Oblique convergence leads to slip partitioning with the coexistence of strike-slip, normal, and thrust motion in major fault system. While such complexity is observed at the surface, the question is to understand how faults interact and accumulate strain at depth. Interferometric synthetic Aperture Radar (InSAR) has the potential to map and localize precisely the deformation over wide areas and thus constrain the deep geometry of these structures. However, its application in natural environments is hindered by strong decorrelation of the radar phase due to vegetation, relief, and freeze and thaw cycles, but also due to variable tropospheric phase delays across topographic features and long-wavelength residual orbital ramps. Here, we develop methodologies to circumvent these limitations and separate tectonic from other parasitic signals. We process data from the Envisat satellite archives, at the northwestern boundary of the Tibetan plateau, over two seismic gaps, which appear interesting to study the partitioning of the convergence: the Haiyuan Fault system in northeastern Tibet and the left-lateral Altyn Tagh Fault, in northwestern Tibet. A specific focus on the permafrost related deformation signal allows us to: (1) correctly unwrap interferograms across sedimentary basins, (2) quantify the temporal behaviour of the freeze/thaw cycles, and (3) isolate bedrock pixels that are not affected by the permafrost signal for further tectonic analysis. We also analyse the atmospheric signal across the high plateau margin to define a proxy for the uncertainty on atmospheric corrections. The propagation of individual errors in the time series analysis allows estimating tectonic velocities with higher reliability. We provide in these two study areas continuous velocity fields that allow identifying the strain partitioning and the contribution of each structure. In parallel to this data acquisition, we also develop Monte Carlo inversion tools in order to explore the various geometries in agreement with observations and estimate the compatibility of actual surface displacements with long-term block models.