Reducing Boundary Discontinuities in 3D Voxel-Based Subsurface Geotechnical Mapping Through Empirical Bayesian Kriging Re-Interpolation

Abstract

The progressive development of 3D subsurface geotechnical maps requires integrating site-based voxel models produced from neighboring engineering-geological investigations, but directly joining separately interpolated classified voxel models can produce artificial boundary discontinuities. This study proposes a GIS-based workflow for reducing such discontinuities through Empirical Bayesian Kriging 3D (EBK 3D) re-interpolation, tested on two adjacent construction sites in Astana, Kazakhstan. Separate 1 × 1 × 1 m classified voxel models were generated for Site A and Site B and compared at their boundary using face-to-face and 1 m offset schemes. Before re-interpolation, the face-to-face boundary matching ratio (BMR) was 49.4%, and the boundary discontinuity ratio (BDR) was 50.6%. Two alternative re-interpolation strategies were then tested: joint-raw EBK 3D interpolation applied directly to the pooled borehole data, and a two-step approach joining and re-interpolating the previously interpolated per-site voxel tables. Both substantially improved face-to-face continuity (BMR rising to 99.1% for joint-raw and 95.7% for the two-step approach), but the two-step approach produced a considerably larger improvement in the surrounding offset neighborhood (BMR increasing to 74.8%, versus 56.9% for joint-raw), indicating it extends greater numerical continuity beyond the immediate contact layer. The two-step approach, used as the primary method, achieved a combined soil-type preservation ratio of 85.9% (88.3% for Site A, 82.7% for Site B). These results demonstrate improved numerical and visual interface continuity rather than independently validated geological accuracy; engineering application would require independent validation and uncertainty quantification. The approach supports the transition from isolated site-scale voxel models toward an expandable 3D subsurface geotechnical mapping system.