## 3 Geospatial Informatics of the Geotechnical Database
### Geospatial Interpolation  
To predict reliable zonal geotechnical characteristics for the study area, the best-fitting geospatial interpolation model with the lowest prediction residuals was selected. [PERSON] et al. [3,55] suggested an optimization procedure for geostatistical analysis of soil properties. A step-by-step adaptive optimization technique that used a GIS platform and geostatistical methods [56]. Cross-validation verification tests were applied using the four interpolation methods IDW, SK, OK, and EBK. The grid-based interpolation and zonation with DEM was assessed to build the reliable surficial geometry assigned with engineering geo-layer thickness and average \(N_{60}^{exp}\) (Figures 6 and 7). The effect of sample size according to distance is arbitrarily weighted by IDW, while kriging requires a variogram that models the spatial autocorrelation of data to give weightings. In IDW, unknown areas are specified only by known z-values and distance weights [57]. Kriging is a representative geostatistical interpolation method that quantifies and analyzes distance by variogram, and the estimators are variants as follows:  
\[\hat{Z}(x_{0})-\mu=\sum_{i=1}^{n}\lambda_{i}[Z(x_{i})-\mu(x_{0})] \tag{4}\]  
where \(\mu\) is a known stationary mean, presumed to be constant across the entire domain and is the average of the data measured [58], \(\lambda_{i}\) is the kriging weight, \(n\) is the number of samples, and \(\mu(x_{0})\) is the mean of samples. SK is modified based on Equation (4) as follows:  
\[\hat{\gamma}(h)=\frac{1}{2h}\sum_{i=1}^{n}(Z(x_{i})-Z(x_{i}+h))^{2} \tag{5a}\] \[\hat{Z}(x_{0})=\sum_{i=1}^{n}\lambda_{i}Z(x_{i})+\left[1-\sum_{i=1}^{n} \lambda_{i}\right]\mu \tag{5b}\]  
Therefore, SK is often referred to as medium kriging as residuals from the reference value \(\mu\)[56]. The OK method is similar to SK, and the only difference is that OK estimates the value of the attribute using Equations (5) and (4) by replacing \(\mu\) with a local mean, \(\mu(x_{0})\) which is the mean of sampleswithin a search window. The variance in ordinary kriging estimates is the sample variance if all the survey sites are measured, and the interpolation variance in the test position is equal to zero [59]. By considering the error in the variogram model calculation, EBK varies from SK and OK. The EBK method includes two geostatistical models: random intrinsic function kriging and a linear mixed model [60; 61]. It simulates variograms for different sub-populations of the initial data. Figure 6: Comparison of geospatial maps of engineering geo-layer thickness between different geostatistical interpolation algorithms including: Inverse Distance Weighting; Simple Kriging; Ordinary Kriging; Empirical Bayesian Kriging. Figures 6 and 7 show geospatial maps of geo-layer thickness and average \(N_{60}^{exp}\) for each of the four interpolation methods. Figure 8 also presents the relationship between measured based on the interpolated multiscale grid (53,791 cells). Figure 7: Comparison of geospatial maps of average \(N_{60}^{exp}\) between different geostatistical interpolation algorithms including: Inverse Distance Weighting; Simple Kriging; Ordinary Kriging; Empirical Bayesian Kriging. Even though there were regional variations in each of the interpolation methods, they all showed soil layers in the vicinity of major urban rivers to be relatively thick where major infrastructure and residential areas were concentrated. In addition, the weathered layers (WS and WR) were relatively thicker in plains and downtown areas. Thus, the soil layer, which is a prominent factor in seismic site effects, is thickly distributed in areas where the population and industry are close, and the risk of damage due to an earthquake is higher. The geological map also showed relatively thick soil centered in areas where the bedrock is overlain by Quaternary sediments. The soil deposits in the river basin is thicker (up to about 40 m), and bedrock depth is deeper (up to about 70 m) than in mountain regions.