## 3 Methods  
### LOS Deformation Rate Derived from Stacking-InSAR  
The collected Sentinel-1A SAR images spanning from 2015 to 2019 were processed by stacking-InSAR technology to obtain the LOS deformation rate. Stacking-InSAR is an enhancement technology that obtains the deformation rate by linearly stacking a set of unwrapped differential interferograms, and is expressed by the following equation [25]:  
\[\text{Ph}_{\text{rate}}=\frac{\sum_{j=1}^{N}\Delta t_{j}\varphi_{j}}{\sum_{j=1}^ {N}\Delta t^{2}} \tag{1}\]  
where \(\text{Ph}_{\text{rate}}\) was the deformation rate; \(N\) was the number of interferograms involved in the estimation; \(\Delta t_{j}\) was the time interval between the master and slave image; and \(\varphi_{j}\) were the unwrapped interferograms. Prior to stacking-InSAR processing, the interferograms with perpendicular baselines shorter than 100 m and temporal baselines longer than 300 days were produced in this study. This operation could mitigate the noise effects and preserved the temporal and spatial coherence characteristics of the interferograms. It should be noted that the temporal baseline threshold of 300 days, which was considered longer than the conventional stacking-InSAR processing, was designed with the purpose of capturing long-term accumulated surface deformation along the Weihe Fault. As a result, 74 interferometric pairs were produced and involved in the deformation rate estimation (Figure 2). The collected SRTM DEM was used to improve co-registration accuracy and correct topographic phase contributions in all interferograms. The process of adaptive spectral filtering with a window size of 32 was executed to suppress interferometric noise [26].  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Satellite** & **Path** & **Orbital Direction** & **Azimuth Angle** & **Data Period** & **No. of Images** \\ \hline Sentinel-1A & 84 & Ascending & \(-\)13 & 12/2015–03/2019 & 26 \\ \hline \end{tabular}
\end{table}
Table 1: Data coverage for SAR images used in this study.  
Figure 1: The location of the study area (**a**), where the white and red rectangles show the coverages of the study area and SAR images, respectively; the blue lines show the rivers in the Weihe Basin. The enlarged study area is shown in (**b**), where the gray lines represent the faults in the Weihe Basin; the black circles represent the historic earthquake events above magnitude 5; the white circles represent the historic earthquake events below magnitude 5; the blue arrows represent the GNSS-derived horizontal deformation rates; and the black arrows represent the leveling-derived vertical deformation rate.  
Phase unwrapping of the minimum cost flow (MCF) method was carried out to retrieve the absolute phase [27]. After processing, the unwrapped interferometric phase may have consisted in residual phase errors, such as orbital error and atmospheric delay error. In this case, the atmospheric delay errors, which were highly correlated in space but poorly in time, were mitigated through the cascade of a low-pass filter implemented in the two-dimensional spatial domain, followed by temporal high-pass filtering [28]. This filtering operation also allowed us to detect possible orbital phase errors caused by inaccurate SAR orbital information. It was found that the orbital errors were not obvious for the generated interferograms; therefore, there was no further manipulation with the orbital error. The detection of possible orbital errors was important in monitoring tectonic deformation since both of them presented the characteristic of a long wavelength. The empirical linear model between the interferometric phase and elevation was constructed to mitigate the residual atmospheric errors with respect to terrain. Finally, the LOS deformation rate was obtained from Equation (1).