## 4 Results
### Migration Vector Decomposition and Intercomparison with GPS Data  
Line of sight (LOS) deformations only showed the projected displacement in the employed sensor directions. Thus, it was necessary to decompose InSAR displacement to analyze surface deformation quantitatively, involving geological contexts. The decomposition of the horizontal and vertical displacement vectors from the ascending-descending time series combinations was performed as follows. First, the descending time series displacement maps from corresponding InSAR pairs (refer to the red boxed portions in Figure 2a) were interpolated spatially to increase observation density and temporally to fit the referencing time of deformations of two time series observations. They were then rearranged into 54 interpolated displacement maps according to the acquisition times of the ascending mode InSAR pairs. The temporal displacement values for specific locations were interpolated using a least squares quadratic equation fit with a 2 nd order polynomial function, and a spatial adaptive filter was applied over newly arranged deformations. For the 54 ascending and interpolated descending displacement pairs which now have better observation densities and the same reference time of  
Figure 5: Temporal migration of LOS deformation in descending mode during the 2015–2018 period. The referencing time of deformation is 25 May 2015. Deformation along the Ulsan fault was apparent first. deformation measurement, i.e., 2015/05/25, vector decomposition was conducted as per the method described in [PERSON] et al. (2015). \[\left\{ \begin{array}{rl}&disp_{\text{{LOS}}_{\text{{asc}}}}=disp_{\text{{H}}} sin\theta_{\text{{asc}}}+disp_{V}sin\theta_{\text{{desc}}}\\ &disp_{\text{{LOS}}_{\text{{desc}}}}=-disp_{\text{{H}}}sin\theta_{\text{{desc}} }+disp_{V}sin\theta_{\text{{asc}}}\end{array} \right. \tag{4}\]  
where \(disp_{\text{{LOS}}_{\text{{asc}}}}\) is ascending mode displacement, \(disp_{\text{{LOS}}disp}\) is descending mode displacement, \(disp_{\text{{H}}}\), and \(disp_{V}\) are horizontal and vertical displacements, respectively, and \(sin\theta_{\text{{asc}}}\) and \(sin\theta_{\text{{desc}}}\) are the look angles of the ascending and descending modes, respectively. The horizontal displacement extracted by decomposition consisted of two components that are related as follows:  
\[disp_{\text{{H}}}=disp_{\text{{N}}}sin\varphi-disp_{\text{{E}}}cos\varphi \tag{5}\]  
where \(disp_{\text{{N}}}\) is the N-S directional displacement, \(disp_{\text{{E}}}\) is the E-W directional displacement, and \(\varphi\) is the heading angle of the satellite. As the heading angles of the satellite can be approximated to 0\({}^{\circ}\) and 180\({}^{\circ}\), the contribution of E-W displacement to horizontal displacement is far more significant (by about three times in Sentinel-1 image acquisition geometry) than that of N-S displacement. In the present study, it was not possible to decompose the E-W and N-S displacements because we only had two observations. Horizontal and vertical displacements in both the ascending and descending total cumulative/time series observations are given in Figure 6. We identified strong deformation in both the vertical and horizontal directions along the Ulsan fault (P1 and P3 in Figure 6) and found stabilities along the Yangsan fault (P6 in Figure 6). Those outcomes were used to analyze the geological context of the industrial facilities, which involved risk factors, together with geophysical models (see Section 5). In order to validate InSAR observations and to extract more information, a comparison with GPS data from the WOLS and ULSN stations was conducted. The LOS deformations around the P3 and P10 areas (Figure 6), which are defined by geological units and a specific deformation pattern (see Section 5 for details), were compared to the nearest WOLS and ULSN GPS data.