Robust variance–covariance estimation of tropospheric turbulence improves InSAR capability for monitoring of small tectonic displacements

Evaluating uncertainties and errors in interferometric synthetic aperture radar (InSAR)-derived displacements is challenging but important for any interpretation or analysis. InSAR observation error mainly arises from tropospheric delays, particularly tropospheric turbulence which is hard to quantify in a deterministic way (e.g., using global atmospheric models). Here we propose a new variance–covariance estimation (VCE) method to robustly model the stochastic properties of the uncorrected tropospheric turbulence in time-series of SAR images. Based on this, we further propose 1) an improved linear estimator to quantify interseismic deformation, and 2) a new minimum variance optimization (MVO) to monitor coseismic displacements of small to moderate earthquakes. Synthetic experiments show that compared with the previous VCE approach, the new VCE method is more than 50 % more accurate in deriving SAR variance components, and estimates of interseismic and coseismic displacements are 40 % and 55 % more accurate than those using conventional time-series analysis. Applying the VCE-based linear estimator to real Sentinel-1 time-series over the North Anatolian Fault, Turkey, interseismic displacements have uncertainties reduced by 28 %, 18 %, and 6 % compared to ordinary least-squares approach, for 2, 3 and 4 years of data, respectively. Applying the MVO approach to the 19 September 2023 Mw 5.6 Mount Harper (New Zealand) earthquake, coseismic displacements have uncertainties reduced by 23 % on average compared to the stacking approach. Our results highlight the importance of considering the spatiotemporal variance of InSAR measurements when mapping small tectonic displacements.