It is well known that SAR (Synthetic Aperture Radar) interferometry is based on the SAR technology. How SAR can detect the deformation in three dimensions after earthquake happen? is it possible to measure the slip rate and fault parameters from SAR technology?
http://ac.els-cdn.com/S0924271614000884/1-s2.0-S0924271614000884-main.pdf?_tid=4efa840c-812f-11e7-893b-00000aab0f26&acdnat=1502742764_5f84dc74ecbc1ac8f830487c2b3e3768
This is a great review that may help you about ground-based SAR interferometry for deformation measurement.
To answer your questions you need to first make interferograms from SAR acquisitions.
So say you have interferograms from scenes captured before and after an earthquake, and you unwrap the interferogram, you essentially have a map of surface displacement caused by the earthquake (with resolution depending on how coherent pixels on the ground are). Now, that allows you to easily invert for coseismic slip distribution on a fault in 3D. But these are only static offsets. You cannot investigate the rupture process with InSAR.
Now, the more fun parts are while dealing with other quasi-static processes like interseismic and post seismic velocity fields (and possible debris flow/landslides). If you collect enough SAR scenes over a particular frame on the ground, you can create a time series of the surface velocity field. Now you can invert that data for slip rates/locking depth of faults/frictional parameters/strain rates (for afterslip/visco-elastic relaxation studies).
The links that have been provided by some of the other responses to this thread are excellent, and should give you a more detailed description of the possibilities with SAR interferometry.
In short SAR interferometry is the most effective way of measuring the field deformations resulting from an earthquake ever since Massonet And colleagues did that for the Landers Californian Earthquake in 1992. The results that can be obtained in say few days of processing are superior to those that could be obtained in years of work by thousands of field seismologists and thousands of topography surveyors and cartographers. Moreover I believe that interferometric techniques are the most promising in monitoring precursory deformations that preceed earthquakes, landslides and other geomorphic hazards generating phenomena. Here are some references
Massonet et al. 1993
http://perso.numericable.fr/~feigkurt/MassonetEtAl1993Nature364138a0.pdf
To answer your question concisely, InSAR uses at least two SAR images of the same area to extract elevation model using phase information of microwave returns (interferogram). So if you constantly monitor an area using InSAR you can detect minor deformations on the surface as it uses phase information of microwave returns to yield elevation which is very sensitive to any deformation. Series of interferogram can be used to obtain Differential elevation model which can detect deformations after earthquakes as well as has the potential to predict earthquakes by detecting deformations that precede the earthquake.
Each year, earthquakes cause tens of thousands of deaths and billions of dollars in property damage worldwide. These numbers will probably increase in the coming years as world population continues to expand, especially along coastal zones and near mountain ranges, which usually represent tectonically active plate boundary zones.
In July 1995, Dixon stated: It is now possible to detect subtle changes in the earth’s land and ice surfaces over periods of days to years with an unprecedented scale (global), accuracy (millimetre-level) and reliability (round-the-clock, all weather). The ability to make these measurements from space without ground control, is a fundamental advance in our monitoring capability.
Compared to the space coverage of measurements points in levelling procedures (including GPS), INSAR has the advantage that the observations are acquired with almost complete coverage.
Dixon (1995) also pointed out that SAR can provide high-resolution imagery of earthquake-prone areas, high-resolution topographic data, and a high resolution map of coseismic deformation generated by an earthquake.
Crustal deformation is a direct manifestation of the processes that lead to earthquakes. Consequently, it is one of the most useful physical measurements we can make to improve estimates of earthquake potential. InSAR Interferometry offers geophysicists their first opportunity to measure surface deformation with continues spatial coverage, yielding completely new view of earthquake related ground deformation.
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