Covariance estimation, geostatistical prediction and simulation for InSAR observations in presence of strong atmospheric anisotropy

The atmospheric phase delays are usually modelled as being isotropic, which is a simplification, as dInSAR images often show directional atmospheric phase anomalies. We present an anisotropic stochastic model based on the theory of Random Functions to describe spatial auto-correlation structures. We calculate experimental semi-variograms of the dInSAR phase in several ERS-1/2 tandem interferograms. We then fit anisotropic variogram-models in the spatial domain, employing Matérn-class and Bessel-family types of functions in nested models to represent complex dInSAR covariance structures. Geostatistical simulation is used to calculate many realisations of anisotropic error structures we use to demonstrate the importance of accounting for anisotropy in geophysical source-parameter inversions. In a sensitivity study we show that the gain of using anisotropic error models is the greater the stronger the anisotropic effects are and the greater the similarity between deformation signal and error signal is.