Lloyd, J.C.Spandler, C.Gilbert, S.E.Hasterok, D.2025-08-252025-08-252025Geochronology, 2025; 7(3):265-2872628-36972628-3719https://hdl.handle.net/2440/147043Down-hole fractionation (DHF), a known phenomenon in static spot laser ablation, remains one of the most significant sources of uncertainty for laser-based geochronology. A given DHF pattern is unique to a set of conditions, including material, inter-element analyte pair, laser conditions, and spot geometry. Current modelling methods (simple or multiple linear regression, spline-based regression) for DHF do not readily lend themselves to uncertainty propagation, nor do they allow for quantitative inter-session comparison, let alone inter-laboratory or inter-material comparison. In this study, we investigate the application of orthogonal polynomial decomposition for quantitative modelling of LA-ICP-MS DHF patterns. We outline the algorithm used to compute the models, apply it to an exemplar U–Pb dataset across a range of materials and analytical sessions, and finally provide a brief interpretation of the resulting data. In this contribution we demonstrate the feasibility of quantitative modelling and comparison of DHF patterns from multiple materials across multiple sessions. We utilise a relatively new data visualisation method, uniform manifold approximation and projection (UMAP), to help visualise the data relationships in this large dataset while comparing it to more traditional methods of data visualisation. The algorithm presented in this research advances our capability to accurately model LA-ICP-MS DHF and may facilitate reliable decoupling of the DHF correction for non-matrix-matched materials, lead to improved uncertainty propagation, and facilitate inter-laboratory comparison studies of DHF patterns. The generalised nature of the algorithm means it is applicable not only to geochronology but also more broadly within the geosciences where predictable linear (x-to-y) relationships exist.en© Author(s) 2025. This work is distributed under the Creative Commons Attribution 4.0 License. Published by Copernicus Publications on behalf of the European Geosciences Union.Down-hole fractionation (DHF); spot laser ablation; application; orthogonal polynomial decomposition; LA-ICP-MS DHF patterns; quantitative modellingJournal article10.5194/gchron-7-265-2025747229Lloyd, J.C. [0000-0002-4429-873X]Spandler, C. [0000-0003-2310-0517]Gilbert, S.E. [0000-0003-3259-7983]Hasterok, D. [0000-0002-8257-7975]