The North Anatolian Fault (NAF) is a major feature of Middle Eastern tectonics, and several previous InSAR studies have measured interseismic deformation across the fault. All previous studies, however, have used SAR data acquired from a single line-of-sight (LOS) direction, leading to large uncertainties on model parameters and necessitating several modelling assumptions to be made. We have measured interseismic deformation across the NAF using both ascending and descending SAR data for the first time, an aim that has previously been limited by the availability of ascending data. By using SAR data from two look directions we have been able to reduce the range of uncertainties in slip rate and locking depth from previous studies by 60%, and by assuming no vertical motion across the fault, we estimate both fault-normal and fault-parallel motion. These results support other evidence for predominantly horizontal strike-slip motion on the NAF. Our data are consistent with a slip rate of 20–26 mm/yr below a locking depth of 13.5–25 km for the NAF.
 The right-lateral North Anatolian Fault (NAF) is a major feature of Middle Eastern tectonics [Barka, 1996], acting together with the East Anatolian Fault (EAF) to facilitate the westward motion of Anatolia, a major crustal block caught in the convergence zone of the Eurasian plate with Arabia and Nubia [McKenzie, 1972] (Figure 1). In order to understand the role that the NAF plays in regional tectonics and the seismic hazard it represents, many slip rate estimates for the NAF have been made over Quaternary and longer time-scales [e.g., Hubert-Ferrari et al., 2002; Kozacı et al., 2009], but few geodetic estimates currently exist [e.g., Reilinger et al., 2006]. Interferometric Synthetic Aperture Radar (InSAR) is a tool that is well suited to studying interseismic strain accumulation due to its high spatial resolution, but is limited to locations where a sufficient number of radar scenes are available. For this reason, previous InSAR studies of the NAF using the European Space Agency's (ESA's) ERS satellites [e.g., Wright et al., 2001; Motagh et al., 2007] have only used descending track data which is more abundant than ascending data. In these studies it was therefore necessary to assume purely horizontal, fault-parallel motion in modelling deformation. SAR data collected since the launch of ESA's Envisat in 2002 presents new opportunities for InSAR studies of the NAF, and here we use data from both ascending and descending Envisat tracks that overlap across the NAF, allowing a check on this assumption, as well as more robust estimates of slip rate.
2. Construction of Displacement Ratemaps From SAR Data
 Repeated radar acquisitions covering the eastern NAF are available for Envisat ascending track 400 and descending track 307, in the same study area as that of Wright et al.  (Figure 1). The SAR data were processed from raw data products using the JPL/Caltech ROI_PAC software [Rosen et al., 2004]. The interferograms were corrected for differences in satellite position using DORIS satellite orbits from ESA, and effects of topography were removed using a 3-arc-second (∼90 m) resolution SRTM DEM [Farr et al., 2007]. Each interferogram was downsampled during construction to 8 or 16 looks (160 or 320 m) and filtered twice using a weighted power spectrum filter [Goldstein and Werner, 1998] to improve the signal-to-noise ratio. Interferograms were unwrapped using the branch-cut method and any errors were fixed manually.
 For ascending track 307, we constructed ten interferograms with a total timespan of ∼20 years. From inspection it was clear that each interferogram contained an orbital error in the form of a planar phase gradient across the scene. To empirically remove these errors, we applied a two-step correction to each interferogram. In the first step, we masked out any data more than a distance L away from the NAF to the south of the fault, and inverted the remaining data for the best-fitting plane with a gradient only in the fault-parallel direction. This plane was then subtracted from the data. This step works on the assumption that since interseismic tectonic signals for strike-slip faults are largely fault-perpendicular, any NAF-parallel phase gradient near the fault is likely to be produced by an orbital error. In the second step, we selected any data that was on the Anatolian Plateau (Figure 2) and was also at least a distance L away from both the NAF and the EAF. We then inverted these data for the best-fitting plane with a gradient only in the fault-perpendicular direction, and again subtracted this plane from the data, to remove any NAF-perpendicular component of the orbital phase gradient. This step works on the assumption that away from the tectonic influence of the NAF and the EAF, there is little expected deformation on the Anatolian Plateau [Reilinger et al., 2006]. We then stacked each corrected interferogram in a pixel-wise fashion and divided each pixel by its total timespan to create a ratemap (Figure 2). A threshold length of time t was used to cull any pixels that had temporal coverage of less than t years, in order to avoid rate estimates with large errors. For ascending track 400, we constructed five interferograms with a total timespan of ∼11 years and used the same method as for the descending data. For both datasets we chose an L value of 36 km, two times the 18 km locking depth (d) calculated previously for both the NAF and EAF [Reilinger et al., 2006; Wright et al., 2001]. The model of Savage and Burford  for elastic strain accumulation across a vertical pure strike-slip fault shows that less than 15% of motion occurs at distances greater than 2d to one side of the fault. A t value of 11 years was chosen for both datasets to match the total timespan of the track with least temporal coverage, track 400. The ratemaps each show a strong gradient of deformation rate across the NAF of similar magnitude but opposing sign; qualitatively consistent with right-lateral slip on the NAF.
 We next constructed NAF-perpendicular profiles across each ratemap (Figure 2), first downsampling the data to a resolution of 1.6 km. The profiles were chosen to go through a point on the NAF covered by both ratemaps, and pixels within 100 km perpendicular to the profile line were projected onto the line. We calculated a mean profile and 1-sigma bounds for each dataset by inverting all the ratemap data within 20 km along-profile bins, weighting the inversion using a variance-covariance matrix to account for spatial correlation between ratemap pixels. The variance-covariance matrix was estimated by fitting a 1-D autocovariance function of the form Ae−d/b to signals in a non-deforming region of each ratemap, where A is maximum variance, b is 1-D e-folding distance and d is distance between pixels.
3. Modelling Strain Accumulation
 We first used the assumption that all deformation is fault-parallel and horizontal and modelled the fault as a buried infinite screw dislocation in an elastic half-space, where during the interseismic period, right lateral aseismic slip occurs at a rate s below a locking depth d. For a displacement y at a perpendicular distance x from the fault, y = (s/π) × arctan(x/d) [Savage and Burford, 1973]. We performed a parameter search over the ranges 10–35 mm/yr for slip rate and 5–35 km for locking depth, at 1 mm/yr and 0.5 km intervals respectively. For each combination of parameters, we found a static offset in LOS rate that minimized the total root-mean-square (RMS) misfit between the model and data profiles for both datasets. Our best-fit model, corresponding to the minimum of RMS misfit, has a slip rate of 23 mm/yr below a locking depth of 19 km (Figure 2). Both datasets were equally weighted during all inversions.
 We used a Monte Carlo method to estimate error bounds on our best-fit model, perturbing our two ratemaps 200 times with spatially realistic noise (using the same variance-covariance matrix as for the mean profiles) [Biggs et al., 2007] and then using the same parameter search on each of these data sets to find the best-fitting model. Using principle component analysis we calculated an ellipse about the mean that contains 68% of the 200 solutions in slip rate/locking depth parameter space. The extents of this ellipse define our range of model values: 20–26 mm/yr slip rate and a locking depth of 13.5–25 km (Figure 3). We also investigated the effect on our results of choosing a different value of L for the orbital correction. We varied L between 18–54 km, but found similar variation of best-fit slip rates and locking depths to that from our Monte Carlo error analysis.
 Unlike previous interseismic InSAR studies, we have also been able to consider deformation in two dimensions. For each pair of InSAR measurements for a single location, we have 3 unknowns in terms of ground deformation; fault-parallel motion, fault-perpendicular motion, and vertical motion. Hubert-Ferrari et al.  have shown that the vertical offset rate across the eastern NAF is negligible and we therefore make the assumption that the long-term vertical rate of motion across the NAF is zero, reducing the number of unknowns to two. We also make the assumption that within the dotted profile box shown in Figure 2 velocities only vary perpendicular to the NAF; enabling us to combine our deformation profiles for T400a and T307d. At each point along the profile where there is both ascending and descending data, we solve the simultaneous equations
where Δra and Δrd are the LOS deformation rates at each point, for the ascending and descending profiles respectively; Δs and Δn are the fault-parallel and fault-normal ground velocities and a1, a2, d1 and d2 are the fault-parallel and fault-normal components of the unit LOS vector for the ascending and descending tracks. Solving these equations we can draw profiles of fault-normal and fault-parallel motion across the NAF (Figure 4). The fault-normal profile is consistent with a zero convergence rate across the NAF, supporting our assumption of pure horizontal fault-parallel motion across the NAF.
 Our interseismic strain accumulation profiles across the NAF are in good agreement with existing GPS measurements [Reilinger et al., 2006; Ozener et al., 2010] (see Figure 2), and with two previous interseismic InSAR studies on neighbouring tracks 35 and 78 [Wright et al., 2001; Holley, 2004] (see Figure 3, and Figure 1 for track footprints). The slip rates and locking depths for the NAF estimated both from these studies and from geological studies [e.g., Kozacı et al., 2009; Hubert-Ferrari et al., 2002] are also consistent with our results. However, in comparison to the results of Wright et al.  which are based on descending track data only, we have been able to reduce the range of uncertainty for both locking depth and slip rate by approximately 60% (Figure 3). This significant improvement shows the importance of using SAR data from two look directions for interseismic InSAR studies. Interseismic InSAR studies using both descending and ascending data are likely to become increasingly common in future years, due to the more frequent data acquisition of upcoming satellite missions such as Sentinel-1 and ALOS-2, and studies similar to this one will hopefully become routine.
 This work was supported by the Natural Environmental Research Council through the National Centre for Earth Observation, of which the Centre for the Observation and Modelling of Earthquakes, Volcanoes and Tectonics (COMET+) is part. All Envisat SAR data were provided and are copyrighted by ESA. We are grateful to JPL/Caltech for use of the ROI_PAC software. We thank John Elliott and Juliet Biggs for helpful comments/discussions, and Rob Reilinger and Meng Wei for careful reviews.
 The Editor thanks Meng Wei and an anonymous reviewer.