## 3 Three-Dimensional Measurements  
Figure 2 shows the along-track and cross-track (LOS) displacements obtained by the stacks of multiple InSAR pairs. Eight and seven pairs were stacked for the ascending and descending data sets, respectively. The measurements in the low-coherence (\(\gamma<0.7\)) areas were masked due to their low reliability. As shown in Figure 2a,c, the LOS deformation based on the InSAR method were clearer than the along-track deformation in Figure 2b,d. In general, the InSAR measurements are much more precise than the MAI measurements. However, previous studies have shown that the MAI interferograms can provide measurement accuracies of approximately 1.0 cm/year by stacking multi-temporal pairs [16,17]. Moreover, MAI measurements might provide more reliable results than InSAR in certain places where atmospheric effects are severe because the MAI technique is not influenced by atmospheric signal delay [16].  
As observed in the InSAR measurements of both ascending and descending data sets, uplift is clearly identified in the vicinity of Kflavaea's summit, but the center of the deformed region is separated from the Kflavaea caldera to the southwest. The along-track deformation from both ascending and descending data sets shows a symmetric deformation pattern in opposite directions in the northern and southern portions from the deformation center (Figure 2b,d). The along-track displacement from the ascending data shows an oblique distribution pattern, whereas this pattern is not clearly visible in the descending data set. Therefore, the deformation source is not uniaxial but might be bi- or triaxial in shape. The magnitudes of the deformation are nearly the same in both data sets. The maximum displacement of the southern part of the caldera in the along-track direction is approximately 16 cm, based on the results from both data sets.  
Two LOS and two along-track displacements from ascending and descending data were jointly inverted to retrieve the east, north, and up components of the 3D deformation around Kflavaea's summit area (Figure 3). Positive values represent movement in the eastward, northward, and upward directions. The maximum displacements measured are approximately 8.2, \(-13.8\), and 11.6 cm in the east, north, and up directions, respectively. As with the individual InSAR and MAI measurements, the typical deformation pattern for the summit's inflation can be observed via the 3D displacement maps. These maps also show that the center of the uplift was not exactly in center of the caldera, whereas the deflation center in association with the Kamoamoa fissure eruption was nearly in the center of the caldera. Therefore, the magma sources for the Kamoamoa fissure eruption and the recent intrusion were not the same. The magma source for the recent intrusion is slightly separated from the caldera center in the southwestward direction  
Figure 4 shows the 3D displacement vectors computed by combining the eastward and northward components of the 3D deformation. Arrows indicate the horizontal movements, and the color map represents the vertical component of the surface deformation. Based on the horizontal vector fields, the pattern of surface inflation is clearly recognizable. The difference is not great, but the movement in the north-south direction is more distinct than that in the east-west direction. As discussed earlier, this means that the magma source for this intrusion is likely not spherical in shape. The 3D measurements enable us to assume the approximate shape and size of the deformation source. These estimates, in turn, are used as an initial parameter determination in modeling.  
Figure 2: Multi-stacked InSAR and MAI measurements. (**a**) LOS and (**b**) along-track deformation based on InSAR and MAI measurements from ascending orbits. (**c**) LOS and (**d**) along-track deformation based on InSAR and MAI measurements from descending orbits.