Modelling diffusion, decay and ingrowth of U–Pb isotopes in zircon

Abstract. Understanding the thermal evolution of geological terranes provides essential insights into tectonic processes, crustal evolution, and mineral resource formation. Zircon U–Pb geochronology is widely used to date geological events, yet these dates are altered by a wide-range of processes, including diffusion of radiogenic isotopes at high (>800 °C) temperatures. This study utilises the Underworld3 numerical code to couple diffusion processes with radioactive decay and ingrowth in two-dimensions. We assess the numerical solutions against a series of benchmarks to test the implemetation, and apply the models to examine lead-loss due to thermal events and complexities that arise from multiple zircon growth episodes. Our approach bridges analytical U-Pb isotope measurements with a diffusion-decay-ingrowth numerical model, providing insights into how the thermal evolution of a region alters zircon U–Pb isotope ratios. We apply the methodology to the Trivandrum block in southern India—a region characterised by a prolonged high-temperature event—comparing multiple temperature–time paths with analytical U–Pb isotope data to provide constraints on the thermal evolution of the region. The modelling framework can be easily modified to investigate diffusion-decay-ingrowth across various minerals and isotopic systems, providing a tool to decipher the thermal history of a region recorded in isotopic data.