Modeling Interferogram Stacks for Sentinel - 1

The dispersion of the optimal estimate of a subsidence motion is determined, and compared with that of Permanent Scatterers, when the targets are progressively decorrelating due to Brownian motion. Approximately, with N consecutive images and revisit time T, the interferogram stack results are equivalent to PS's, if the pixel count in the window grows with N2T, independently of the frequency. In the case of Sentinel – 1, it is possible to expect that, in lightly vegetated areas and in one year time, less than 100 pixels will create an interferogram stack as efficient as a PS 1 . Interferogram stacks Many targets in a SAR image are not coherent over long temporal intervals, but they can be exploited nevertheless for motion estimation using "conventional" DInSAR techniques. Despite the widely developed literature on differential interferometry, starting from the very first InSAR references, there is a substantial lack of estimates of the decorrelation of distributed targets, after the paper by Zebker, and of optimal techniques to provide an estimate of the motion field [1, 2, 5]. Most approaches can be generally defined as "interferogram stacks", and new and appealing methodologies appear that could be classified in this category [4]. I establish a model for target decorrelation for interferogram stacks, and provide a statistically consistent estimator, to be used mainly for the assessment of the ground motion accuracy. Modeling the decorrelation Exponential model: Brownian motion I suppose that the time decorrelation mechanism is primarily due to the motion of the scatterers in the resolution cell [8]. I model this motion as a Brownian motion, or the sum of many successive independent and equally distributed motions so that the normal 1 This work was partly carried out within ESA contract 19142/05/NL/CB. approximation holds. It is possible to substitute the variable describing motion in the line of sight with the variable describing the unwrapped phase because of the linear relation between the two. The decorrelation law is [8]: with τ=2/σ2. For instance for a Brownian motion in the look direction with a standard deviation in a day of , with say the phase deviation would be: