Implementation of a Markov-Chain Monte Carlo algorithm for high temperature thermal history inversion using the Fast Grain Boundary model

Guillaume Siron – Chrono-Environnement

Lundi 3 Février 2025 à 15h30
Chrono-environnement – salle -107M

Retrieving time-temperature (t-T) histories of metamorphic rocks is vital to understanding the geodynamics of orogens and subduction zones. While many thermochronological systems have been developed for low to medium temperatures (< 400 °C), retrieving t-T histories at higher temperature remains complicated.
Here I will discuss the development of a Markov chain Monte Carlo (MCMC) algorithm for inversion of the Fast Grain Boundary model[1], which couples equilibrium fractionation of oxygen isotopes between minerals and intragrain oxygen isotope diffusion within minerals. The first implementation of MCMC convergence algorithm used a Metropolis-Hastings sampler that randomly selects a point in the t-T history and then randomly modifies that temperature using a normal distribution centered on 0 with a standard deviation of 1, multiplied by a scale factor. A prior is set to minimize the difference between adjacent t-T points in order to minimize large variations that are unrealistic. The number of iterations has been set to 2000 with 1000 iterations for the burn-in. The scale factor has been set to 50. These hyper-parameters were selected by testing the MCMC algorithm for synthetic data, either computed from a linear cooling t-T history or a linear cooling t-T history with a superimposed heating spike. The starting profile with the greatest deviation from the actual cooling history converged after >600 iterations, necessitating the burn-in of 1000 iterations.
The model successfully reproduces linear t-T histories and identifies the presence of a heating spike, though not always at the correct temporal location of the spike, especially for starting profiles far from the actual t-T history. Therefore, a transdimensional (or reversible jump) MCMC was attempted to resolved non-linear cooling histories. This second implementation allows more transitions between models, with the possibility of removing and adding t-T points, as well as moving the time location of a pre-existing point.
This model is currently under development and still requires more fine-tuning of the hyper-parameters to assess whether it truly improves the accuracy of t-T history inversion using the FGB model, but its current status will be discussed during the seminar together with perspectives for future development.

[1] Kropf, Bonamici, Borchers (2021) Computers & Geosciences 151, 104753.