Hamiltonian Monte Carlo applied to inverse petrological problems

Dimitrios Moutzouris , Annalena Stroh, Simon Schorn, Evangelos Moulas

Inversion is inherent in petrology and is used to investigate both experimental and natural field data. When field observations, petrography, geochronology and geochemistry are combined with numerical models, inversion is used to quantify important parameters that provide insights into natural processes involved in the petrogenesis of rocks. Additionally, with the current advances in the field of petrology, a large number of parameters can be explored. However, an increase in the number of parameters also raises the overall computational cost. Therefore, appropriate algorithms are needed to efficiently explore such high-dimensional parameter spaces. In this contribution, we demonstrate the use of Hamiltonian Monte Carlo for inverse diffusion modeling within a petrological framework. We begin by describing the theoretical background of the approach. We show that Hamiltonian Monte Carlo is a powerful tool to explore high-dimensional parameter spaces and therefore quantify the uncertainties of key parameters in petrological forward models. By using compositional garnet data and geochronological Ar-muscovite data from the Pindos metamorphic sole as an example, we invert for the initial cooling rate, initial equilibration temperature and the effective grain size of the investigated minerals. A key finding in our work is the strong agreement between inverse garnet diffusion modeling and Ar diffusion in muscovite, even though the two approaches are entirely independent. Our joint approach shows that an initial equilibration temperature of 637.6 ± 8.3 °C and an initial cooling rate of 241.3 ± 76.5 °C/Myr is required to explain not only previous thermobarometric and geochronological data but also the major-element zonation of garnets and the 40Ar/39Ar age of muscovite from the Pindos metamorphic sole. Moreover, our inversion showed that the effective grain size of muscovite plays a negligible role in fitting the observed 40Ar/39Ar age of the mineral. The calculated cooling rates and the preservation of high equilibration temperatures, garnet zonation and residual quartz-in-garnet pressures strongly support shear heating as the primary mechanism for the formation of the Pindos metamorphic sole.