Auxiliary materials for
The potential for a very large earthquake along the southernmost Ryukyu
subduction zone
Ya-Ju Hsu1, Masataka Ando1, Shui-Beih Yu1, and Mark Simons2
1. Institute of Earth Sciences, Academia Sinica, Nankang, Taipei, Taiwan
2. Seismological Laboratory, California Institute of Technology, California, U.S.A.
GPS Data
The collected GPS data are processed with GAMIT/GLOBK software packages, version 10.3
[Herring et al., 2002] using the double-difference phase observable and the tropospheric and
ionospheric modeling.
To obtain a more accurate and consistent regional deformation pattern in
Taiwan, we use continuous GPS data from 362 Taiwan sites, 8 Ryukyu sites, and 17 IGS sites in the
Asia-Pacific region.
Fourteen IGS sites with long observation history surrounding the study area
are constrained to their 2005 International Terrestrial Reference Frame (ITRF2005, [Altamimi et al.,
2007]) coordinates in GLOBK processing, together with the parameters from GAMIT solutions to
produce ITRF2005 coordinates of the other GPS sites.
We perform a least squares linear fit to
estimate station velocity (linear rate), annual and semi-annual periodic motions, post-seismic
relaxation, and offsets caused by coseismic jumps and instrument changes from station position time
series. We remove outliers, annual and semi-annual variations, post-seismic relaxation, as well as
offsets caused by coseismic jumps and antenna changes.
GPS dilatation rates and stress regimes in Taiwan
The dilatation rate and principal strain rates are estimated using GPS velocities in this study and
the method proposed by Hsu et al. [2009]. The orientations of maximum horizontal stress axes are
computed using earthquake focal mechanisms with depths less than 30 km between 2005 and 2010
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as well as the method proposed by Lund and Townend [2002]. The trends of maximum horizontal
compressive axes correspond to the direction of the normal of the vertical plane experiencing
maximum normal stress.
(a)
(b)
Figure S1. (a) Dilatation and principal strain rates. The color scale indicates dilatation rates in
μstrian/yr. Black vectors denote the two principal strain-rate axes. Major faults are indicated as green
lines. The white dots denote GPS sites. (b) Black bars and texts show the orientations of maximum
compressive horizontal stress axes derive from the earthquake focal mechanisms at the depth range
less than 30 km between 2005 and 2010 (Wu et al., 2010). Gray bars indicate the 95% confidence
regions of the maximum compressive horizontal stress axes. Major faults are indicated as black lines.
LVF: Longitudinal Valley Fault.
A backslip model simultaneously investigate strain accumulation effects on the LVF and the
Ryukyu thrust
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Here we address the trade-off of strain accumulation effects on the LVF and the Ryukyu
megathrust. We construct a backslip model including the northern and southern portions of the LVF
as well as the Ryukyu megathrust. The northern LVF (NLVF) and southern LVF (SLVF) consists of
25°- and 22°-trending segments with dip of 60° and 45°, respectively. Both NLVF and LVF extend
from the surface to a depth of 25 km following the distribution of local seismicity. The Ryukyu fault
(RyukyuT) is a 290°-trending segment with dip 10° to the north. The fault extends about 70 km from
the Ryukyu Trench to a depth of 13 km. We fix aforementioned fault parameters and solve for
slip-deficit rate and the long-term slip rate of each fault using a prioir constraints from previous
studies (Hsu et al., 2003; Ching et al., 2011) and the plate convergence rate of 80~85 mm/yr between
the EU and PSP.
Figure S2 below shows the derived slip-deficit rate, inferred long-term slip rates
of each fault, and residuals. The reduced-chi square of this model is 9.4. The slip deficit rate is 85
mm/yr on the shallow Ryukyu thrust if we take account both strain accumulation effects on the LVF
and the Ryukyu megathrust. This value is similar to the inferred slip-deficit rate of 86 mm/yr
considering only the strain accumulation effect on the Ryukyu megathrust in the main text. The
accumulated strain north of latitude 23.5°N seems to be better explained by fault coupling on the
Ryukyu megathrust.
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(a)
(b)
Figure S2. (a) Fault slip-deficit rate (color scale) and inferred long-term slip rates (magenta vectors)
on the northern (NLVF) and southern (SLVF) portions of the LVF and the Ryukyu thrust fault
(RyukyuT). Black and blue vectors indicate observed and predicated GPS velocities. (b) Horizontal
residuals (difference between black and blue vectors in (a)).
Gird search
We use a grid search to find the optimal fault parameters, which give the minimum misfit. We
vary the rate and the orientation of block motion from 80 to 90 mm/yr and 290° to 320°, respectively,
according to the plate convergence rate of 80-85 mm/yr in the direction of 300°~310° between the
EU and the PSP [Seno et al., 1993; Yu et al., 1997; Sella et al., 2002; Hsu et al., 2009]. We also vary
fault dip from 5° to 15°, fault width from 30 to 80 km and location of the fault. The fit to the data is
quantified from the mean of the normalized square residuals,  r2 .
on average the model fits the data within uncertainties.
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A  r2 value of 1 indicates that
Fault models with variable plate coupling ratios
To explore the impact of a non-uniform slip-deficit rate perpendicular to the Ryukyu Trench, we
consider a forward model where we parameterize plate coupling as a Gaussian function along the
down-dip direction of the fault. We then predict surface velocities at each model and compare with
GPS observations. If the shallow Ryukyu subduction zone is fully locked, the slip-deficit rate equals
to the long-term plate motion such that the plate coupling ratio, defined as the ratio between the
slip-deficit rate and the plate convergence rate, is equivalent to 1. Figure S3 shows the values of  r2
from fault models with plate coupling ratios vary as a Gaussian function, c  exp (d 2 / D 2 ) , where
c is the coupling ratio, d is the distance, and D is the distance-decay constant controlling the spatial
variation of the coupling ratio.
We consider two scenarios, one where c varies from 1 at trench axis
to 0 below Suao (Figure S3(a)) and the complementary model whereby c varies from 0 at trench axis
to 1 below Suao (Figure S3(b)). We search for a wide range of D and find the fault model with a
large plate coupling ratio gives the smallest misfit.
The smallest values of  r2 are 12.5 in these
two models, comparable to that in a uniform slip model. We find these two forward models require
plate interface to be fully coupled from the trench to a depth of 13 km.
(a)
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(b)
Figure S3. Plate coupling models with coupling ratios vary as a Gaussian function. (a) The
coupling ratio varies from 1 at trench axis to 0 at the bottom of the fault; (b) from 0 at trench axis
to 1 at the bottom of the fault. The color lines in left panels show a variety of plate coupling
patterns. The optimal model with the smallest reduced chi-squares is shown in thick line. The right
panel indicates the values of reduce chi-squares from all models given a wide range of the
distance-decay constant (D). The optimal model with the smallest reduced chi-squares is shown as
a red dot.
GPS observation at Yonaguni CGPS site
The majority of the CGPS sites used in this study are located along the eastern coast of Taiwan.
There is one CGPS site at Yonaguni Islands located in Ryukyu Arc.
The inferred velocity of
Yonaguni Island has a trenchward motion of 71.5 mm/yr with respect to the CGPS site, S01R, and is
very different from velocities along the Fengping-Suao coast. We do not use the Yonaguni site in our
modeling because there is no GPS sites trenchward in this area to help constrain any model
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complexities associated with the site (Figure 3a).
The Yonaguni site shows mostly trench-normal motion about 51.9 mm/yr with respect to SUAO
(Figure S4 below). If we assume the variation of GPS velocities perpendicular to the Ryukyu Trench
at longitude 123°E is similar to the variation between Fengping and Suao, the shortening rate in
trench-normal component is ~85 mm/yr, significantly larger than 40 mm/yr in Figure 3b.
Hence the
large trenchward motion suggests that the reverse component of slip-deficit rate is 2.1 times the
value of 35.9 mm/yr obtained using only GPS data between Fengping and Suao. We use our
preferred model in the previous section to predict GPS velocity on Yonaguni Island and find slightly
northward motion of 3.7 mm/yr, much less than the observed GPS velocity of 51.7mm/yr trenchward.
The trench-normal motion at Yonaguni is considerably underestimated such that it suggests the
slip-deficit rate may be larger in this section of the fault compared to the western section close to
Taiwan.
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Figure S4. The GPS velocity field with respect to SUAO between 2005 and 2010. Horizontal
velocities are shown in black vectors with 95% confidence ellipses from GLOBK. Vertical velocities
are shown by circles with uplift and subsidence indicated by red and blue colors, respectively. The
rectangle denotes the potential rupture fault along the Ryukyu Trench with a white arrow showing
the slip-deficit rate. LV: Longitudinal Valley, LVF: Longitudinal Valley Fault.
Resolution tests
The Figure S5 below shows the checkerboard resolution tests using the distribution of GPS
observations available for the backslip model. The first column shows the input models and the
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second column shows the inversion results by adopting the same data covariance and inversion
method as when using the actual GPS observations in this study. These tests demonstrate our ability
to resolve slip close to the east coast of Taiwan. However, the resolution is poor if the distance is
beyond 40 km from the coast.
Input models
Inversion results
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Figure S5. The first column shows the input slip models and the second column shows the inversion
results. The color scale indicates fault slip in meter.
Earthquake recurrence interval
The southern Ryukyu Islands were already populated by 1700. There are detailed records
documenting the 1771 tsunami. If a large shallow thrust earthquake (like the fault inferred in our
manuscript) along the southern Ryukyu Trench did occur after 1700 or even as far back as 1600, it
would have produced a large tsunami which we expect would have been documented in Japan or
Taiwan. Given the absence of any such records,, we assume the latest event occurred at least
400~500 years ago.
References
Altamimi, Z., X. Collilieux, J. Legrand, B. Garayt, and C. Boucher (2007), ITRF2005: A new release
of the International Terrestrial Reference Frame based on time series of station positions and
earth orientation parameters, J. Geophys. Res., 112, doi:10.1029/2007JB004949
Ching, K. E., R. J. Rau, K. M. Johnson, J. C. Lee, and J. C. Hu (2011), Present-day kinematics of
active mountain building in Taiwan from GPS observations during 1995-2005, J. Geophys. Res.,
116, doi:10.1029/2010JB008058
Herring, T. A., R. W. King, and S. C. McClusky (2002), Documentation for the GAMIT Analysis
Software, release 10.0 ed., Massachusetts Institute of Technology, Cambridge, MA.
Hsu, Y. J., M. Simons, S. B. Yu, L. C. Kuo, and H. Y. Chen (2003), A two-dimensional dislocation
model for interseismic deformation of the Taiwan mountain belt, Earth Planet. Sci. Lett., 211,
287-294.
Hsu, Y. J., S. B. Yu, M. Simons, L. C. Kuo, and H. Y. Chen (2009), Interseismic crustal deformation
10
in the Taiwan plate boundary zone revealed by GPS observations, seismicity, and earthquake
focal mechanisms, Tectonophysics, 479, 4-18.
Lund, B. and J. Townend, (2007), Calculating horizontal stress orientations with full or partial
knowledge of the tectonic stress tensor, Geophys. J. Int. 170, 1328-1335.
Sella, G. F., T. H. Dixon, and A. L. Mao (2002), REVEL: A model for Recent plate velocities from
space geodesy, J. Geophys. Res., 107, doi:10.1029/2000JB000033.
Seno, T., S. Stein, and A. E. Gripp (1993), A model for the Motion of the Philippine Sea Plate
consistent with Nuvel-1 and geological Data, J. Geophys. Res., 98, 17941-17948.
Wu, Y. M., Y. J. Hsu, C. H. Chang, L. S. Teng, and M. Nakamura (2010), Temporal and spatial
variation of stress field in Taiwan from 1991 to 2007: Insights from comprehensive first motion
focal mechanism catalog, Earth Planet. Sci. Lett., 298, 306-316.
Yu, S. B., H. Y. Chen, and L. C. Kuo (1997), Velocity field of GPS stations in the Taiwan area,
Tectonophysics, 274, 41-59.
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