Can we predict the provenance of a soil sample for forensic purposes by reference to a spatial database?

In forensic soil science it is sometimes necessary to address a question of the form: `what is the most likely place of origin of this soil material', where the possible provenances are in a large area. This `intelligence' problem may be distinguished from the `evidence' problem where we need to evaluate the grounds for believing that some soil material is derived from one site rather than another. There is interest in the use of soil databases to solve intelligence problems. This paper proposes a geostatistical method to tackle the intelligence problem. Given data on a sample of unknown provenance, and a database with the same information from known sites, it is possible to define a likelihood function, the argument of which is location in space, which is the likelihood that the sample is from that location. In this paper we show how an approximation to this likelihood can be computed, using a principal component transformation of the data and disjunctive kriging. The proposed likelihood function is tested using a geochemical database on the soil of the Humber Trent region of north-east England. This shows that the function is a useful way to make a statistical prediction of the provenance of a soil sample. The region can be stratified according to the value of the likelihood function. A validation data set showed that if we defined a stratum with the top 4.5% of values of the likelihood function, then there was a 50% probablity that it included the true provenance of the sample, and there is a 90% probability of finding the true provenance of the sample in a stratum with the top 30% of values of the likelihood function. Note also that the spatial likelihood function could be integrated with other sources of information on the likely provenance of the sample by means of Bayes law. We conclude that this approach has value for forensic problems. The main difficulty is how to define the geostatistical support of the forensic specimen, and the reliability of analytical data on relatively small forensic samples, but this is a generic problem for forensic geoscience.