Chemical Discrimination of Rutile From Different Metamorphic Source Rocks: Dealing With Hierarchical Data Structures in Random Forest Classification

ABSTRACT Rutile provides a wealth of petrochronological information in metamorphic geology and due to its high stability during processes of the sedimentary cycle, rutile takes a special position in sedimentary provenance analysis. Besides being one of the classical minerals datable using the U–Pb system, rutile incorporates a broad range of trace elements, many of those being incompatible in most of the common metamorphic minerals. Although numerous multivariate statistical or machine‐learning tools are available, current rutile discrimination schemes suffer from focusing on uni‐ and bivariate approaches leading to large compositional overlaps. Here we compiled and enlarged a dataset of 2335 rutile trace‐element analyses (1646 new analyses) from 110 metamorphic rock samples of 48 localities covering a wide range of pressure–temperature conditions. After showing that the subsampling and testing strategy of the classical random forest algorithm is inappropriate for such hierarchical data structures, we introduce a modified version (random forests for hierarchically structured data) which provides realistic and generalized error estimates, improving hyperparameter tuning and performance. By applying this concept, we present a novel and multivariate rutile discrimination scheme, using the concentrations of 16 elements. The model correctly predicts the source rock composition (felsic versus mafic) in ~89% of the cases and the metamorphic gradient (≤ 350 °C/GPa versus > 350 °C/GPa) in ~84%. Combined with U–Pb dating, this will enable time‐resolved insights into the geodynamic evolution of the hinterland, taking rutile provenance analysis to the next level. This approach furthermore highlights specific elements and ratios — previously understudied — that reflect bulk‐rock and partitioning effects, making them valuable for future investigation of metamorphic processes. For the ease of application, a user‐friendly “rutileRF‐HSD” web application is provided.