Data transformation in geoscience has typically been motivated by three objectives: (1) creating normally distributed data; (2) creating data that are additive; and (3) making errors constant across the range of the data.
Historically, transformation of geochemical concentrations has been undertaken to achieve normality. Unfortunately, most geochemical distributions are multi-modal and derived from several geological sources. Thus no continuous, monotonic transformations exist that can convert these into (even approximately) normal distributions, and thus transformation for this purpose is neither generally achievable nor justified. Transformations that create additivity are rare in geochemical applications, although they are important in error treatment and lithogeochemical data analysis. These transformations effectively convert data into a form that can be sensibly manipulated, and thus facilitate subsequent data analysis. Transformation to stabilizing errors in geochemical data is also not common, although it is a useful attribute in subsequent geochemical data analysis.
Another type of data transformation, designed to maximize geochemical contrast (or maximize data variance), may be achieved by raising geochemical concentrations to a power after transforming the data to the 0 ↔ 1 interval. The power that produces the maximum variance in the transformed result creates the maximum geochemical contrast, affording the geochemist an opportunity to extract the most information from the geochemical data.
The ‘maximum data variance’ transformation is based not on the subsequent data analysis result (e.g. recognizable geochemical patterns; circular reasoning where ‘the end justifies the means’), but on an optimal property created by the transform. As a result, this transformation provides significant advantage in subsequent data analysis because results achieved are not subjective.