| Numeric data for earth sciences often represent fractions or percentages of a whole, such as the chemical or mineralogical composition of a rock. The individual components are non-negative and have a constant sum of 100%. Satisfying these constraints at unsampled locations after estimation or simulation is a practical requirement, but not guaranteed by conventional mapping and modelling techniques. The components are constrained to the constant sum, which means that they are not free to vary independently, and there is at least one negative correlation. Standard statistical techniques are therefore not suited to compositional data, so transformations using the logarithms of the component ratios (logratios) are used to overcome these problems. Linear averaging and back-transformation of logratios results in a geometric rather than an arithmetic mean, which will result in a bias. A procedure using normal scores transformation of the logratio values and multiGaussian kriging was devised to overcome this bias. The key objective is to avoid estimating the logratios directly and then back-transforming into original data units. Instead, the conditional distributions of the components are modelled. Ordinary kriging, multiGaussian kriging and conditional simulation were used on data from the Alberta Oil Sands to assess the performance of the compositional geostatistics approach. |
