A multiscale approach to estimating topographically correlated propagation delays in radar interferograms

When targeting small amplitude surface deformation, using repeat orbit Interferometric Synthetic Aperture Radar (InSAR) observations can be plagued by propagation delays, some of which correlate with topographic variations. These topographically-correlated delays result from temporal variations in vertical stratification of the troposphere. An approximate model assuming a linear relationship between topography and interferometric phase has been used to correct observations with success in a few studies. Here, we present a robust approach to estimating the transfer function, K, between topography and phase that is relatively insensitive to confounding processes (earthquake deformation, phase ramps from orbital errors, tidal loading, etc.). Our approach takes advantage of a multiscale perspective by using a band-pass decomposition of both topography and observed phase. This decomposition into several spatial scales allows us to determine the bands wherein correlation between topography and phase is significant and stable. When possible, our approach also takes advantage of any inherent redundancy provided by multiple interferograms constructed with common scenes. We define a unique set of component time intervals for a given suite of interferometric pairs. We estimate an internally consistent transfer function for each component time interval, which can then be recombined to correct any arbitrary interferometric pair. We demonstrate our approach on a synthetic example and on data from two locations: Long Valley Caldera, California, which experienced prolonged periods of surface deformation from pressurization of a deep magma chamber, and one coseismic interferogram from the 2007 Mw 7.8 Tocapilla earthquake in northern Chile. In both examples, the corrected interferograms show improvements in regions of high relief, independent of whether or not we pre-correct the data for a source model. We believe that most of the remaining signals are predominately due to heterogeneous water vapor distribution that requires more sophisticated correction methods than those described here.