The 2013 Balochistan Earthquake-Suppl.-11/21/2013 1

The 2013, Mw 7.7 Balochistan Earthquake, seismic slip boosted

on a misoriented fault

Jean-Philippe Avouaca,*, Francois Ayouba, Shengji Weia, Jean-Paul Ampueroa, Lingsen Menga, Sebastien

Leprincea, Romain Joliveta, Zacharie Duputela and Don Helmbergera

a Geology and Planetary Science Division, Caltech Institute of Technology, Pasadena, USA

* Corresponding Author (avouac@gps.caltech.edu)

SUPPLEMENTS

Optical images correlation

Landsat 8 imageryWe 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.

DatasetTwo 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 correlationThe 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 destrippingThe 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 mosaickingOnce 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 estimationTo 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 extractionThe 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) on the fault is represented by D × S jk(t ), where S jk(t ) is the slip-rate function, which specifies 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 slip-rate 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.

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).

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.

We define the best fit model as having the lowest objective function, given as:

Misfit= Ewf+ WI *EI +WS *S + Ww*M,

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).

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.

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.

References

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, 327-345.

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).

PDEQ2013 9 24 11 29 49.00 27.0000 65.5100 20.0 0.0 7.7 PAKISTANevent name: 201309241129Atime shift: 21.0000half duration: 21.0000latitude: 26.6400longitude: 65.1519depth: 11.5000Mrr: 5.197801e+26Mtt: -4.000970e+27Mpp: 3.481190e+27Mrt: 1.918599e+27Mrp: -2.717967e+27Mtp: 3.336192e+25

Table S2: Velocity Model Used to Compute the Greens Functions.

Top Depth(km)

Vp(km/s)

Vs(km/s)

Density(103kg/m3)

Qp Qs

0 5.44 3.00 2.50 300 1504 6.25 3.45 2.60 400 20016 6.53 3.60 2.70 500 25030 6.80 3.90 2.90 600 30042 7.50 4.30 2.90 800 40045 8.11 4.49 3.30 100

0500

Table S2: Characteristic of the 6-segment fault model (ordered from North to South).

Segment Strike Dip Depth Extent (km)

North End (top)

South End (top)

1 216 70 29.0 65.689/27.348 65.507/27.1252 203 60 26.8 65.505/27.140 65.321/26.7543 223 47 22.6 65.314/26.745 65.158/26.5964 230 47 22.6 65.154/26.593 64.979/26.4625 238 56 25.6 64.967/26.466 64.706/26.3206 242 56 25.6 64.704/26.316 64.431/26.1877 251 56 25.6 64.434/26.184 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.

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