Correcting Phase Unwrapping Errors in X-band Coseismic Interferograms using Pixel Offsets and Quadtree Partitioning
Wang, Teng; Jónsson, Sigurjón; Ahmet, Akoglu
King Abdullah University of Science and Technology, SAUDI ARABIA

Interferograms of large earthquakes and other strong deformation events often include high phase gradients that make phase unwrapping a challenging task, in particular for X-band data due to their short wavelength. In Practice, we can reduce the density of fringes in coseismic interferograms by removing an initial model deformation field. While this operation often works, we still have significant high fringe-rate residuals when the initial model prediction is poor. However, coseismic displacements can also be measured in the line-of-sight direction from coordinate differences (range pixel offsets) between SAR pixels in images spanning the seismic event, although the accuracy is significantly lower than for the phase observations. In order to improve the pixel-offset accuracy, we can concentrate our pixel-offset measurements on pre-detected image patches that are dominated by bright point-like targets [Hu et al, 2012]. Pixel-offsets from point-like targets reach centimeter-level accuracy for high-resolution X-band SAR images [Bamler and Eineder, 2005, Eineder et al, 2011]. However, despite the improved accuracy, pixel-offsets are still less accurate than phase observations and are usually spatially sparse.

Here we present a strategy that makes use of pixel offsets in combination with quadtree partitioning to correct phase unwrapping errors in X-band coseismic interferograms. InSAR data are commonly downsampled before model parameter estimations to reduce computational burden, e.g. with quadtree partioning [Jónsson, 2002, Lohman and Simons, 2005]. In our approach, we first apply the standard quadtree downsampling algorithm on the initial unwrapped coseismic interferogram to acquire a quadtree structure, and we use that quadtree structure on the range pixel-offset data. We then calculate the differences between displacements derived from unwrapped phase and range pixel-offsets within each quadtree quadrant at the location of the pixel-offset measurements. By analyzing the differences from these two independent techniques, phase unwrapping errors are easily identified and can be corrected with a compensating integer number of phase cycles. We applied this strategy on a pair of COSMO-SkyMed images acquired before and after the magnitude 7.1 Van earthquake that struck eastern Turkey on 23rd October 2011. The model parameter estimation results from the initial unwrapped interferogram and the corrected interferogram show that the latter is more consistent with field observations and other deformation data, demonstrating the capability of our method in correcting phase unwrapping errors.

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