Covariance Estimation, Geostatistical Prediction and Simulation for InSAR Observations in Presence of Strong Atmospheric Anisotropy
Steffen Knospe(1) and Sigurjón Jónsson(1)
(1) ETH Zurich, Schafmattstrasse 30, CH-8093 Zurich, Switzerland
The dInSAR phase signal is a superposition of different contributions, such as surface deformation, tropospheric delay, topographic residual and other error sources. Usually, we are only interested in the surface deformation part of the signal. Therefore, to obtain high quality results, we would like to remove other phase components. However, it is not trivial to distinguish between deformation and atmospheric signals in single interferograms, because tropospheric delay signals and moderate deformation (e.g. inter-seismic deformation, mining subsidence) can have similar amplitudes and sometimes comparable spatial extent, i.e. similar ‘structure of variability’ in the spatial domain.
Although several ways of estimating the tropospheric phase contribution have already been described in the literature, its removal is still challenging. One way is to use independent data from other sources, like GPS or MERIS. Another way is to analyse a stack of coregistered SAR scenes in the temporal domain. A third way is to use a stochastic model and a priori information about the surface deformation. A stochastic model based on spatial autocorrelation in terms of elementary turbulence theory has been found to be appropriate to describe atmospheric phase delay in dInSAR applications.
The atmospheric phase delays are usually modelled as being isotropic, which is a simplification, as dInSAR images often show directional atmospheric phase anomalies (from topographic structures and wind). 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 fit anisotropic variogram-models in the spatial domain, employing Matérn-class and Bessel-family types of functions in nested models, to represent the complex dInSAR covariance structures. The estimated parameter sets for suitable models indicate the variety of atmospheric ‘structures’ with variance and correlation-range differences of more than one order of magnitude.
Two different strategies are commonly used to introduce information about error structure into further data processing: removal (screening) of the atmospheric phase delay and consideration of the atmospheric delay as auto-correlated error in modelling (in terms of a full covariance matrix). We explore geostatistical prediction methods and demonstrate their capabilities for estimating anisotropic atmospheric signals and noise filtering. Geostatistical simulation is used to calculate thousands of realisations of anisotropic auto-correlated error structures based on the analysed tandem-interferograms. We use these realisations to demonstrate the importance of accounting for anisotropy in geophysical source-parameter inversions that make use of dInSAR surface deformation data.
Keywords: ESA European
Space Agency - Agence spatiale europeenne,
observation de la terre, earth observation,
satellite remote sensing,
teledetection, geophysique, altimetrie, radar,
chimique atmospherique, geophysics, altimetry, radar,