###### Abstract  
Traditional inverse distance weighting (IDW) interpolation is a process employed to estimate unknown values based on neighborhoods in 2D space. Proposed in this study is an improved IDW interpolation method that uses 3D search neighborhoods for effective interpolation on vertically connected observation data, such as water level, depth, and altitude. Borehole data are the data collected by subsurface boring activities and exhibit heterogeneous spatial distribution as they are densely populated near civil engineering or construction sites. In addition, they are 3D spatial data that show different subsurface characteristics by depth. The subsurface characteristics observed as such are used as core data in spatial modeling in fields, such as geology modeling, estimation of groundwater table distribution, global warming assessment, and seismic liquefaction assessment, among others. Therefore, this study proposed a seismic liquefaction assessment and mapping workflow using an improved IDW application by combining geographic information system (GIS) (ArcGIS (Esri, Redlands, CA, USA)), NURBS-based 3D CAD system (Rhino/Grasshopper (Robert McNeel & Associates, Seattle, WA, USA)), and numerical analysis system (MATLAB (MathWorks, Natick, MA, USA)). The 3D neighborhood search was conducted by the B-rep-based 3D topology analysis, and the mapping was done under the 2.5D environment by combining the voxel layer, DEM, and aerial images. The experiment was performed by collecting data in Songpa-gu, Seoul, which has the highest population density among the OECD countries. The results of the experiment showed between 7 and 105 areas with liquefaction potentials according to the search distance and the method of the approach. Finally, this study improved users' accessibility to interpolation results by producing a 3D web app that used REST API based on OGC ISS Standards. Such an approach can be applied effectively in spatial modeling that uses 3D observation data, and in the future, it can contribute to the expansion of 3D GIS application.  
3D search neighborhoods; spatial interpolation; inverse distance weighting (IDW); seismic liquefaction; geographic information system (GIS) +
Footnote †: journal: Applied Sciences
modeling [3], landslide risk assessment [4], and even medical image analysis [5]. The estimation of an unknown value in interpolation is determined by the spatial relationship, which can be defined differently by the neighborhood search method. In the case of a square-based grid, the neighborhoods are typically Rook, Bishop, and Queen that determine four or eight neighboring cells, and to minimize the edge effect of the square grid, a hexagon grid can be used (Figure 1) [6; 7]. However, such traditional raster-based neighborhood analysis is performed based on the assumption of a 2D vector space and is limitedly applied to observation data distributed in 3D space (i.e., fine dust assessment by altitude using a drone [8], borehole-based geology modeling [9], marine environment assessment [10]). As such, the data observed in the spatial context, such as water level, depth, or altitude, exhibit both horizontal and vertical connectivity. Thus, a neighborhoods search during interpolation also needs to be performed in 3D space, and a more realistic spatial modeling can be possible via 3D interpolation. Therefore, this study proposed an improved interpolation method using 3D search neighborhoods and attempted to examine the results by applying them to actual cases.