Spatial Elevation Interpolation for 3D Underground Voxel Models in Urban Environments Using Mathematical Surface Correlations

Abstract The use of three-dimensional models in urban environments is becoming an increasingly key strategy for the sustainable management of existing resources, as it can provide detailed information on a wide range of subsoil conditions. This is why the development of procedures that facilitate the automatic modelling of a reality that is difficult to sense is a topic of scientific interest. This research presents a methodology for assigning global heights (elevations) to geotechnical survey points in the metropolitan area of Seville (Spain) in the absence of such data. Based on the use of mathematical surface models for an improvement of the interpolation possibilities, methods based on Ordinary Kriging (OK) and Triangulated Irregular Network Cubic Interpolation (TIN cubic) have been shown to be much more robust than Inverse Distance Weighting (IDW). For this purpose, different distribution hypotheses (random and regular, with and without gaps) and quantities of points have been considered in a simulation study on various mathematical surfaces. The final results, applied in representative areas of the metropolitan area, have demonstrated an improvement of the global interpolated height error up to 15 times better with respect to the real data used as a sample in the period 2000–2024. Furthermore, they illustrate that the classified LIDAR data currently employed in the development of Digital Terrain Models (DTM) can result in considerable modelling errors when applied directly in highly anthropised environments. Consequently, the developed method proves valid for the realisation of adjusted proposals of topographies in urban environments and shows an interesting potential for proposing future coherent depth distributions in subsurface strata.