# The Survey of Lava Tube Distribution in Jeju Island by Multi-Source Data Fusion
## 5 Discussions
Regarding the instability points around Manjang cave (_E_), it corresponds to the exit of Manjang cave which has shallow a double cave structure as shown in Figure 9a. Groups _F1_-_F3_ demonstrate the potential LTDPs and alignment with lava flow directions from cinder cones to the coastline. Groups _G1_ and _G2_ are ambiguous as their alignments do not fit with lava flow directions in that area. Although subsidence and/or alignment with corresponding lava flow was not observed, constant attention to the potential LTDP distribution in the south-western side is still required. Along the northern coastline, some lava tubes are at the risk of collapsing due to their shallow cavity and proximity to road-crossing (see the Geamcheon and Gammadap caves shown in the laser scanned data given in Figure 9b together with Figure 9a 2D profile of the Manjang cave). The potential LTDP distributions in the northwestern coastline, Jeju city areas, and Seogwipo tourist complex (red dotted ellipses in Figure 8b) are irregularly distributed along the coastline and ongoing construction places; thus are not likely genuine signals of lava tubes. The issue is whether these 3D cave structures create deformations as observed in InSAR analyses. Since numerical modeling, for instance, the FEM using 3D cave data and estimated tensile stress, is beyond the scope of this study, clues can be found in precedent studies regarding tunnel stability. In particular, [69] established the relationship between the dimensions of collapsing parts, which are defined with L1, L2, and radius R on the approximated circular cavity as shown in Figure 9c, stresses, and material properties. The cave shape of Figure 9c was extracted from the TLS of Gammadmap cave, and it fits well to the known cave geometry in Jeju Island. Thus, the displacement induced by collapse will be dominated by the vertical way but mixed with the horizontal deformations which are applied symmetrically at the center of the approximated circular shape as shown in [70]. Therefore, H-migrations detected by PS InSAR mainly contained part of horizontal deformations directed toward the SAR sensor. In contrast, the detected V-migrations represented mainly vertical and horizontal deformations away from the SAR sensor position. The magnitude of deformations around circular tunnels is very different, according to the applied tensile stress, materials properties (hard/soft rocks and soil), and the dimension of the tunnel. If the tunnel depths are limited to very shallow (<10-20 m), the deformation values calculated in the case studies vary from sub-millimeter depending on the scenarios [70; 71; 72]. However, the fractures in the weathering wall of the lava tubes and the relatively weak brittle strength of basaltic rocks, combined with anthropogenic or structural stresses certainly cause sufficiently high deformations, which can be detected by InSAR observations. Figure 9: Examples of 2D/3D cave models and instability check. (**a**) The 2D profile of Manjang caves and the location of detected LTDPs on the terminus of the tube, which are digitized from [56]. (**b**) 3D LiDAR map in Gammamdap cave with thin topography. (**c**) Diagram of expected deformations on cross-sectional lava tube (H: depth of cave, R: radius of approximated circular shape on lava tube, L1 and L2: the lengths of upper and lower parts of collapsing part, dh and dv: hypothesized H/V deformations at certain collapsing points). Refer to Figure 1 to identify cave locations. The map projection system of (**b**) is Korea 2000/Central Belt 2010. InSAR LOS migrations can be expressed using the quantities in Figure 9c and the relationship by [73] as  
\[disp_{los}=-sin\theta cosadisp_{h}+cos\theta disp_{v} \tag{3}\]  
where \(disp_{los}\) is LOS displacement, \(disp_{h}\), and \(disp_{v}\) are horizontal and vertical displacements, \(\theta\) represents the incidence angles and \(\alpha\) is the heading angle. Thus, the observed \(disp_{los}\) can be estimated using the angles in Table 1 and Equation (3) in the case of Figure 9c.