Covariance estimation for dInSAR deformation measurements in presence of strong atmospheric anisotropy

The dInSAR phase signal is a superposition of different contributions. When studying geophysical processes, we are usually only interested in the surface deformation part of the signal, and therefore, to obtain high quality results, we would like to remove other phase components. Although several ways of estimating the tropospheric phase delay contribution have already been described in the literature, a correct error treatment or removal are still challenging. A stochastic model based on the theory of Random Functions has been found to be appropriate to describe atmospheric phase delay in dInSAR images. However, these phase delays are usually modelled as being isotropic, which is a simplification, because InSAR images often show directional atmospheric anomalies. Here we analyse anisotropic structures based on the theory of Random Functions and show validation results using simulated and real data. We calculate experimental semi-variograms of dInSAR image examples and fit anisotropic variogram models to them. With these variogram models we calculate covariance matrices for a given point raster, which we use to simulate multiple anisotropic phase delay realisations. We add these realisations as noise to simple forward model calculations of surface deformation. Then we invert for the source parameters of the deformation model and compare the results for different error scenarios, which shows the importance of including the anisotropic data covariance information.