Compositional data-driven alternatives to single geochemical component maps

Conventional practice in Regional Geochemistry includes as a final step of any geochemical campaign the generation of a series of maps, to show the spatial distribution of each of the components considered. Such maps, though necessary, do not comply with the compositional, relative nature of the data, which unfortunately make any conclusion based on them sensitive
to spurious correlation problems. This is one of the reasons why these maps are never interpreted isolated. This contribution aims at gathering a series of statistical methods to produce individual maps of multiplicative combinations of components (logcontrasts), much in the flavor of equilibrium constants, which are designed on purpose to capture certain aspects of the data.
We distinguish between supervised and unsupervised methods, where the first require an external, non-compositional variable (besides the compositional geochemical information) available in an analogous training set. This external variable can be a quantity (soil density, collocated magnetics, collocated ratio of Th/U spectral gamma counts, proportion of clay particle fraction, etc) or a category (rock type, land use type, etc). In the supervised methods, a regression-like model between the external variable and the geochemical composition is derived in the training set, and then this model is mapped on the whole region. This case is illustrated with the Tellus dataset, covering Northern Ireland at a density of 1 soil sample per 2 square km, where we map the presence of blanket peat and the underlying geology. The unsupervised methods considered include principal components and principal balances
(Pawlowsky-Glahn et al., CoDaWork2013), i.e. logcontrasts of the data that are devised to capture very large variability or else be quasi-constant. Using the Tellus dataset again, it is found that geological features are highlighted by the quasi-constant ratios Hf/Nb and their ratio against SiO2; Rb/K2O and Zr/Na2O and the balance between these two groups of two variables; the balance of Al2O3 and TiO2 vs. MgO; or the balance of Cr, Ni and Co vs. V and Fe2O3. The largest variability appears to be related to the presence/absence of peat.

Geostatistical Fisher discriminant analysis

A geostatistical version of the classical Fisher rule (linear discriminant analysis) is presented.This method is applicable when a large dataset of multivariate observations is available within a domain split in several known subdomains, and it assumes that the variograms (or covariance functions) are comparable between subdomains, which only differ in the mean values of the available variables. The method consists on finding the eigen-decomposition of the matrix W-1B, where W is the matrix of sills of all direct- and cross-variograms, and B is the covariance matrix of the vectors of weighted means within each subdomain, obtained by generalized least squares. The method is used to map peat blanket occurrence in Northern Ireland, with data from the Tellus
survey, which requires a minimal change to the general recipe: to use compositionally-compliant variogram tools and models, and work with log-ratio transformed data.

What defines a geochemical map? Implications for environmental assessment.

The environmental quality of land is often assessed by the calculation of threshold values which aim to differentiate between concentrations of elements based on whether the soils are in residential or industrial sites. In Europe, for example, soil guideline values exist for agricultural and grazing land. A threshold is often set to differentiate between concentrations of the element that naturally occur in the soil and concentrations that result from diffuse anthropogenic sources. Regional geochemistry and, in particular, single component geochemical maps are increasingly being used to determine these baseline environmental assessments. The key question raised in this paper is whether the geochemical map can provide an accurate interpretation on its own. Implicit is the thought that single component geochemical maps represent absolute abundances. However,because of the compositional (closed) nature of the data univariate geochemical maps cannot be compared directly with one another.. As a result, any interpretation based on them is vulnerable to spurious correlation problems. What does this mean for soil geochemistry mapping, baseline quality documentation, soil resource assessment or risk evaluation? Despite the limitation of relative abundances, individual raw geochemical maps are deemed fundamental to several applications of geochemical maps including environmental assessments. However, element toxicity is related to its bioavailable concentration, which is lowered if its source is mixed with another source. Elements interact, for example under reducing conditions with iron oxides, its solid state is lost and arsenic becomes soluble and mobile. Both of these matters may be more adequately dealt with if a single component map is not interpreted in isolation to determine baseline and threshold assessments. A range of alternative compositionally compliant representations based on log-ratio and log-contrast approaches are explored to supplement the classical single component maps for environmental assessment. Case study examples are shown based on the Tellus soil geochemical dataset, covering Northern Ireland and the results of in vitro oral bioaccessibility testing carried out on a sub-set of archived Tellus Survey shallow soils following the Unified BARGE (Bioaccessibility Research Group of Europe).

William Smith - 200 years of geomodelling celebrated at IAMG

The International Association for Mathematical Geosciences (IAMG) commemorated William Smith (23rd March 1769 - 28th August 1839) and 200 years of geomodelling with geological surveys and academics across the globe at the 17th annual conference of the IAMG in Freiberg, Germany from the 5th to 13th September 2015. The aim of the IAMG is to promote the use of mathematics, statistics and geoinformatics in the geosciences. The annual IAMG conference is an opportunity for geoscientists to collaborate with mathematicians and statisticians and present their recent work. The

17th annual IAMG conference, with 300 participants from across the world, differed from previous IAMG conferences in that it included a special ‘Day of Surveys’ to acknowledge 200 years of science and methodologies to construct maps.