Voronoi Natural Neighbours Tessellation: An interpolation and grid agnostic approach to forensic soil provenancing

Abstract

Recently there has been an increase of work dedicated to developing a more objective soil provenancing capability. Notwithstanding the significant progress made, the presented provenancing techniques have predominately been based upon interpolation grids, generated from often arbitrary decisions of the user (e.g., grid cell size, grid placement, interpolation model, etc.). To address the acknowledged reproducibility issues, this paper introduces a spatial modelling technique based upon Voronoi Tessellations that is free from arbitrary user decisions. Termed herein as Voronoi Natural Neighbours Tessellation (VNNT), the proposed approach segments the survey area into many “honeycomb-like” polygons. Of which, the exact number, shape, location, and orientation of polygons are inherently dependent upon the original density of input sampling points from the survey, not a user’s subjective decision.

Utilising compositional geochemistry data from a fit-for-purpose topsoil survey and eleven “blind” soil samples from Canberra, Australia, we compare this proposed VNNT approach against a simpler Voronoi Tessellation, and a previously presented 500 m × 500 m grid following a modified and upscaled Natural Neighbour interpolation. Aside from also being computationally less intensive, our results indicated the proposed VNNT approach regularly yielded at least equal, or often more accurate provenance predictions than that of the gridded Natural Neighbour interpolation. Importantly, the delineation of individual polygons is fundamentally dependent upon the survey’s real sampling design, and most truthfully reflects the underlying sampling density, and associated uncertainties. Consequently, the VNNT approach is significantly less susceptible to expert bias as a result of subjective decision-making and “fine-tuning” of interpolation parameters.