Improved IDW Interpolation Application Using 3D Search Neighborhoods: Borehole Data-Based Seismic Liquefaction Hazard Assessment and Mapping

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 I3S 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.

Optimizing Interpolation Methods and Point Distances for Accurate Earthquake Hazard Mapping in Gas Pipeline Routing

“…The local neighborhood approach predicts the value of a variable at an unknown location by calculating the weighted average of values from nearby locations. This method utilizes a subset of input points located within a specified distance or quantity to estimate the value at each output location (Kim et al, 2022). On the other hand, the geostatistical approach estimates the value of a variable at an unknown location by considering the statistical properties of measured values in nearby locations.…”

Lake Water Quality Assessment Through GIS based Interpolation Method: A Case Study of Beris Dam, Kedah, Malaysia

“…The IDW technique can be improved by removing the pre-set size of the "search radius" and focusing on several linked measurement locations [32]. The inverse-distance-weighted approach uses a weighted linear combination of a set of sampled points to calculate values for non-sampled sites [33,34]. The weight is a function of the inverse distance multiplied by any mathematical exponent.…”

Optimizing Interpolation Methods and Point Distances for Accurate Earthquake Hazard Mapping

“…The local neighborhood approach predicts the value of a variable at an unknown location by calculating the weighted average of values from nearby locations. This method employs a subset of input points located within a specified distance or quantity to estimate the value at each output location [57]. On the other hand, the geostatistical approach estimates the value of a variable at an unknown location by considering the statistical properties of measured values in nearby locations.…”