Using Isometric Logratio Transformations (ILR) to interpret enzyme leach geochemical surveys

Enzyme selective extractions (ESE) aids in the detection of mineral deposits at depths ranging from a few meters to 800 metres and sometimes more. This selective extraction technique was developed over the past 25 years and it has been utilized successfully to locate many types of mineral deposits. Ore bodies are indicated by a host of elements that are distributed into positive and negative patterns at surface, above and around the margins of mineral deposits. Trace elements become trapped at parts-per-billion and parts-per-trillion levels within amorphous oxide coatings on sand and silt grains in the soil or sediment in the near-surface environment. Selective extraction by Enzyme Leach of amorphous MnO within these coatings and subsequent analysis for up to 68 trace and major elements by ICP-Mass Spectrometry reveals repeatable patterns that indicate blind mineral bodies. One big advantage of this method is the simplicity of the sampling procedure and the small amount of material needed (10 g of the -60 Mesh fraction). Samples can be taken from any depth, although constancy in the depth of sampling is necessary. In the creation of the ILR matrix, the Author used the suite of elements provided by the ESE method (oxidation, base metals, chalcophile base metals, High Field Strength Elements (HFSE), Rare Earth Elements (REE), lithophile, Platinum Group Element (PGE), and Major Oxides suites). This provides the opportunity of introducing a geological concept into the actual processing of the data and the creation of a new sort of geochemical prospecting map- one that looks for deposit type instead for individual elements or their combinations. The method was applied to several datasets that allowed the detection of new targets in Armenia, Colombia, Chile, Mozambique, and elsewhere.

The Mathematics of Compositional Analysis

The term compositional data analysis is historically associated to the approach based on the logratio transformations introduced in the eighties. Two main principles of this methodology are scale invariance and subcompositional coherence. New developments and concepts emerged in the last decade revealed the need to clarify the concepts of compositions, compositional sample space and subcomposition. In this work the mathematics of compositional analysis based on equivalence relation is presented. The two principles are essential attributes of the corresponding quotient space. A logarithmic isomorphism between quotient spaces induces a metric space structure for compositions. Using this structure, the statistical analysis of compositions consists of analysing logratio coordinates.