Principles of Modern Radar - Volume 2 1891121537

8.8 Other Coherent Exploitation Techniques 387InSAR static terrain mapping, we again assume that the reflectivity ρ(x,y) of each pixeldoes not change between images. Two images a(x,y) and b(x,y) of a scene are collectedfrom identical vantage points (no spatial baseline) and coregistered. If the terrain elevationchanges between the two acquisition times but the reflectivity does not, then the only term inthe pixel phase of equation (8.10) that will change between images a and b is the slant rangeR. Denoting the change in range along the LOS as R ab , the phase difference will then satisfyφ ab =− 4π λ (R a − R b ) =− 4π λ δR ab (8.53)For a scatterer at a given ground range, and assuming planar wavefronts for simplicity, achange in elevation of δh will result in a change in LOS range of δh · sin ψ. Consequently,the elevation change can be estimated aŝδh(x,y) ≈λ4π sin ψ φ ab(x,y) (8.54)This equation assumes that the terrain motion between passes is in the vertical dimensiononly. In fact, in many cases, such as earthquakes or glacial flows, the motion is primarilyhorizontal. Any change in slant range between a scatterer and the radar will result ina detectable change in the IPD, and suitable generalizations of equation (8.54) can bedeveloped for horizontal motion of the terrain.Clearly, terrain motion mapping requires repeat-pass operation. The time intervalcould be on the order of days or weeks to study the effects of such phenomena as earthquakesor volcanic explosions, or it could be years to study phenomena such as glaciermovement or ground subsidence. The processing operations are essentially the same asdiscussed earlier.Figure 8-27 is an example of using terrain motion mapping to monitor land subsidence.The map is of the Las Vegas, Nevada, area and is based on data collected over nearlyfour years. Figure 8-27a is the InSAR terrain motion map; outlines have been addedto indicate the areas of greatest subsidence. Notice the sensitivity of the technique: the(a)(b)FIGURE 8-27 InSAR-based terrain motion map showing land subsidence in Las Vegas,Nevada, over a nearly four-year period. (a) InSAR-based terrain motion map. Subsidence issignificant primarily in the outlined regions, with the subsidence being greatest in the darkerregion in the upper left quadrant. (b) Three-dimensional visualization of subsidence effects.(Courtesy of the Radar Interferometry Group, Stanford University.)