Sparse isocon analysis: A data-driven approach for material transfer estimation

Isocon analysis has been widely applied to various geoscientific problems as a simple standard tool for quantitative estimation of material transfer. Despite its usefulness, similar to all material transfer calculations, this method generally requires the presumptive specification of immobile elements or the assumption of conservation of mass or volume. However, the validity of such assumptions is particularly controversial. Here we propose a novel data-driven method that automatically estimates the mass gain or loss of elements based on compositional data of multiple samples that have been altered from the original rock without assuming immobile elements. The proposed method uses a mathematical framework, called sparse modeling, that can extract essential information from high-dimensional datasets based on the sparsity of the system. In this case, it is assumed that some elements show higher immobility than others (i.e., the material transfer of such elements is near zero). By optimizing the evaluation function, the immobile elements are automatically selected. By inputting only the bulk compositional datasets, the user can obtain the material gain or loss with total mass change ratio for each sample relative to the reference (original) rock. The effectiveness of the method is validated and discussed using synthetic and natural sample data. Software packages are available from the authors in MATLAB function and Excel workbook forms.