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Geophysical Research Letters
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Supporting Information for
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Ongoing deformation of Antarctica following recent Great Earthquakes
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Matt A. King1 and Alvaro Santamaría-Gómez1,2
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1Surveying
and Spatial Sciences, School of Land and Food, University of Tasmania, Australia
2LIENSs, Université de La Rochelle/CNRS, La Rochelle, France.
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Contents of this file
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Introduction
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Supplementary materials provide detailed summary of the GPS data processing plus seven figures.
The tables summarize previously published slip distribution models for the A98 Earthquake and the
modelled co-seismic displacements.
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Text S1.
GPS analysis
Undifferenced ionosphere-free GPS data were processed using the GIPSY/OASIS II software,
version 6.3, developed at NASA Jet Propulsion Laboratory (JPL). Satellite orbits, satellite clocks bias
and Earth orientation parameters were fixed to the JPL final fiducial-free products.
Text S1
Figures S1 to S7
Tables S1 to S2
Elevation-dependent observation weighting was applied and observations below 10 degrees were
not included in order to minimize the effects of mismodelled low-elevation troposphere and
antenna PCV errors. Satellite arcs of less than 20 min duration were rejected. Absolute phase center
offsets with azimuth-dependent and elevation-dependent absolute PCV corrections were applied
for the ground antennas from the IGS08 compilation (GPS week 1793). For the GPS satellite
antennas, satellite-specific antenna phase center offsets and block-specific nadir angle-dependent
absolute PCV corrections were applied.
Second-order ionospheric refraction was corrected using the International Geomagnetic Reference
Model and following Kedar et al. [2003]. The slant Total Electron Content was extracted from the
International Reference Ionosphere 2012 model with the effective ionosphere shell height set to
600 km. Satellite-dependent P1-C1 differential code bias corrections were applied for the whole
period using monthly tables from the Astronomical Institute of the University of Bern.
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The motion of the Earth’s crust due to solid Earth tides, including frequency-dependent corrections,
and solid Earth / ocean pole tides, were corrected following the International Earth Rotation and
Reference Systems Service (IERS) Conventions 2010 [Petit and Luzum, 2010]. Ocean tide loading
deformation with respect to the center of mass of the solid Earth and oceans was corrected using
the IERS2010 conventions and 11 tidal constituents from the FES2004 model [Lyard et al., 2006].
We did not remove the effects of deformation due to interannual variation in Earth’s rotation pole
[King and Watson, 2014] as the effect is small in this region.
Station positions were estimated on a daily basis with real-valued phase ambiguities, receiver clock
biases and tropospheric delays. Station positions were estimated in 24h intervals while clock bias
and tropospheric delays were estimated at 5 min intervals. The a priori zenith tropospheric delay
was extracted from the European Centre for Medium range Weather Forecast (ECMWF)
meteorological data through the VMF1 grids [Boehm et al., 2006]. The residual zenith tropospheric
delays were adjusted using a random walk process assuming they were dominated by the
unmodeled wet component. The VMF1 mapping functions were used to relate the slant line-ofsight path delay to the zenith delay. Atmospheric gradients were estimated using a random walk
process following Bar-Sever et al. [1998]. Real-valued phase ambiguities were adjusted to integer
values [Bertiger et al., 2010].
Our procedure to transform fiducial-free station coordinates to a terrestrial reference frame differ
somewhat to those conventionally used in GIPSY analysis in two ways. First, we estimated our own
transformation parameters by estimating fiducial-free station coordinates for stations in global
geometrically-optimized daily networks drawn from the IGb08 core network. These were aligned to
the GPS realization of the International Terrestrial Reference Frame 2008 (ITF2008) [Altamimi et al.,
2011] (IGb08), estimating daily rigid 3-component translations and rotations between the fiducialfree frames and IGb08 using the GLOBK software[Herring et al., 2010]. Between-site correlations
are not available and were set to zero. A scale parameter was not estimated as it may absorb
vertical station motion, especially at the annual period. The vertical component of the coordinates
was down-weighted to minimize the impact of the non-linear station motion which are largest in
the vertical coordinate component. These six daily transformation parameters were then applied to
the fiducial-free station coordinates at Dumont D’Urville (DUM1). Comparison of DUM1 time series
using JPL transformation parameters revealed small differences, especially noticeable in longitude,
although this difference was not substantial enough to affect our choice of preferred viscous
models.
Second, the full variance-covariance of the estimated transformation parameters was propagated
into the aligned station coordinates. This had non-negligible effect on coordinate uncertainties
prior to 2000, and especially 1995 and 1996, when the transformation parameters are uncertain as a
result of the sparse distribution of reference frame sites.
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Figure S1. Subsets of the GPS and DORIS time series at Dumont D’Urville focusing on the coseismic displacement. GPS and DORIS are shown in red and grey, respectively. Some of the DORIS
data points have been cropped to show the details of the displacement. GPS offset uncertainties
are 1-sigma (68% confidence interval). Data uncertainties are discussed in Supplementary Text 2.
The orange-shaded area marks the time period over which the co-seismic displacement was
estimated.
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Figure S2. DORIS coordinate time series at Dumont D’Urville. Same as Figure 2, but just showing
the DORIS series and with the addition of a 0.25 y median smoother of the DORIS time series (blue
line).
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Figure S3. Detail of horizontal site motion from GPS at Dumont D’Urville. Evolution of the North
and East coordinate components and their ratio (N/E) are shown. The pre-earthquake DORIS
background rate has been subtracted prior to plotting or calculations. The cyan symbol marks the
ratio of the computed co-seismic displacements; its error bar is 1-sigma (68% confidence interval).
Data uncertainties are discussed in Supplementary Text 2. The dashed vertical line marks the time
of the 2004 Macquarie Island earthquake.
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Figure S4. Agreement between GPS and modelled time series at Dumont D’Urville between the
1998 and 2004 Earthquakes. a) Goodness-of-fit (2 per degree-of-freedom) with varying
lithospheric thickness and asthenospheric viscosity, with the base of the asthenosphere set to
220 km and upper mantle viscosity set to 1x1019 Pa s. The dashed lines shows the region of 2 per
degree-of-freedom less than 1. The stars show the best-fitting model for each coordinate
component for this set of models. b) Biases in estimated velocities when assuming the full time
series is unaffected by post-seismic deformation and is linear.
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Figure S5. Modelled A98 post-seismic deformation within a half-space considering lateral viscosity
variation. The map shows the displacement direction without (black) and with (magenta) lateral
variation in mantle viscosity. The orange lines show the effect of including the lateral variation (at
enlarged scale). The grey region shows the region of high mantle viscosity in the model. The star
marks the A98 earthquake location, the triangle the location of Dumont D’Urville (DUM1). Also
shown are the North and East time series based on the two models. Only part of the model domain
is shown.
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Figure S6. Predicted instantaneous velocities at long-running Antarctic GPS sites due to the A98
post-seismic deformation. Modelled (using VISCO1D) post-seismic site velocities for long-running
GPS sites in Figure 3 (inset, line colors match the site marker colors). Only the A98 event is
considered here. The strong rheology is that using an asthenosphere and upper mantle viscosity of
6x1019 Pa s and the weak rheology is using an asthenosphere viscosity of 1.2x1019 Pa s and upper
mantle viscosity of 1.4x1019 Pa s. Both have 90 km elastic lithosphere and 130 km thick
asthenosphere.
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Figure S7. GPS coordinate time series and velocities for Terra Nova Bay (TNB1). Coordinate time
series are shown relative to the background rate computed before the A98 event. No offsets have
been removed. The light blue line is a 0.5 year median filtered version of the time series. Velocities
are computed for data segments governed by equipment changes, marked with vertical dotted
lines. The times of the A98 and M04 events are shown as dashed brown lines. Velocities and 1sigma uncertainties were computed using the CATS software assuming a white plus flicker noise
model. Magenta and orange lines are as for Figure 2. GPS data were provided by Luca Vittuari with
1996 data from the SCAR Campaign database (http://tpg.geo.tudresden.de/ipg/forschung/scargps/scarstation.htm)
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Model
Solution
Henry et al.[Henry et
al., 2000] (H008)
Solution 8
Plane 1
Solution 8
Plane 2
Solution 5
Henry et al.[Henry et
al., 2000] (H005)
Nettles et al.[Nettles et
al., 1999; Toda and
Stein, 2000] (N00)
Mcguire et al.[McGuire
et al., 2000] (M00)
This study
Latitude Longitude Depth Strike Dip Rake Length1 Length2 Slip
(°)
(°)
(km) (°)
(°) (°)
(km)
(km)
(m)
-63.10
148.40
15.0
96 69
-18
20
110 18.99
-63.04
144.23
15.0
96
69
-18
0
60 20.74
-63.10
148.40
15.0
96
69
-18
95
Plane 1
-62.90
149.50
15.0
281
84
17
100
10 23.50
Plane 2
-62.90
-62.74
146.30
148.01
15.0
11.0
271
277
84
84
17
17
50
86
0 25.63
86 49.06
-62.74
148.01
11.0
277
84
17
86
86 41.93
225
8.88
Table S1. Published slip distribution models used in the study for the 1998 Mw 8.2 Antarctic Plate Earthquake. Location refers to the rupture
initiation location. Slip was assumed to be on a fault from the specified depth to the surface. Length1 is rupture distance in the direction of
strike, Length2 is in the opposite direction.
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Site
Dumont D’Urville
Casey
Terra Nova Bay
McMurdo
Davis
Mawson
Syowa
Vesleskarvet
Distance from North(mm) East(mm) Up(mm)
epicentre
(km)
640
10.8
13.0
2.9
1800
-0.1
1.4
0.0
1430
-1.3
1.4
-0.1
1760
-0.7
0.5
0.0
3150
-0.2
0.5
0.0
3800
-0.2
0.3
0.0
4400
-0.2
0.1
0.0
4970
0.0
0.0
0.0
Table S2. Modelled co-seismic displacements at long-running Antarctic geodetic sites for the 1998 Mw 8.2 Antarctic Plate Earthquake
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Supplementary References
Altamimi, Z., X. Collilieux, and L. Metivier (2011), ITRF2008: an improved solution of
the international terrestrial reference frame, J. Geodesy, 85(8), 457-473, doi:
10.1007/s00190-011-0444-4.
Bar-Sever, Y. E., P. M. Kroger, and J. A. Borjesson (1998), Estimating horizontal
gradients of tropospheric path delay with a single GPS receiver, Journal of Geophysical
Research, 103(B3), 5019-5035.
Bertiger, W., S. Desai, B. Haines, N. Harvey, A. Moore, S. Owen, and J. Weiss (2010),
Single receiver phase ambiguity resolution with GPS data, J. Geodesy, 84(5), 327-337,
doi: doi: 10.1007/s00190-010-0371-9
Boehm, J., B. Werl, and H. Schuh (2006), Troposphere mapping functions for GPS and
very long baseline interferometry from European Centre for Medium-Range Weather
Forecasts operational analysis data, Journal of Geophysical Research, 111, B02406,
doi:02410.01029/02005JB003629.
Henry, C., S. Das, and J. H. Woodhouse (2000), The great March 25, 1998, Antarctic
Plate earthquake: Moment tensor and rupture history, Journal of Geophysical Research:
Solid Earth, 105(B7), 16097-16118, doi: 10.1029/2000jb900077.
Herring, T. A., R. W. King, and S. C. McClusky (2010), Documentation for the GAMIT
GPS analysis software, version 10.40 Rep., Massachusetts Institute of Technology,
Cambridge.
Kedar, S., G. A. Hajj, B. D. Wilson, and M. B. Heflin (2003), The effect of the second
order GPS ionospheric correction on receiver positions, Geophys. Res. Lett., 30(16),
1829, doi:1810.1029/2003GL017639.
King, M. A., and C. S. Watson (2014), Geodetic vertical velocities affected by recent
rapid changes in polar motion, Geophys. J. Int., 199(2), 1161-1165, doi:
10.1093/gji/ggu325.
Lyard, F., F. Lefevre, T. Letellier, and O. Francis (2006), Modelling the global ocean
tides: modern insights from FES2004, Ocean Dynamics, 56(5-6), 394-415,
doi:310.1007/s10236-10006-10086-x.
McGuire, J. J., L. Zhao, and T. H. Jordan (2000), Rupture dimensions of the 1998
Antarctic Earthquake from low-frequency waves, Geophys. Res. Lett., 27(15), 23052308, doi: 10.1029/1999gl011186.
Nettles, M., T. C. Wallace, and S. L. Beck (1999), The March 25, 1998 Antarctic Plate
Earthquake, Geophys. Res. Lett., 26(14), 2097-2100, doi: 10.1029/1999gl900387.
Petit, G., and B. Luzum (2010), IERS Conventions IERS Technical Note Rep. 36, 179 pp,
Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main.
Toda, S., and R. S. Stein (2000), Did stress triggering cause the large off-fault aftershocks
of the 25 March 1998 Mw=8.1 Antarctic Plate earthquake?, Geophys. Res. Lett., 27(15),
2301-2304, doi: 10.1029/1999gl011129.
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