Geochemical-process extraction and interpretation using matrix factorization: a framework for verifying effectiveness through forward modeling and inversion analysis

Matrix factorization techniques, such as principal component analysis (PCA) and independent component analysis (ICA), are widely used to extract geological processes from geochemical data. However, their effectiveness in accurately identifying geological processes remains uncertain due to the heuristic nature of these methods. This study introduces a synthetic data-based framework to evaluate the validity of matrix factorization for geochemical process extraction. By constructing a forward model that simulates geochemical weathering, we generated synthetic datasets replicating real-world geochemical compositions, incorporating both the elemental leaching during fluid-rock interactions and the compositional heterogeneity of the original rocks. These datasets were analyzed using PCA and ICA, with preprocessing steps that included standardization and log-ratio transformation to address the challenges posed by compositional data. The results indicate that PCA and ICA effectively extracted the two key geological processes -elemental leaching and original rock heterogeneity-from the synthetic datasets. Among these methods, ICA combined with log-ratio transformation provided the most accurate separation of independent geochemical processes, particularly under ideal conditions with sufficient samples. To quantitatively validate the extracted basis vectors, we estimated elemental mobility parameters during weathering and compared them with known values in the synthetic dataset, demonstrating the applicability of our approach in quantifying geological processes. This study highlights the advantages of a bilateral approach that integrates forward modeling and inversion analysis to enhance the reliability of geochemical process interpretation. The proposed framework offers a systematic methodology for identifying and quantifying underlying geological processes from high-dimensional geochemical data, with potential applications in geochemistry, environmental science, and resource exploration.