An 8 year archive of Envisat synthetic aperture radar (SAR) data over a 300 × 500 km2 wide area in northwestern Tibet is analyzed to construct a line‐of‐sight map of the current surface velocity field. The resulting velocity map reveals (1) a velocity gradient across the Altyn Tagh fault, (2) a sharp velocity change along a structure following the base of the alluvial fans in southern Tarim, and (3) a broad velocity gradient, following the Jinsha suture. The interferometric synthetic aperture radar velocity field is combined with published GPS data to constrain the geometry and slip rates of a fault model consisting of a vertical fault plane under the Altyn Tagh fault and a shallow flat décollement ending in a steeper ramp on the Tarim side. The solutions converge toward 0.7 mm/yr of pure thrusting on the décollement‐ramp system and 10.5 mm/yr of left‐lateral strike‐slip movement on the Altyn Tagh fault, below a 17 km locking depth. A simple elastic dislocation model across the Jinsha suture shows that data are consistent with 4–8 mm/yr of left‐lateral shear across this structure. Interferometric synthetic aperture radar processing steps include implementing a stepwise unwrapping method starting with high‐quality interferograms to assist in unwrapping noisier interferograms, iteratively estimating long‐wavelength spatial ramps, and referencing all interferograms to bedrock pixels surrounding sedimentary basins. A specific focus on atmospheric delay estimation using the ERA‐Interim model decreases the uncertainty on the velocity across the Tibet border by a factor of 2.