## 3 Status and Application
### Repeat-Pass Interference
#### 3.1.1 D-InSAR
With the phase information of the master SAR image and slave SAR image, and with the assistance of DEM data and orbit data, through differential interferometry processing, differential interferograms reflecting ground surface deformation can be obtained. It can be seen from this that the phase of the differential interferograms shows periodic fringe changes, and each cycle represents a fringe, indicating a phase change of 2\(\pi\) radians, corresponding to half a radar wavelength of deformation. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Geophysical Phenomenon**} & \multicolumn{5}{c}{**Process Classification**} & \multirow{2}{*}{\
\begin{tabular}{c} **Spatial** \\ **Scale/km** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Deformation** \\ **Scale/mm** \\ \end{tabular} } \\ \cline{2-2} \cline{5-6}  & **Instantaneous** & & & & & & \\ \hline Active volcano rises or sinks & —\({}^{1}\) & ✓\({}^{2}\) & ✓ & — & \textless{}20 & \textless{}5 \\ Volcanic eruption & ✓ & — & — & ✓ & \textless{}20 & \textless{}50 \\ Earthquake co-seismic deformation & ✓ & — & — & ✓ & 50–100 & \textgreater{}50 \\ Deformation before and after & — & ✓ & — & ✓ & 50–100 & \textless{}5 \\ earthquake & — & ✓ & — & ✓ & \textgreater{}20 & \textless{}5 \\ Crustal fault movement & — & ✓ & — & ✓ & 0.5–20 & 1–20/a \\ Surface settlement & — & ✓ & — & ✓ & 0.1–10 & 1–100/d \\ Mining subsidence & ✓ & — & — & ✓ & 1–20 & 1 \\ Landslide (foreboding) & ✓ & — & — & ✓ & 1–20 & \textgreater{}1000 \\ Landslide (eruption) & ✓ & — & — & ✓ & 1–20 & \textgreater{}1000 \\ \hline \end{tabular} \({}^{1}\) No. \({}^{2}\) Yes.  
\end{table} 
Table 1: Classification of typical surface deformation phenomena [4]. data before event or simulated data using existing DEM  
The size of deformation corresponding to each radian of phase change in the differential interferogram is also called the interferometric sensitivity to displacement of the SAR system. The interferometric sensitivity of the SAR system to deformation is an important indicator for surface deformation monitoring. Taking C-band ERS SAR data as an example [26], a deformation of 1 cm along the radar line corresponds to a radar differential interferometric phase change of 2.2 radians (129\({}^{\circ}\)), while the same deformation in the L-band PALSAR differential interferogram corresponds to a differential phase change of 0.5 radians (31\({}^{\circ}\)) [27]. It can be seen that the D-InSAR interferometric phase shows high sensitivity to ground surface displacement, with short-wave data exhibiting greater sensitivity than long-wave data. Therefore, if different band SAR data are used to measure the same deformation field, the shorter the radar wavelength, the more fringe periods there will be corresponding to the differential interferogram. Similarly, in the same differential interferogram, the place with a larger deformation gradient will correspond to a denser deformation phase fringe. From the above analysis, by observing the density of phase fringes in the differential interferogram, the concentrated range and intensity of ground surface deformation can be evaluated. Figure 4 shows the differential interferogram of the Izmit earthquake, and the red line segment indicates the location of the fault rupture. Notably, the differential interferogram fringes run through the entire interferogram, and deformation occurred within 100 km around the fault rupture due to the earthquake. Moreover, the fringes near the fault are relatively dense, while the ground surface deformation fringes far from the fault are relatively sparse, which is caused by the larger deformation gradient near the fault compared to the far-field region. According to the rule that a surface deformation of 2.8 cm in the line of sight corresponds to a striped pattern cycle, the number of fringes in the deformation field can be observed to estimate the deformation amount in the epicentral area.