Phase Gradient Approach to Stacking Interferograms

David T. Sandwell and Evelyn Price, Institute of Geophysics and Planetary Physics,

Scripps Institution of Oceanography, La Jolla, CA 92093-0225
Submitted to Journal of Geophysical Research January 9, 1998

Revised June 30, 1997

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Abstract
The phase gradient approach is used to construct averages and differences of interferograms without phase unwrapping. Our objectives for change detection are to increase fringe clarity and decrease errors due to tropospheric/ionospheric delay by averaging many interferogram. The standard approach requires phase unwrapping, scaling the phase according to the ratio of the perpendicular baseline and finally forming the average or difference; however unique phase unwrapping is usually not possible. Since the phase gradient due to topography is proportional to the perpendicular baseline, phase unwrapping is unnecessary prior to averaging or differencing. Phase unwrapping may be needed to interpret the results but it is delayed until all of the largest topographic signals are removed.

We demonstrate the method by averaging/differencing 6 interferograms, having a suite of perpendicular baselines ranging from 18 to 406 m. Cross spectral analysis of the difference between two tandem interferograms provides estimates of spatial resolution which are used to design pre-stack filters. A wide range of perpendicular baselines provides the best topographic recovery in terms of accuracy and coverage. Outside of mountainous areas, the topography has a relative accuracy of better than 2 m. Residual interferograms (single interferogram - stack) have tilts across the unwrapped phase that are typically 50 mm in both range and azimuth reflecting both orbit error and atmospheric delay. Smaller scale atmospheric waves with amplitudes of 15 mm are interpreted as atmospheric lee waves. A few GPS control points within a frame could increase the precision to about 20 mm for a single interferogram; further improvements may be achieved by stacking residual interferograms.