On Closure Phase and Systematic Bias in Multilooked SAR Interferometry

Abstract

In this article, we investigate the link between closure phase and the observed systematic bias in deformation modeling with multi-looked SAR interferometry. Multi-looking or spatial averaging is commonly used to reduce stochastic noise over a neighborhood of distributed scatterers in InSAR measurements. However, multi-looking may break consistency among a triplet of interferometric phases formed from three acquisitions leading to a residual phase error called closure phase. Understanding the cause of closure phase in multi-looked InSAR measurements and the impact of closure phase errors on the performance of InSAR time-series algorithms is crucial for quantifying the uncertainty of ground displacement time-series derived from InSAR measurements. We develop a model that consistently explains both closure phase and systematic bias in multi-looked interferometric measurements. We show that nonzero closure phase can be an indicator of temporally inconsistent physical processes that alter both phase and amplitude of interferometric measurements. We propose a method to estimate the systematic bias in the InSAR time-series with generalized closure phase measurements. We validate our model with a case study in Barstow-Bristol trough, California. We find systematic differences on the order of cm/year between InSAR time-series results using subsets of varying maximum temporal baseline. We show that these biases can be identified and accounted for.

On the Phase Nonclosure of Multilook SAR Interferogram Triplets

“…The mentioned phase triplets inconsistencies could arise, for instance, when in the multi-look averaging box different populations of scatterers, characterized by independent phase histories, interfere with one another [9]. Indeed, both the spatial and temporal inconsistency in the multi-look averaging window can give rise to non-zero closure phases [38]. To investigate the origin of these phase inconsistencies, let us consider the n-th phase triplet, namely , which involves the three SAR images collected at times , see Figure 1.…”

“…where the symbol denotes the spatial average operation . Of course, in order to describe the characteristics of the scatterers' families involved in the multi-look window, other speckle noise models, such as the one proposed in [38], might be applied. Accordingly, considering the speckle noise model described by Eq.…”

“…Experimental results have evidenced that the systematic phase bias is a short-lived signal that rapidly decays as the temporal baseline increases [34], [36]- [38], [55]. For small values of , we can locally expand the (full) phase bias related to the interferogram as: (7) where is a constant decay phase velocity factor and is a temporal-baseline-dependent phase velocity difference term.…”

“…Because the phase bias is a shortlived signal, with significant phase rates only at very short temporal baselines and negligible rates at medium-to-long baselines, it is reasonably assuming that (e.g., see [9]). On the other hand, using polygons of interferograms (e.g., see [37], [38]), the probability that the absolute value of the non-closure phases could exceed increases as the number of polygon sides increases. This probability is assumed low in [37], however, in the case that these long phase loops exceed π in moduli, there would be a corrupt estimate and compensation of the bias.…”

“…Moreover, recent works [34]- [36] have claimed that the phase non-closure signals could lead to a bias in the estimate of the mean ground deformation velocity through small-baseline (SB)-oriented Mt-InSAR algorithms. Moreover, some phase bias mitigation approaches have very recently been proposed (e.g., see [37], [38]). These methods share some similarities: They exploit long polygon-shaped phase loops and hold the simplified assumption that the phase bias depends on the interferograms temporal baseline (i.e., one phase bias correction for each group of interferograms with a specific temporal baseline).…”