A robust interpolation-based method for forensic soil provenancing: A Bayesian likelihood ratio approach

Soil is a complex and spatially variable material that has a demonstrated potential as a useful evidence class in forensic casework and intelligence operations. Here, the capability to spatially constrain police search areas and prioritise resources by triaging areas as low and high interest is advantageous. Conducted between 2017 and 2021, a forensically relevant topsoil survey (0-5 cm depth; 1 sample per 1 km²) was carried out over Canberra, Australia, aiming to document the distribution of chemical elements in an urban/suburban environment, and of acting as a testbed for investigating various aspects of forensic soil provenancing. Geochemical data from X-Ray Fluorescence (XRF; for total major oxides) and Inductively Coupled Plasma-Mass Spectrometry (ICP-MS; for trace elements) following a total digestion (HF + HNO₃) of the fused XRF beads were obtained from the survey's 685 topsoil samples (plus 138 additional quality control samples and six "Blind" simulated evidentiary samples). Using those "Blind" samples, we document a likelihood ratio approach where for each grid cell the analytical similarity between the grid cell and evidentiary sample is attributed from a measure of overlap between the two Cauchy distributions, including appropriate uncertainties. Unlike existing methods that base inclusion/exclusion on an arbitrary threshold (e.g., ± three standard deviations), our approach is free from strict binary or Boolean thresholds, providing an unconstrained gradual transition dictated by the analytical similarity. Using this provenancing model, we present and evaluate a new method for upscaling from a fine (25 m x 25 m) interpolated grid to a more appropriate coarser (500 m x 500 m) grid. In addition, an objective method using Random Match Probabilities for ranking individual variables to be used for provenancing prior to receiving evidentiary material was demonstrated. Our results show this collective procedure generates more consistent and robust provenance maps when applied to two different interpolation algorithms (e.g., inverse distance weighting, and natural neighbour), with different grid placements (e.g., grid shifts to the north or east) and by different theoretical users (e.g., different computer systems, or forensic geoscientists).