Figure 1: Imaginggeometry for a repeat-pass interferometer. One interferogram is formed with images acquired from positions A1 and A2. If a ground resolution element scatters identically for each observation, then the difference of the two phases depends only on the path length difference, dr (delta-ro). If a second interferogram is formed with the image A1 and an image A2' acquired over the same region, but in this case an earthquake has displaced each resolution element between observations, there is now an additional phase change due to the radar line-of-sight component of the displacement, Dr (DELTA-ro). Note that the baseline length has been greatly exaggerated for figure clarity. Typical (usable) baselines for a C-band (wavelength = 5.6 cm) spaceborne system orbiting at an elevation h=~700 km range from 0 to ~200 m. Using image pairs with longer baselines leads to geometrical decorrelation due to the difference of lines of sight between the two images (Zebker and Villasenor, 1992). This baseline length requirement scales linearly with the wavelength of the system.
Single look complex (SLC) SAR data are arrays of complex numbers. The modules of the complex values produce the traditional radar images where variations of the brightness (the amplitude of the signal) reflect spatial variations of the physical characterisitcs of the ground surface (the reflector). In each SAR image pixel, the phase (the argument of the complex value) represents a measure modulo-l/2 (l is the radar wavelength) of the distance between the radar antenna and the ground. An interferogram is obtained by averaging the product of one complex SAR image and the complex conjugate of another image, after sub-pixel coregistration. The phase of each pixel in an interferogram is the difference of the phase of the corresponding pixels in the two SAR images. It is an image of interference where interferometric fringes depict variations of the antenna-ground path lengths difference between the two images. If the two images are acquired from slightly different locations (satellite repeat orbits are in general not exactly co-located), the interferometric phase is sensitive to the surface topography due to the small parallax between the two lines of sight. If the two images are acquired at two different times, the interferometric fringe is sensitive to any displacement of the ground parallel to the radar line of sight, occurring during the acquisition time interval. The sensitivity of the interferogram to topography increases with the interferometric baseline (the spatial separation of the two orbits), whereas the sensitivity to ground displacement is independent of the satellite configuration. For spaceborne systems, sensitivity to ground displacement is in general a few thousand times greater than the sensitivity to topography, allowing scientists to detect displacements of a few millimeters (e.g., Gabriel et al., 1989; Zebker et al., 1994).
To analyze interferometric maps it is first necessary to separate the topographic signal from the surface change signal. Two techniques can be used. In areas where digital topographic maps are available, it is possible to compute the interferometric phase field due to topography and remove it from the observed phase. In areas where digital topographic maps are not available, or are of poor quality, it is possible to combine 3 radar images (A1,A2,A2') of the same area to form two interferograms (with image pairs A1A2 and A1A2'). If a ground displacement event occurs during the time interval between images A1 and A2', the difference between interferogram A1A2 and interferogram A1A2' eliminates topographic fringes common to both interferograms. Note that this step requires that the phase of the interferogram A1A2 is first scaled by the ratio of the baseline lengths BA1A2'/BA1A2 to match the sensitivity to topography of the interferogram A1A2'. The resulting interferogram obtained by "double-difference" contains, in principle, only the signal due to changes between times A1 and A2'. The first technique is called "two-pass technique" because it requires only two passes of the satellite over the study area; the second technique is called "three pass" because three images are required. When the orbits configuration is not favorable to the three-pass method, it is possible to use four images to produce the two interferograms that are subsequently differenced (four-pass).
The second step required to extract measurable quantities from interferograms is the phase unwrapping. Several algorithms have been developed to perform this task (e.g., Goldstein, 1988). The success of unwrapping depends on the SNR in the image and the fringe density. This step is probably the most difficult part of the processing chain. Note that the three-pass technique requires one phase field to be scaled to the same (topographic) fringe rate as the other, so at least one phase field must be unwrapped before making the double-difference.