction: 1.1. 2011 Tohoku Earthquake:
The Tohoku earthquake occurred at 5:46, Mar. 11, 2011 UTC in offshore Tohoku region,
Japan. This earthquake, with moment magnitude ranging from 9.0 (JMA, 2011) to 9.1
(Nettles et al., 2011), is the largest in magnitude ever recorded in Japan (JMA, 2011), the 2nd
largest in magnitude and the 7th in fatalities in the world since 1990 (USGS, 2015). A
devastating tsunami was also observed throughout the Pacific Ocean, especially around
near-‐shore of Tohoku region, with maximum height of 9.3m in Sōma (JMA, 2012). This
earthquake and the induced tsunami led to a death toll of 19225 (till 3/1/2015) and heavily
damaged over 500,000 buildings (Fire Disaster Management Agency of Japan, 2015).
1.2. Tidal Triggering of Earthquakes:
The relationship between tidal stress fluctuation and earthquake occurrence has been
discussed for over a century. To date, over a hundred studies have focused on this topic,
reaching almost opposite results. Most studies, however, reached the result that tidal stress
is not correlated with earthquake; except for special earthquake sequences such as
earthquake swarms, aftershock sequences, earthquakes in volcanic areas (Tanaka et al.,
2002), and tremors (Ide et al., 2015).
Of course, research methods have improved gradually throughout the century. The
stress level was previously considered as the stress on the epicenter at sea level, until
Heaton (1975), who first calculated the stress on the fault plane, providing a more accurate
estimation of stress either along the slip direction or normal stress. In addition to this
improvement, the “tidal stress” part is also modified. There are two parts of tides on the
Earth that may lead to stress changes on the fault plane: body tide and ocean tide. The body
tide, also the direct tide, is caused directly by the gravitational stress between the Earth and
the Sun, which is easier to calculate, therefore included in most previous studies. The ocean
tide, on the other hand, is the indirect term, the effect of ocean water loading fluctuation that
is acted on by the gravitational stress on the ocean water. This term is the easiest to visualize;
but due to the lack of oceanic tidal data, is ignored in most previous studies until Sauck
(1975) first include this into his calculation. The oceanic tidal model is further improved
later on the early 21st century by using satellite altimeter to calibrate the readings, so Tanaka
et al. (2012) can apply all the improved methods and datasets to create a comprehensive
study of global data, which showed very interesting results but out of the scope of this paper.
After the 2011 Tohoku earthquake, Tanaka (2012) took advantage of all the
improvements, and applied the result to the earthquake sequence prior to the mainshock.
She found that as the sampling time window of 3000 days approaches the mainshock in time
steps of 500 days, the correlation between tidal stress fluctuations and earthquake
occurrence increases significantly. In fact, this kind of pattern can be observed in several
large earthquakes such as the 2004 Sumatra earthquake and the 1982 South Tonga
earthquake (Tanaka, 2012). As this is rather interesting, I’ll mainly focus on her method,
trying to reproduce the same result, and modify it a little bit and discuss the results.
2. Data and Method: 2.1. Tide:
The “tide” taken into consideration in this study includes body tide and ocean tide. For
body tide, we simply sum up the gravitational stress acted on Earth by the Sun and the Moon.
For ocean tide, we apply the SPOTL software (Agnew, 2012), which convolutes the oceanic
tidal model and the Green function in PREM structure configuration (Dziewonski & Anderson,
1981). The oceanic tidal model we use is developed by Matsumoto et al. (2000), which is
calibrated by using TOPEX/POSEIDON satellite altimeters. The spatial resolution of this
model is 0.5° globally (NAO.99b and NAO.99L), and 5” regionally around Japan (NAO.99Jb).
Tidal components included in this study are: M2, S2, K1, O1, N2, P1, K2, Q1, Mf, and Mm, which
includes diurnal, semidiurnal and longer period tidal components caused by effect of either
the Sun, the Moon, or both.
2.2. Earthquake: For the earthquake catalog, we used the Harvard Global CMT catalog (Dziewonski et al.,
1981) (Ekström et al., 2012), which is the most prestigious global earthquake catalog in the
literature that includes the fault plane geometry and slip direction data (including strike, dip,
and rake). However, due to the nature of the matter, we would get two fault planes that
produce the same focal mechanism solutions. In this study, we are only focusing on the shear
stress along the slip direction; hence we can actually just take either one of the two fault
planes and simply use the rake data, since either one of the two rake data can be applied
along with its corresponding fault plane geometry, and will give the same result of along-‐slip
shear stress.
In this study, I made a change to the study by Tanaka at 2012 — applying the
declustering technique to the earthquake catalog, and see if this will change the result. The
method I apply in my study is described in (Reasenberg, 1985), which is the standard
method regarding declustering. The reason to apply this is that in previous studies, strong
correlation is found in aftershock sequence but rarely elsewhere (Tanaka et al., 2002).
Therefore, if declustering, which is technically aftershock removing does changes the result,
this might give us information on either aftershock is more sensitive to tidal stress
fluctuation or less, comparing to other “mainshocks”. In fact, Tanaka et al. (2002) had done
this in their comprehensive study, reaching the result that there is difference in the
outcomming readings; but the result of correlated or not is basically not changed.
2.3. Stress: For each earthquake, we calculate the tidal stress tensor resulting from both body tide
and ocean tide. We do this calculation for a 24-‐hour time span, centering at the time of
mainshock. The time resolution is 4 minutes, creating 360 sampling points in a day. The 360
sampling points in 24 hours is able to create a 1° phase resolution as mentioned in the next
section. From the stress tensor, we get the traction vector on the fault plane by multiplying
the stress tensor by the normal vector of the fault plane specified by the fault geometry and
rake information in the earthquake catalog. After that, we project the traction onto the fault
plane in the coordinate of normal to fault plane, rake, and the direction on the fault plane that
is orthogonal to both. This allows us to acquire the shear stress along the slip direction, as is
my main focus in this study. In Tanaka’s study, the trace of stress tensor, which represents
the confining stress, is also evaluated in addition to the shear stress along the slip direction
with very different results (Tanaka et al., 2002), but is out of scope here.
2.4. Statistical Analysis From the previous step, we have already acquired the fluctuation of shear stress along
the slip direction in a timespan of 24 hours. From that, we apply the Schuster test, the
standard method to evaluate the phase angle of occurrence of earthquakes that is used in
(Tanaka et al., 2002) and many other previous studies. First, we define the phase angle as
follows: 0° is the closest maximum of stress to the earthquake; 180° is the minimum directly
following the maximum, and -‐180° represents the first minimum directly before the
maximum, as shown in figure 1. From this definition, we could get the phase angle of all
earthquakes we’d like to study.
After getting the phase of each event, we then calculate the p-‐value given as follows:
𝑝 = 𝑒(!!!
! )
where 𝐷2 = 𝑐𝑜𝑠𝜃𝑖𝑁
𝑖=1
2
+ 𝑠𝑖𝑛𝜃𝑖𝑁
𝑖=1
2
In the above equations, N is the total amount of earthquake in question, and 𝜃! is the
phase angle of any particular earthquake. In statistics, the p-‐value is the confidence in
rejecting the null hypothesis; higher p-‐value indicates less confidence while small p-‐value
indicates strong confidence in rejecting the null hypothesis. In this study, the null hypothesis
is that earthquake occurrence is not correlated with tidal stress fluctuation. Hence, very
small p-‐value indicates that earthquakes tend to occur at around phase angle 0°, which
means the peak tidal stress; and p=1 indicates that there is no correlation between the two,
i.e., the phase angle of earthquakes is evenly distributed.
From all the aforementioned, we could now start to find the relation. First, select a
region or apply any criteria of interest (i.e. magnitude, depth, location, rupture type, etc),
calculate the phase of all the earthquakes in it, acquire the p-‐value of that area, and then we
could judge if tidal stress fluctuation is correlated with earthquake occurrence in the region.
The entire procedure is summarized and visualized as in figure 2:
0° 180°
90°
-‐180°
Shear stress along
slip direction
Figure 1: Schematic figure of the definition of phase. For all other phase angle, we
simply divide the time interval linearly. The resolution of angle is 1°.
3. Results: 3.1. Study Area and Criterions:
In this study, since tidal stress has stronger effect on shallower earthquakes, we only
used earthquakes of depth within 70 km, which is by the definition of shallow earthquakes.
In addition, since the research area of this study is mainly offshore, to ensure the
completeness of earthquake events, we apply the cutoff magnitude of MW 5.0. Furthermore,
since one of the main focuses of this study is to reproduce the result of (Tanaka, 2012), I
choose to include the earthquake within 10 years prior to the Tohoku earthquake, which is
close to but slightly longer than the 3000-‐day period she applied.
Similar to (Tanaka, 2012), the study area is chosen to be region close to the epicenter of
Tohoku earthquake. For comparison, I did the same calculation in 15 regions around the
region for area of 200×200 𝑘𝑚! , with each center of region expressed in figure 3 as
50×50 𝑘𝑚!, since these regions are moved around in steps of 50 km. As an example, Figure 4
Determine the correlation!
Earthquake catalog
Stress components on fault plane
Phase of each earthquake
P-‐value of earthquakes of interest
Tidal stress tensor at focus
Earth and body tide data
Focal mechanism and rake
Figure 2: The basic flow chart of this study
expresses the actual region of 200×200 𝑘𝑚! with its center is indicated in figure 3 as the
blue patch.
For each area, I plotted a histogram that shows the distribution of phases as well as
calculate the p-‐value for each region. For easier reading, the bin color of the histogram
represents the p-‐value of each area: Deep blue indicates a <0.05 p-‐value, which represents
high correlation; turquoise indicates p-‐value within 0.1~0.05; and red represents p>0.1,
which indicates that the correlation is weak between the two.
3.2. Result: Following is the result for all 15 regions as 15 histograms in figure 5, as well as the
result for the declustered catalog in figure 6. The regions the histograms indicate are located
as in the order of the 15 patches in figure 3.
140˚
140˚
142˚
142˚
144˚
144˚
146˚
146˚
34˚ 34˚
36˚ 36˚
38˚ 38˚
40˚ 40˚
42˚ 42˚
Figure 3: The “centers” of the 15 study
areas. The actual area of the blue patch
is indicated in figure 4. The red star is
the Tohoku earthquake mainshock.
Figure 4: The square represents the
patch in blue in figure 3; the small
dots are all the earthquakes in the
catalog used in the study.
140˚
140˚
142˚
142˚
144˚
144˚
146˚
146˚
34˚ 34˚
36˚ 36˚
38˚ 38˚
40˚ 40˚
42˚ 42˚
3.2.1. Not Declustered:
Figure 5: The result for the un-‐declustered catalog. We can clearly see that for the northern
region, a higher correlation is found; some could even reach quite significant p-‐value.
3.2.2. Declustered:
Figure 6: The result for the declustered catalog. Comparison with the previous
result clearly indicates that there’s now no correlation in all of the regions.
4. Discussion: From figure 5, we can observe that for the earthquake sequence 10 years prior to the
Tohoku earthquake mainshock, there is strong correlation between tidal stress fluctuation and
earthquake occurrence in some regions to the north of the mainshock. The lowest p-‐value, as can
be seen in figure 5, reaches as low as 0.019. However, as for figure 6, we can see that in the
declustered catalog, no correlation is found in all regions, however how well they are correlated
in the region before applying declustering.
Comparing the above two figures, we can clearly see that there is significant difference
between declustering or not. Since declustering is basically removing the aftershocks, we can see
that after removing the aftershocks, there is now no correlation. From that, we can say that the
aftershocks we have removed are the most sensitive earthquakes regarding the tidal stress
fluctuation. This is basically the same conclusions as many previous studies as summarized in
Tanaka et al., (2002); yet the opposite from the declustering they did in the same study.
Comparison with previous studies, especially (Tanaka, 2012), we found very similar results,
either the pattern of the histogram or the regions with low p-‐values. However, the lowest p-‐value
in her study is 0.0034, which is about 5.5 times smaller than mine. This may be resulting from the
fact that the region and sampling time is slightly different from hers. Note here that the program
used in calculating the tidal stress in this study is different from hers. The program she used is
derived from GOTIC2 (Matsumoto et al., 2001); while the one I applied is SPOTL (Agnew, 2012).
However, Yabe Suguru of Dept. EPS, Univ. Tokyo had confirmed the consistency between the two
programs, hence this difference is quite unlikely to be the causation of the difference in result.
As for the declustering part, Tanaka et al. (2002) found that removing the aftershocks in
global catalog doesn’t change the conclusion of either correlated or not, even though the readings
changed a bit. However, I reached a dramatically different result, saying that the aftershocks are
rather sensitive to the tidal stress fluctuation, which is quite similar to the many previous studies
listed in Tanaka et al. (2002). The observation that aftershocks of earthquakes before the Tohoku
mainshock are sensitive to tidal stress, together with the fact that there are more correlation in
the earthquake sequence prior to the Tohoku mainshock comparing to all earthquakes in the
study by Tanaka et al., (2002), we can gather that these are special effects of either the Tohoku
earthquake, or any earthquakes with very large magnitude.
5. Conclusion: By calculating tidal shear stress by ocean tide and body tide in slip direction on the fault
plane of earthquakes in 10 years prior to the Tohoku earthquake, we found strong correlation
between tidal stress fluctuation and earthquake occurrence in some region close to the location
of the Tohoku earthquake, confirming the result of Tanaka (2012). Applying decluster showed no
correlation in all region, indicating that aftershocks of mainshocks before the Tohoku earthquake
are very sensitive to the tidal stress fluctuation.
6. Acknowledgement: The author thanks Tomoaki Nishikawa and Suguru Yabe for offering all the help in his stay in
Univ. Tokyo. In addition, the author is grateful to the International Liaison Office of School of
Science, UTokyo for all the help in all the administrative work. Helpful comments and suggestions
by Dr. Satoshi Ide during the study such as to apply declustering are highly appreciated.
Discussion with the Ide lab, together with Kate Huihsuan Tsai, is very helpful. The code of
calculating tidal stress is developed by Suguru Yabe, which combined SPOTL program by Agnew
and tidal model by Matsumoto et al. Figures 3 and 4 are plotted using GMT software by (Wessel &
Smith, 1991). A. Allmann writes the declustering program in the ZMAP software package
(Wiemer, 2001). Comments on the manuscript by Dr. Satoshi Ide are highly beneficial. The UTRIP
program is funded by the GSS-‐UTRIP Scholarship.
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