The 2013 Balochistan Earthquake-Suppl.-11/21/2013
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The 2013, Mw 7.7 Balochistan Earthquake, seismic slip boosted
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on a misoriented fault
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Jean-Philippe Avouaca,*, Francois Ayouba, Shengji Weia, Jean-Paul Ampueroa, Lingsen Menga, Sebastien
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Leprincea, Romain Joliveta, Zacharie Duputela and Don Helmbergera
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* Corresponding Author ([email protected])
Geology and Planetary Science Division, Caltech Institute of Technology, Pasadena, USA
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SUPPLEMENTS
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Optical images correlation
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Landsat 8 imagery
We correlate pre- and post-earthquake Landsat-8 (L8) images to obtain the surface rupture maps.
L8 is an optical satellite system, launched by NASA in February 2013 and now operated by the
USGS, which images the earth every 16 days. Each acquisition is a multi-spectral image
composed of 11 bands in the visible, near infrared, short wave infrared, and thermal infrared
spectrum, and quantized on 12 bits. The images have a pixel resolution of 15, 30, or 100 m
depending on the wavelength, cover an area of approximately 185x185 km, and are acquired at
nadir, which limits topographic distortions. The USGS orthorectifies and projects the images on
a UTM grid and releases them to the public within 24h after acquisition.
Dataset
Two adjacent images along the satellite track are necessary to cover the entire ground rupture.
The pre- and post-earthquake images IDs of the southern area are LC81540422013253LGN00
and LC81540422013269LGN00, respectively. The pre- and post-earthquake images IDs of the
northern area are LC81540412013253LGN00 and LC81540412013269LGN00, respectively. The
pre-earthquake images were acquired on September, 10, 2013 (14 days before the event), and the
post-earthquake images were acquired on September, 26, 2013 (2 days after the event). The
orthorectified images were downloaded from Earthexplorer (http://earthexplorer.usgs.gov/), and
processed using COSI-Corr14 as follows.
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COSI-Corr correlation
The co-registration between the pre- and post-earthquake images is good enough (<1/10 pixel) to
correlate them directly without the necessity of a pre-registration step. We correlate band 8 of
each image, which is the panchromatic band at 15 m/pixel, using a window size of 64x64 pixels
(960x960 m) and a sliding step of 16 pixels (240 m), and obtain displacement fields in East/West
and North/South directions with a ground sampling distance of 240 m.
Displacement fields destripping
The raw displacement fields (from correlation) (Fig S1) contains along-track stripes that result
from the staggered CCD arrays in the focal plane – a common artifact in pushbroom systems.
These artifacts are removed during a destripping process: we extract profiles across the swath
(over an area free of ground deformation), and average them in the along-track direction to
characterize the CCD bias (Fig S1). Once the bias is characterized, it is subtracted from the entire
field map. East/West and North/South displacement fields of both the southern and northern
areas are destripped using this procedure.
Displacement fields mosaicking
Once the displacement fields are cleaned from CCD stripes, southern and northern areas are
mosaicked into one single displacement field, based on their respective georeferencing. The
northern and southern areas are overlapping over a distance of about 32 km (Fig. S2). To limit
mosaicking effect (tile border effect), we subtract a ramp in the northern part displacement field
which we define from the difference between the displacement fields (southern and northern) on
the overlap.
Measurement error estimation
To estimate a confidence on the displacement, we extract East/West and North/South
measurements over an area (Fig S2) presumably free of ground deformation, and compute the
mean and deviation. Less than 1 m of deviation is observed despite small topographic residual,
which are limited in amplitude due to the nadir acquisition of L8 images. We estimate the 1-σ
uncertainty of the displacement for the East/West and North/South direction to 47 and 60 cm
respectively.
Fault slip extraction
The surface fault slip displayed in Fig.2 (inset) is obtained from approximately 30 measurements
evenly spread along the fault. We extract slip in East/West and North/South directions and
project them in strike-slip/fault-normal components. To minimize the noise on the estimated slip,
we stack all measurements in a 5 km swath centered at each fault slip measurement point.
Finite source modeling and inversion procedure
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We approximate the fault geometry with 7 planar fault segments, each discretized in 8 × 4 km2
subfaults. The model assumes that the rupture consists of a propagating rupture front with slip
accruing in the wake of the passage of the rupture front. The slip history at each grid point (j,k)
̇ (𝑡), where 𝑆𝑗𝑘
̇ (𝑡) is the slip-rate function, which specifies
on the fault is represented by 𝐷 × 𝑆𝑗𝑘
how a point on the fault slips in time, and D is the cumulative (or ‘static’) slip. The rise-time
function is represented by a cosine function parametrized by the duration of slip, the so-called
rise-time. Because the seismograms are band-filtered, the rather smooth slip-rate function chosen
in those inversions is adapted to the frequency band of the inversion although a more abrupt sliprate function would probably be more realistic (Tinti et al., 2005). For each subfault, we solve for
the slip amplitude and rake, rise time and rupture velocity.
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The Green’s functions are generated assuming a 1-D model derived from combining PREM with
a local body waves and surface tomographic studies (Maggi and Priestley, 2005; Yamini-Fard et
al., 2007) (Table S1). If the fault model does not match exactly the location of the surface
displacement discontinuity, slip on the shallow fault patches is artificially damped. This problem
is alleviated by enforcing shallow surface slip to match surface slip measurements (inset of
Figure 2) to within 2−σ (Avouac et al., 2006).
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The determination of a finite fault slip model is an underdetermined problem due to the large
number of unknowns and numerous trade-off among model parameters, such as rise time and
rupture velocity. In the present case the trade-offs are significantly reduced if coseismic geodetic
observations are available and inverted jointly with the seismological data. Even though, the
determination of a finite fault source remains generally underdetermined if the fault
discretization is too fine. One way to regularize the inversion is to set some constraints on the
roughness of the slip distribution which is the approach adopted here.
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We define the best fit model as having the lowest objective function, given as:
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Misfit= Ewf+ WI *EI +WS *S + Ww*M,
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where Ewf is the waveform misfit, EI is the geodetic misfit, S is a normalized, second derivative
of slip between adjacent patches (a so-called Laplacian smoothing). M is a normalized seismic
moment, and WI, WS and Ww are the relative weighting applied to the geodic misfit, smoothing,
and moment, respectively. The least squares misfits are calculated for the teleseismic and
geodetic data. Here we test different values of WI, and we found that setting the weight for the
geodetic misfits twice larger than the waveform misfits did not significantly degrade the fits to
the teleseismic or geodetic data between the individual and joint inversions given the
normalizations schemes. The static green’s functions at free surface are calculated by using the
same 1D velocity model (Table S1) as used in teleseismic body-wave calculation. The weight
placed on smoothing was chosen based on the L-curve (Hansen and Oleary, 1993).
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We use a simulated annealing algorithm (Ji et al., 2002) to find the best fitting model parameters
for the joint inversions for coseismic slip. This nonlinear, iterative inversion algorithm is
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designed to avoid local minima by searching broadly through the parameters space in initial
steps, and then in later iterations by focusing on regions that fit well the data.
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Figure S3-S4 compares the predicted and observed surface displacements. Figure S5 compares
the predicted and recorded waveforms and show the rise-time and slip-distributions
corresponding to our best fitting model.
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References
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Avouac, J.P., Ayoub, F., Leprince, S., Konca, O., Helmberger, D.V., 2006. The 2005, M-w 7.6
Kashmir earthquake: Sub-pixel correlation of ASTER images and seismic waveforms analysis.
Earth and Planetary Science Letters 249, 514-528.
Duputel, Z., Rivera, L., Kanamori, H., Hayes, G., 2012. W phase source inversion for moderate to
large earthquakes (1990-2010). Geophysical Journal International 189, 1125-1147.
Hansen, P.C., Oleary, D.P., 1993. THE USE OF THE L-CURVE IN THE REGULARIZATION OF
DISCRETE III-POSED PROBLEMS. Siam Journal on Scientific Computing 14, 1487-1503.
Ji, C., Wald, D., Helmberger, D.V., 2002. Source Description of the 1999 Hector Mine, California
Earthquake, Part I: Wavelet Domain Inversion Theory and Resolution Analysis. Bull. Seismol.
Soc. Am. 92, 1192-1207.
Leprince, S., Barbot, S., Ayoub, F., Avouac, J.P., 2007. Automatic and precise orthorectification,
coregistration, and subpixel correlation of satellite images, application to ground
deformation measurements. Ieee Transactions on Geoscience and Remote Sensing 45,
1529-1558.
Maggi, A., Priestley, K., 2005. Surface waveform tomography of the Turkish-Iranian plateau.
Geophysical Journal International 160, 1068-1080.
Tinti, E., Bizzarri, A., Cocco, M., 2005. Modeling the dynamic rupture propagation on
heterogeneous faults with rate- and state-dependent friction. Annals of Geophysics 48, 327345.
Yamini-Fard, F., Hatzfeld, D., Farahbod, A.M., Paul, A., Mokhtari, M., 2007. The diffuse
transition between the Zagros continental collision and the Makran oceanic subduction
(Iran): microearthquake seismicity and crustal structure. Geophysical Journal International
170, 182-194.
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Table S1: W-phase moment tensor solution. The tensor was determined based on 139
seismological records manually selected based on data-quality at epicentral distances larger than
90°. Waveforms were filtered between 200s and 600s. For details about the inversion procedure
see Duputel et al (2012)(Duputel et al., 2012).
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Table S2: Velocity Model Used to Compute the Greens Functions.
PDEQ2013 9 24
event name:
time shift:
half duration:
latitude:
longitude:
depth:
Mrr:
Mtt:
Mpp:
Mrt:
Mrp:
Mtp:
11 29 49.00 27.0000
201309241129A
21.0000
21.0000
26.6400
65.1519
11.5000
5.197801e+26
-4.000970e+27
3.481190e+27
1.918599e+27
-2.717967e+27
3.336192e+25
65.5100
20.0 0.0 7.7 PAKISTAN
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Top Depth
(km)
0
4
16
30
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Vp
(km/s)
5.44
6.25
6.53
6.80
7.50
8.11
Vs
(km/s)
3.00
3.45
3.60
3.90
4.30
4.49
Density
(103kg/m3)
2.50
2.60
2.70
2.90
2.90
3.30
Qp
Qs
300
400
500
600
800
1000
150
200
250
300
400
500
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Table S2: Characteristic of the 6-segment fault model (ordered from North to South).
Segment
Strike
Dip
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2
3
4
5
6
7
216
203
223
230
238
242
251
70
60
47
47
56
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Depth Extent
(km)
29.0
26.8
22.6
22.6
25.6
25.6
25.6
North End
(top)
65.689/27.348
65.505/27.140
65.314/26.745
65.154/26.593
64.967/26.466
64.704/26.316
64.434/26.184
South End
(top)
65.507/27.125
65.321/26.754
65.158/26.596
64.979/26.462
64.706/26.320
64.431/26.187
64.066/26.071
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Figure S1: Raw East/West displacement map of the south part of the ground rupture. Along-track
stripes are due to geometric residual of the staggered disposition of the CCD arrays in the focal
plane. The bias is characterized (red profile) from the average in the along-track direction of the
displacement over the light color box, and then subtracted from the displacement map (Fig. 2).
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Figure S2: Complete surface displacement field measured from cross-correlation of pre EQ
images acquired 09/10/13 (LC81540412013253LGN00 and LC81540422013253LGN00) and
post
EQ
images
acquired
09/26/13
(LC81540412013269LGN00
and
LC81540422013269LGN00). We used Landsat-8 images (15m GSD) which we correlated using
COSI-Corr (Leprince et al., 2007). Color scale shows EW component of the displacement field
with a 240 m Ground Sampling Distance measured with a 64x64 correlation window. Inset
shows histogram of EW and NS displacements within the two areas with presumably null
displacement outlined with dashed line boxes in map view. The overlap between the south and
north part images is located by the dashed lines.
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Figure S3: Comparison between measured (‘data’) and synthetic (‘model’) horizontal
displacements for the pair of images covering the northern area (pre EQ image:
LC81540412013253LGN00 acquired 09/10/13; post EQ image: LC81540412013269LGN00
acquired 09/26/13).
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Figure S4: Comparison between measured (‘data’) and synthetic (‘model’) horizontal
displacements for the pair of images covering the southern area (pre EQ image:
LC81540422013253LGN00 acquired 09/10/13; post EQ image: LC81540422013269LGN00
acquired 09/26/13).
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Figure S5: Distribution of stations selected for inversion of teleseismic waveforms. (b)
Comparison between measured (black) and synthetic (red) teleseismic waveforms on the selected
stations with P-waves shown on the left and SH-waves on the right. Stations names are shown on
the left of each waveform comparison along with azimuth (upper) and epicenter distance (lower)
in degree. Stations are arranged such that the azimuth increases from bottom to the top. Note that
the SH-waves are much broader in the direction away from the rupture than that towards the
rupture, as indicated by the red arrows. (c) Slip distribution in depth view. Arrows indicate the
rake angle and the slip amplitude is color coded. Rupture times are indicated by the contours. (d)
Rise times distribution in depth view. Slip patches with slip amplitude larger than 2 m only are
displayed.