Toward Absolute Phase Change Recovery With InSAR: Correcting for Earth Tides and Phase Unwrapping Ambiguities

Radar interferograms provide a map of the phase difference between the reference and repeat acquisitions modulo ${2\pi }$ . Under ideal conditions, the phase can be unwrapped to provide an absolute phase connection across the map, although there is always an unknown integer phase ambiguity (i.e., ${N2\pi }$ ) for the entire map. Here, we demonstrate a practical time series method to solve for these integer ambiguities in order to recover the absolute phase change between the first and last SAR images. An important first step is to correct the phase of each SAR image for the well-known solid earth tide, which typically produces a line of sight offset ±150 mm, as well as, trends along and across each image of ~20 mm. This tide correction significantly reduces the noise in the InSAR time series, especially at the L-band. These tidally corrected interferograms are then unwrapped and used to solve for a set of integer ambiguities that achieves phase closure when summing around loops in the stack. There is an infinite number of ambiguity combinations that achieve loop closure; thus, regularization is required. In contrast to previous studies that use a least-squares approach to find the ambiguities, we adopt an ${L}_{1}$ -norm approach to find the minimum number of ambiguity corrections needed to achieve loop closure. We note that the split-spectrum ionospheric correction can introduce ${N\pi }$ ambiguities and suggest two approaches for correcting both ${N2\pi }$ and ${N\pi }$ ambiguities.