InSAR uncertainty due to orbital errors

Errors in the satellite orbits are considered to be a limitation for Interferometric Synthetic Aperture Radar (InSAR) time-series techniques to accurately measure long-wavelength (> 50 km) ground displacements. Here we examine how orbital errors propagate into relative InSAR line-of-sight velocity fields and evaluate the contribution of orbital errors to the InSAR uncertainty. We express the InSAR uncertainty due to the orbital errors in terms of the standard deviations of the velocity gradients in range and azimuth directions (range and azimuth uncertainties). The range uncertainty depends on the magnitude of the orbital errors, the number and time span of acquisitions. Using reported orbital uncertainties we find range uncertainties of less than 1.5 mm yr(-1) 100 km(-1) for ERS, less than 0.5 mm yr(-1) 100 km(-1) for Envisat and similar to 0.2 mm yr(-1) 100 km(-1) for TerraSAR-X and Sentinel-1. Under a conservative scenario, we find azimuth uncertainties of better than 1.5 mm yr(-1) 100 km(-1) for older satellites (ERS and Envisat) and better than 0.5 mm yr(-1) 100 km(-1) for modern satellites (TerraSAR-X and Sentinel-1). We validate the expected uncertainties using LOS velocity fields obtained from Envisat SAR imagery. We find residual gradients of 0.8 mm yr(-1) 100 km(-1) or less in range and of 0.95 mm yr(-1) 100 km(-1) or less in azimuth direction, which fall within the 1 sigma to 2 sigma uncertainties. The InSAR uncertainties due to the orbital errors are significantly smaller than generally expected. This shows the potential of InSAR systems to constrain long-wavelength geodynamic processes, such as continent-scale deformation across entire plate boundary zones.