GSA DATA REPOSITORY 2010252
He and Peltzer
InSAR data analysis: Three pairs of satellite images (Table DR1) are processed into
interferograms using the ROI_PAC software (Rosen et al., 2000). The processing follows
the standard 2-pass approach using the Shuttle Radar Topography Mission (SRTM) data
to remove the topographic phase. To avoid aliasing of the phase in the region of high
phase gradient, the data are processed at one range look and referenced to a latitudelongitude grid with a step of 1 arc second. Unwrapping is done using the ROI_PAC
default branch-cut algorithm for the pairs on tracks 341 and 348. Higher phase noise
required using the SNAPHU unwrapper (Chen et al., 2001) for the pair on track 427. The
phase fields of the three interferograms are then masked with a phase correlation
threshold of 0.3. The results are shown in Figure 1, b, c, and d.
Data inversion: Observed displacement field shows that two distinct faults broke in the
sequence (Fig. DR1a). A series of forward models using uniform slip on faults embedded
in an elastic half space (Okada, 1992) are performed and compared to displacement
profiles perpendicular to the faults to determine an a-priori dip angle for each fault. The
main and the second faults are divided into 10  10 and 5  5 rectangular patches,
respectively, to resolve slip variations on the two planes. The dip of each fault is later
refined using a data-model misfit adjustment.
The displacement data of the 3 interferograms are decimated to retain only a sub-set
of points (Fig. DR1b). The decimation is based on the local phase gradient in order to
keep a denser distribution of points in areas of large deformation (Lasserre et al., 2005).
The data subsets are then inverted using a standard least-square procedure to solve
for the down-dip and strike-slip components of slip on the faults. Solution smoothing is
used in the inversion to reduce high oscillations in the slip distribution on faults and the
optimum weight for the smoothing equations is adjusted to minimize the solution
roughness without affecting significantly the data-model misfit (Fig. DR1c).
Finally a parameter grid search is performed to refine the dip angles of the two faults
(Fig. DR1d). Optimum dip angles of 45˚ for the main fault and 58˚ for the second fault
are chosen in the region of minimum misfit under the condition that the two faults do not
intersect at depth. The optimum fault solution leads to a good agreement between the
observed and synthetic interferograms (Fig. DR2). The largest discrepancies occur in the
areas where the faults reach the surface and are due to the simplified geometry and
discretization of the faults at shallow depth.
Pore fluid flow and post-seismic Coulomb Stress change model: The fault geometry
and variable slip solution for the main fault are used to calculate the changes of Coulomb
stress and pore pressure due to poroelastic deformation of the crust. The Coulomb stress
is computed throughout the volume on a direction parallel to the down-dip direction of
the second fault. Because we focus on the stress-pressure evolution in a relatively short
time period after the Jan. 9, 2008 event (~2 weeks), poroelastic deformation of the crust
1
is assumed to follow the Biot’s theory (Wang, 2000). The components of the stress
change  ij due to the earthquake-related strain ( ij ) in the solid are given by
 ij  2G  (ij 
u
1 2 u
kk  ij ) ,
(1)
where G is the shear modulus, kk the trace of the strain tensor,  u the undrained
Poisson’s ratio and  the Kronecker delta symbol. The change of pore fluid pressure p
due to bulk elastic deformation is calculated using (Screaton and Ge, 2007)
ij
p  B  G  (
2(1  u )
)  ii ,
3(1 2 u )
(2)
where B is the Skempton’s coefficient. The evolution of the pore fluid pressure is
assumed to be governed by the mass diffusion equation
D   2h 
h
t
(3)
where D is the diffusivity of fluids, h the hydraulic head, and t the time (Screaton and
Ge, 2007).
We construct a three-dimensional, finite-element model using the Finite Element
Program Generator (FEPG) software to compute the coupled solution of elastic
deformation and pore fluid flow. The split-node technique is used to impose slip on Fault
1 based on the slip distribution determined by inversion of InSAR data (Fig. 2). Fault 2 is
modeled as a planar zone of finite thickness with specific permeability. The thickness of
damaged fault zones could range from ~200 m to ~1-2 km (Ben-Zion, et al., 2003;
Cochran, et al., 2009). Fault 2 is a relatively small fault and its thickness is assumed to be
80 m (Fig. DR3). To achieve hydrostatic equilibrium in the entire volume before the first
seismic event, we run the model over 60 years with 1-year time steps. At t=0, the coseismic displacement of the Jan. 9, 2008 event is imposed on Fault 1 and a poroelastic
solution is computed at regular time steps for 10 days. To avoid numerical instabilities
immediately after the event, time steps of 1 hour are used for the first 2 days and steps of
12 hours are used between day 2 and day 10 after the first event.
2
Figure DR1. (a) Co-seismic interferogram of Figure 1b draped over shaded topography
model of study area. White arrows point at morphologic fault scarps and black, dashed
lines indicate approximate location of fault-surface intersection for the two modeled fault
planes. (b) Spatial distribution of 966 data points kept in model inversion. Colors refer to
3 interferograms in tracks 341, 348, and 427. See the section on data inversion for details.
(c) Trade-off between L2 norm of least-squares solution misfit and model roughness
(average slip gradient). Our preferred model has a roughness of ~0.8 cm/km. (d) Model
misfit variations represented in the Fault 1 – Fault 2 dip angles parameter space. White
dashed line separates regions where faults intersect at depth (upper left), and are
disconnected (lower right). White triangle represents the preferred set of dip angles of the
two faults.
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Figure DR2. Comparison between observed and modeled radar line of sight
displacement. (a), (b) and (c) are observed interferograms of Track 348, 341 and 427,
respectively. (d), (e) and (f) are synthetic interferograms based on fault model for the
same tracks, respectively. (g), (h) and (i) are residuals between observed and synthetic
displacement on same tracks, respectively. Solid lines show upper edges of modeled fault
planes.
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Figure DR3. (a) 3-dimentional grid of finite elements used in poroelastic model.
Earthquake faults are placed in the center of large volume to minimize boundary effects
on numerical solution. The volume is divided into 106,200 hexahedral elements with
higher node density near the faults. Boundary conditions are: Vertical walls of models are
fixed (no movement) in horizontal directions (x,y) and free in vertical (z) direction.
Bottom surface is fixed in vertical direction and free in horizontal directions. Upper
surface is free in three directions. We assume there is no input and output of pore fluid
across the 6 edges of the model, and under the gravitational field the hydraulic head is at
the upper surface. Blue rectangle on upper surface is area shown in (b). (b) Details of grid
geometry along two modeled faults. Blue box shows map view from top of fault area (see
location in (a)).
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Table DR1. Parameters of Envisat data used in this study. Heading is azimuth clockwise
from North of satellite heading direction. Incidence angle is angle between radar line of
sight and vertical direction at center of study area. Bp is perpendicular component of
baseline between orbits in interferometric pair. T is time interval between two acquisition
dates. Dates are written as day/month/year.
Track
341
427
348
Date 1
Date 2
09/08/2007 31/01/2008
28/03/2007 06/02/2008
23/11/2007 01/02/2008
Heading (˚)
Inc. angle (˚)
-13.24
-13.28
-166.5
26.0
42.0
20.4
Bp
(m)
131
38
25
T
(days)
175
311
70
Additional references:
Ben-Zion, Y., Peng, Z., Okaya, D., et al., 2003, A shallow fault-zone structure
illuminated by trapped waves in the Karadere-Duzce branch of the North Anatolian
Fault, western Turkey: Geophysical Journal International, v. 152, p. 699–717, doi:
10.1046/j.1365–246X.2003.01870.x.
Chen, C. W., Zebker, H. A., 2001, Two-dimensional phase unwrapping with use of
statistic models for cost functions in nonlinear optimization: Journal of optical
Society of America (A), v. 18, p. 338-351.
Cochran, E., Li, Y.-G., Shearer, P., et al., 2009, Seismic and geodetic evidence for
extensive, long-lived fault damage zones: Geology, v. 37(4), p. 315–318; doi:
10.1130/G25306A.1
Lasserre, C., Peltzer, G., Crampe, F., Klinger, Y., van der Woerd, J., Tapponnoer, P., 2005,
Coseismic deformation of the 2001 Mw=7.8 Kokoxili earthquake in Tibet, measured
by synthetic aperture radar interferometry: Journal Geophysical Research, v. 110,
B12408, doi:10.1029/2004JB003500.
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