Radarsat-2 Processing
We used three co-seismic interferograms listed in Table S1: two interferograms from Wide Multi-Look
Fine 22 beam (MF22W) with a common master image and one interferogram from Wide Multi-Look
Fine 21 beam (MF22W). These images were acquired from the ascending orbit with an azimuth of 348 degrees and with incidence angles of 34.0 and 36.1 degrees, correspondingly for MF22W and MF21W beams. The SAR data was obtained in the Single Look Complex (SLC) format and consequent frames from the same acquisition were concatenated into a single image using the seven point SINC interpolation function. The archived coverage of the MF22W beam from 29 March, 2012 consisted of 12 frames but the first post-event acquisition on 17 April 2013 consisted of only five frames, therefore, the first interferogram 20120329 – 20130417 had a limited coverage. The second post-event acquisition on
11 May 2013 from MF22W beam consisted of 12 frames precisely matching the archived coverage.
The archived coverage of the MF21W beam from 22 March 2012 consisted of 7 frames located northwest from MF22W data and the post-even acquisition on 4 May 2013 precisely matched the archived data.
Interferograms were processed with the GAMMA software [ Wegmuller and Werner , 1997]. The pre-event image was selected as a master and post-event images were re-sampled into the master geometry. The interferograms were calculated with multilooking of 6 in range and 10 in azimuth and the topographic phase was removed using the 90 m resolution SRTM DEM [ Farr et al.
, 2007]. Differential interferograms were filtered using the adaptive filtering with filtering function based on local fringe spectrum [ Goldstein and Werner , 1998] and unwrapped using the branch-cut region growing algorithm [ Goldstein et al.
, 1988].
The baseline refinement was performed to remove the residual orbital ramp and the corrected interferograms were geocoded to the DEM grid.
Finite Fault Modeling: InSAR
In order to generate a finite fault model from the InSAR observations, we first down-sample the three geocoded co-seismic interferograms onto a variable grid optimized for resolving slip on an approximate location for the fault at depth, while simultaneously estimating the noise covariance in each interferogram
[Lohman and Simons, 2005]. We then conduct a two-part inversion. First, we invert the resampled displacements for the orientation, location, slip magnitude, and slip direction of a single rectangular fault dislocation with uniform slip in a homogeneous elastic halfspace [Okada, 1992], using the Neighborhood
Algorithm [Sambridge, 1999]. We also invert for a quadratic orbital ramp for each interferogram. We test both north and south dipping focal planes without a-priori assumptions of the focal mechanism other than that the inverted planes should exhibit dominantly normal motion and that there are two oppositely dipping focal planes in the strike ranges of 0-180 and 180-360 degrees. We find that the surface displacements are best fit by the north-dipping plane, in agreement with teleseismic solutions (next section). We are not able to find a reasonable single fault plane solution for the south dipping focal plane, so we fix the strike and dip and invert for location, slip magnitude, and rake instead. Secondly, to determine the spatial distribution of slip for both fault planes, we fix the best-fit single fault dislocation orientation and location, and extend the fault dimensions down-dip and along-strike. We then discretize the fault plane with triangular dislocations
[Meade, 2007] whose size varies as a function of model resolution [Barnhart and Lohman, 2010]. Finally we invert for the distribution of slip on the fault in a homogeneous elastic halfspace, imposing non-negative slip constraints and minimum moment spatial smoothing. The smoothing weight and best-fit model is chosen using the jRi criterion [Barnhart and Lohman, 2010]. We fix rake to the best-fit slip distribution determined by the Neighborhood Algorithm.
In order to constrain the impact of correlated atmospheric noise and inferred orbital ramp corrections on inverted slip (Figure S2b), we implement a Monte Carlo error propagation technique. We simulate 1000 noisy data sets by adding spatially correlated noise and orbital ramps of varying geometry (linear, bilinear, quadratic) to the predicted displacements from our best-fit slip inversion [Barnhart et al., 2011; Barnhart and Lohman, 2013]. We then invert each synthetic dataset for slip and a quadratic orbital ramp using the same fault geometry and smoothing used to generate the slip distribution in Figure 2b. The error bounds of slip are non-Gaussian, so we extract the 16th and 84th percentiles (equivalent to 1-sigma error envelope) of slip from the population of slip models at each depth. We follow the same procedure with the
Neighborhood Algorithm in order to place confidence bounds on fault model source parameters for the
single patch inversions. Specifically, we address errors in geometry, depth, and orientation using 100 synthetic data sets for north and south orientation (Table S2).
Finite Fault Modeling: Teleseismic
To derive a kinematic slip distribution for this event, we model the earthquake source as a rupture front of finite width propagating on a two-dimensional planar fault segment of prescribed orientation (assumed to match the NEIC W-phase moment tensor, with strike and dip of 231° and 61°, respectively, linked to the
NEIC hypocenter). We use a simulated-annealing algorithm [Ji et al., 2002] to invert azimuthally distributed P-, SH- and Surface-waves for the combinations of slip amplitude, rake angle, rupture velocity and rise-time at each sub-fault element that best explains the teleseismic records. To improve the robustness and the efficiency of this optimization problem, the seismic data are decomposed in the wavelet domain, and the error function is defined as a combination of an L1 and an L2 norm. We also apply a
Laplacian smoothing operator. Rake angle is constrained to between 210° and 290° (W-phase moment tensor rake ±40°). The rupture velocity is allowed to vary between 1.0 and 3.5 km/s. The dataset is made up of 40 P- and 23 SH waveforms band-pass filtered from 2 s to 100 s, and 63 surface waves filtered from 200 s to 500 s, selected from globally distributed broadband seismometers on the basis of the quality of their signal-to-noise ratios and their contributions to even azimuthal coverage. Because of the large difference between the hypocentral and CMT centroid depths for this earthquake (80 and 50 km, respectively), we have tested sensitivity of the finite fault model to the depth of rupture initiation by varying depth in increments of 5 km, from 50-85 km. Waveform fits marginally favor a depth of 65 km, and at that depth the model implies a slip centroid similar to that of the CMT solution. In the absence of better (local) data to constrain depth, we choose the 60 km model as our favored solution. This model is shown in Figure S3a.
Waveform fits are shown in Figure 2 and S4.
This inversion solution explains ~83% of the seismic data, fitting body-wave data well except for misfits at northwestern azimuths, where an early peak to P-wave data is not matched by synthetics. The systematic and azimuth-limited nature of this misfit suggests it may be structural in origin, as corroborated by similar misfits in similar azimuth and distances for the 2011 Dalbandin earthquake - identifying a regional structural feature not accounted for in PREM [Dziewonski and Anderson, 1981] and Crust2.0 based synthetics.
Forward modeling displacements from this solution predicts a surface displacement field that is approximately the same shape and amplitude as that inferred from InSAR data, but which is shifted to the south and west by approximately 30 km. To account for this offset, we shift the hypocenter of the teleseismic inversion, since the kinematic slip distribution is inherently linked to the point at which rupture is initiated, to a new location of (62.15º, 27.86º). We perform an identical inversion at this location, deriving a model that fits teleseismic data a few percent better than the previous model, and leads to a much better match to the surface displacement field inferred from InSAR data. In a second step, we use the
InSAR inversion to inform the seismic inversion further by constraining slip to zero in shallow sub-faults, which are well resolved with InSAR data, but where low-amplitude, late slip is found in our best seismic inversion. Doing so only reduces seismic data fits by a few tenths of a percent, and results in improved fits to surface displacements and a better visual match to the InSAR-derived solution. This favored model is shown in Figure 2, S5a.
To explore how well constrained are the major features of the solution, we follow the procedure of [Hayes,
2011], analyzing the spatial resolution of slip with respect to input data by performing a bootstrap analysis
(with variable Vr), in which we randomly select N ‘new’ data from the N input data, and re-invert. This resampling is repeated N times, and an average is taken of the resulting models (Fig. S5b).
Results show consistency in source time functions throughout the inverted time window, indicating the timing of moment release is well resolved. The major features of the average model are quite similar to the reference solution (Fig. S5a), particularly near the hypocenter, though peak slip is lower and moment release more distributed spatially in the bootstrap analysis, likely an artifact of averaging many models with
variable rupture velocity. To quantify resolution of these models, we compute the standard deviation of slip in each sub-fault over the model suite, normalized by the average slip in the cell (%SD, Fig. S4c).
Following this approach, low values of %SD indicate only small variations in sub-fault slip over the suite of inversions in regions where slip is relatively high; implying high resolution. For our average model,
%SD values are lowest around the hypocenter, and in a swath from the portion of the fault down-dip and southwest, to up-dip and east of the hypocenter, implying the dominant features of our model are well resolved with respect to the data we have inverted.
To add additional constraint on the hypocentral depth and uncertainty, we model body-wave depth phases and source duration using symmetric triangular source time functions, constructed using the ak135 velocity model [ Kennett et al.
, 1995]. We assess depths from 40-100km and source time function durations of 8-
30s. Seismic waveform fits are computed using the fit function of Herrmann et al.
[2011] and Hudson synthetic seismograms [ Hudson , 1969]. Results show a nominally preferred depth of 80km (defined by the lowest RMS misfit) with reasonable fits between 65-95km. These depths are consistent with the teleseismic slip distribution that showed similar fits for models using depths of 65-80km as the starting depth.
Slab Geometry
To generate an approximation of the Makran slab geometry (Figure S6) in the vicinity of the Khash earthquake, we combine a series of complementary datasets, including earthquake locations from the ISC
[International Seismological Centre, 2011], ISC-GEM [Anon, 2013], and USGS PDE catalogs, centroid moment tensor solutions from the gCMT catalog (www.globalcmt.org), local active source seismology interpretations of the slab surface from [Kopp et al., 2000], locations of trench breaks on the seafloor (from the plate boundary files of [Tarr et al., 2010] and the Marine Geoscience Data System (MGDC) bathymetry database, http://www.marine?geo.org), and trench sediment thicknesses interpreted from the National
Geophysical Data Center (NGDC) global sediment thickness map
(http://www.ngdc.noaa.gov/mgg/sedthick/sedthick. html). We then follow the approach of Hayes et al.
[2009] and Hayes et al., [2012], using these data as spatial proxies for the slab surface. Two-dimensional slab profiles are oriented N-S from the trace of the Makran trench, approximately 50-100 km apart along the strike of the slab. To account for the low seismicity rates in this subduction zone, and thus a sparsity of subduction-related earthquakes, we hand contour the slab surface with two-dimensional splines instead of following the automated approach used in Hayes et al., [2012], making sure shallow thrust earthquakes and active source seismic data describe the subduction zone interface, while intermediate depth earthquakes occur within the subducting slab (above-slab earthquakes in Figure 1 occur east of the profile shown).
Finally, digitized two-dimensional profiles are interpolated into a three-dimensional slab surface in the same manner as other slabs modeled by Hayes et al., [2012], which form the USGS Slab1.0 database.
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