Auxiliary material for Paper 2013GL059178
Improved Constraints on Seismic Source Parameters of the 2011 Tohoku Earthquake from
GRACE Gravity and Gravity Gradient Changes
Chunli Dai
Division of Geodetic Science, School of Earth Sciences, The Ohio State University, Columbus,
Ohio 43210, USA
GFZ German Research Centre for Geosciences, Section 2.1: Physics of Earthquakes and
Volcanoes, Telegrafenberg, D-14473 Potsdam, Germany
Division of Seismology, Geology, and Tectonophysics, Lamont-Doherty Earth Observatory,
Columbia University, Palisades, New York 10964, USA
Dai, C., C.K. Shum, R. Wang, L. Wang, J. Guo, K. Shang, B. Tapley (2014), Improved
Constraints on Seismic Source Parameters of the 2011 Tohoku Earthquake from GRACE
Gravity and Gravity Gradient Changes, Geophys. Res. Lett.,…
Introduction
The auxiliary material contains a text file, 1 table, 12 figures, 3 animations.
1. 2013GL059178-sup-text01.pdf
Text S1. Details of generating the gravity and gravity gradient change corresponding to the
coseismic and postseismic slip distribution model. Details of the sensitivity analysis of gravity
and gravity gradient change to various fault parameters. Description of some formulas used in
the paper.
2. 2013GL059178-ts01.pdf
Table S1. RMS and relative differences between the GRACE observation and two slip model
predictions.
4. 2013GL059178-ps01.png
Figure S1. GRACE-observed seismic gravity and gravity gradient change from JPL product.
From left to right: gN, Txx, Txy, Txz changes, using 98 monthly JPL L2 RL05 geopotential field
solutions complete to spherical harmonic degree 60, from 1 January 2004 to 19 Apr 2012. The
GOCO02S reference model [Goiginger et al., 2011] is adopted. The uncertainties for gN, Txx,
Txy, Txz, are around 1.3 μGal, 0.09 mE, 0.07 mE, 0.12 mE (mean values), respectively. Other
descriptions are the same as in Fig. 2.
5. 2013GL059178-ps02.png
Figure S2. GRACE-observed seismic gravity and gravity gradient change from GFZ product.
From left to right: gN, Txx, Txy, Txz changes, using 114 monthly GFZ L2 RL05 L2 geopotential
field solutions complete to spherical harmonic degree 60, from January 2003 to November
2012. Other descriptions are the same as in Fig. 2.
6. 2013GL059178-ps03.pdf
Figure S3. Gravity change, vertical displacement and ‘equivalent’ vertical displacement on
ocean floor. The coseismic and postseismic slip distribution model [Wei et al., 2012; Ozawa et
al., 2011] is adopted. Left: Gravity change (μGal) (without free air correction) corresponding to
solid Earth change; Middle: Vertical displacement, H (meter) with upward as positive direction;
Right: ‘Equivalent’ vertical displacement caused by topography with horizontal displacement.
Black Rectangle is the coseismic fault boundary.
7. 2013GL059178-ps04.pdf
Figure S4. Gravity (down component) change at ocean floor from three sources. Left: gD due to
solid Earth deformation; middle: gD from passive ocean response; right: gD due to the
approximate topographic correction. The black rectangle is the coseismic fault plane boundary,
and the black star is the estimated Global Centroid Moment Tensor Project (GCMT) epicenter
(143.05°E, 37.52°N).
8. 2013GL059178-ps05.pdf
Figure S5. Gravity change at Earth’s surface. North (left), east (middle), down (right)
components of gravity change for both solid Earth deformation and passive oceanic response.
Use the spherical harmonic expansion (truncated to degree 899) to upward continue to the Earth
surface.
9. 2013GL059178-ps06.pdf
Figure S6. Spectra comparison for JPL product. Percentage of degree variance as a function of
spherical harmonic degree, for the JPL-product-derived and model-predicted north component
of gravity, gN, and gravity gradient changes, Txx, Txy, Txz. It shows gN has the lowest noise
level by the smallest discrepancy between GRACE and model predicted degree variance for
degree above 48. The nth degree variance of gN is defined as the sum of the squares of all
spherical harmonic coefficients at degree n.
10. 2013GL059178-ps07.pdf
Figure S7. Sensitivity to length. Model derived gN change for the fault length: 300 km (a), 600
km (b), 900 km (c). Fault parameters are: strike angle 200°, fault width 300 km, dip angle 9°,
depth 5 km, slip magnitude 2 m, rake angle 90°. The black rectangle is the fault plane boundary,
and the black star is the Tohoku-Oki earthquake epicenter. White line is a chosen profile (70° to
the strike direction) across main peaks.
11. 2013GL059178-ps08.pdf
Figure S8. Sensitivity to strike and rake. Model derived Txx change for the fault strike angle of
210° (a), 240° (b), 270° (c), and model derived Txz change for the slip rake angle of 30° (d), 60°
(e), 90° (f). Fixed fault parameters are: fault length 600 km, fault width 300 km, dip angle 9°,
depth 5 km, slip magnitude 2 m. Rake angle is 90° for the strike angle case, and strike angle is
200° for the rake angle case. Other markings represent the same as in Fig. S7.
12. 2013GL059178-ps09.pdf
Figure S9. Sensitivity to width. Coseismic gN change (left) and gravity gradient change (right)
along the profile in Fig. S7 for width of 100 km, 200 km, 300 km, respectively. Center of the
fault plane is fixed. Fault strike angle, length, dip angle, depth, slip, rake angle, are fixed at
200°, 600 km, 9°, 5 km, 2 m, 90°, respectively. Circles are the local maxima.
13. 2013GL059178-ps10.pdf
Figure S10. Sensitivity to dip. Coseismic gN change (left) and gravity gradient change (right)
along the profile in Fig. S7 for dip angle of 3°, 9°, and 15°, respectively. Fault strike angle,
length, width, depth, slip, rake angle, are fixed at 200°, 600 km, 300 km, 5 km, 2 m, 90°,
respectively. Center of the fault plane is fixed.
14. 2013GL059178-ps11.pdf
Figure S11. Sensitivity to depth. Coseismic gN change (left) and gravity gradient change (right)
along the profile in Fig. S7 for depth of 5 km, 30 km, 50 km. Fault strike angle, length, width,
dip angle, slip, rake angle, are fixed at 200°, 600 km, 300 km, 9°, 2 m, 90°, respectively.
15. 2013GL059178-ps12.pdf
Figure S12. Solution uncertainty for rake angle. Each red dot is a trial of rake angle, fault length,
width, slip, and location during inversion. The minimum relative difference would give the
optimal solution, which is 77° for rake angle as shown. The red horizontal line is corresponding
to 0.1 plus the minimum relative difference. In figure, the rake angle range [75, 79] can give
relative differences lower than the red line. This range is defined as solution uncertainty.
16. 2013GL059178-ms01.mp4
Animation S1. Spatial orientation changes between GRACE-observed and model-predicted
gravity and gravity gradient change. The data and other descriptions are the same as in Figs. 2–
3.
17. 2013GL059178-ms02.mp4
Animation S2. Sensitivity of gravity and gravity gradient change for different strike angles.
18. 2013GL059178-ms03.mp4
Animation S3. Sensitivity of gravity and gravity gradient change for different rake angles.