## 3 Research Results
### Improved IDW Interpolation and Mapping
#### 3.3.2 Mapping of Seismic Liquefaction Assessment  
For the 3D mapping of the seismic liquefaction assessment results, the Excel document generated from the interpolation results is converted into vector data format in GIS (Shapefile). Here, for the effective visualization of the assessment grid densely populated in a vertical direction, the vertical coordinates in the 3D point use the altitude on which the elevation exaggeration factor was reflected. Later, the 3D mapping is completed by creating a voxel cube for each 3D point location. By the risk grade, the color of the voxel cubes is set to red, yellow, or green according to the vulnerability attribute, and the size of the cube is set by the horizontal and vertical search distances set above (Figure 10).  
The biggest differentiation of the nearest neighbors analysis approach which is the most simple method in determining neighbors in a 3D environment (in this study NP\(-\)III) and the suggested spheroid-based 3D search neighborhoods is that the estimation results of proposed method efficiently reflect the vertical and horizontal anisotropy (Figure 11). The nearest neighbors approach is highly effected by neighbors on horizontal directions, whereas the suggested method generates results that maintain the direction of the data that is distributed vertically.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{6}{c}{**Parameter**} & \multicolumn{6}{c}{**Vulnerability**} \\ \cline{2-11}  & & **H-Dist** & **V-Dist** & **EXZ** & **Nbrs** & **Low** & **Moderate** & **High** & **NoData** & **Total** \\ \hline \multirow{4}{*}{NP} & I & 500 & 2 & 100 & 12 & 5 & 8476 & 3759 & 105 & - & 12,340 \\  & I & 500 & 2 & 100 & 12 & 5 & (68.69\%) & (30.46\%) & (0.85\%) & - & (100\%) \\ \cline{2-11}  & II & 1000 & 2 & 100 & 12 & 2 & 8190 & 4045 & 105 & - & 12,340 \\  & II & 1000 & 2 & 100 & 12 & 2 & (66.37\%) & (32.78\%) & (0.85\%) & - & (100\%) \\ \cline{2-11}  & III & - & - & 100 & 12 & - & 8232 & 4008 & 100 & - & 12,340 \\ \cline{2-11}  & III & - & - & 100 & 12 & - & (66.71\%) & (32.48\%) & (0.81\%) & - & (100\%) \\ \hline \multirow{4}{*}{FD} & I & 500 & 2 & 100 & - & 5 & 7986 & 4285 & 69 & - & 12,340 \\  & II & 1000 & 2 & 100 & - & 5 & (64.72\%) & (34.72\%) & (0.56\%) & - & (100\%) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of final interpolation results.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{6}{c}{**Parameter**} & \multicolumn{6}{c}{**Vulnerability**} \\ \cline{2-11}  & & **H-Dist** & **V-Dist** & **EXZ** & **Nbrs** & **Repeat** & **Low** & **Moderate** & **High** & **NoData** & **Total** \\ \hline \multirow{4}{*}{NP} & I & 500 & 2 & 100 & 12 & 5 & 8476 & 3759 & 105 & - & 12,340 \\  & I & 500 & 2 & 100 & 12 & 5 & (68.69\%) & (30.46\%) & (0.85\%) & - & (100\%) \\ \cline{2-11}  & II & 1000 & 2 & 100 & 12 & 2 & 8190 & 4045 & 105 & - & 12,340 \\  & II & 1000 & 2 & 100 & 12 & 2 & (66.37\%) & (32.78\%) & (0.85\%) & - & (100\%) \\ \cline{2-11}  & III & - & - & 100 & 12 & - & 8232 & 4008 & 100 & - & 12,340 \\  & II & 1000 & 2 & 100 & - & 5 & (64.72\%) & (34.72\%) & (0.56\%) & - & (100\%) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of 1 st interpolation results.