Random Walk Approach for Wave Propagation through Atmospheric Layers for DInSAR Applications

The accuracy and reliability of the measured differential path in satellite synthetic aperture radar (SAR) interferometry are strongly affected by the uncertainty in the estimation of the atmospheric contribution. Changes in the physical parameters of the medium, due to turbulence layers or gas concentrations, induce slight variations in the curvature of the propagation path that finally generate an overall disturbance term that is usually comparable, or even larger, than the displacement to be observed. A stochastic model for the three dimensional path field is derived by considering a plane wave propagating in a random layered medium. In the vertical direction a piecewise-linear walk, made by straight ray subpaths, is assumed, wherein the length of each path (thickness of the layer) and the number of paths are modelled as random variables. Along the horizontal plane mutual interactions among cells are defined through an interaction equation that closely resembles typical competitions in biological evolution models. The resulting parametric model is fitted with observations from the residual atmosphere, as measured after topographic removal in SAR images, and results are shown.