A critical comparison of interpolation techniques for digital terrain modelling in mining

Digital modelling of a surface is crucial for Earth science and mining applications for many reasons. These days, high-tech digital representations are used to produce a high-fidelity topographic surface in the form of a digital terrain model (DTM). DTMs are created from 2D data-points collected by a variety of techniques such as traditional ground surveying, image processing, LiDAR, radar, and global positioning systems. At the points for which data is not available, the heights need to be interpolated or extrapolated from the points with measured elevations. There are several interpolation/extrapolation techniques available, which may be categorized based on criteria such as area size, accuracy or exactness of the surface, smoothness, continuity, and preciseness. In this paper we examine these DTM production methods and highlight their distinctive characteristics. Real data from a mine site is used, as a case study, to create DTMs using various interpolation techniques in Surfer® software. The significant variation in the resulting DTMs demonstrates that developing a DTM is not straightforward and it is important to choose the method carefully because the outcomes depend on the interpolation techniques used. In mining instances, where volume estimations are based on the produced DTM, this can have a significant impact. For our data-set, the natural neighbour interpolation method made the best predictions (R2 = 0.969, β = 0.98, P < 0.0001).