Fully coupled petrological/thermo-mechanical models of magmatic systems

Simulating the chemical evolution of magmatic systems can be done with thermodynamic equilibrium modelling and recently developed melting models do quite a good job of predicting observations and reproducing experiments for a wide range of compositions. Yet, it remains a significant computational challenge as some of the most recent melting models include 11 oxides along with pressure and temperature, which makes this a 13-dimensional Gibbs energy optimisation problem. We recently developed the open-source parallel software package MAGEMin [1], along with an easy-to-use Julia interface (MAGEMin_C.jl [2]). Over the last year, we also developed a web-based graphical user interface, MAGEMinApp [3], with which users can easily compute pseudo-sections, do fractional crystallization experiments, or predict seismic velocities.

However, despite the progress, each point-wise thermodynamic calculation still takes 10-50 milliseconds (depending on the complexity of the system). This is too slow if one wishes to directly couple thermodynamic and thermo-mechanical simulations of the magmatic system, as those may require 1000’s-100’000s of calculations per timestep.

An alternative approach is to develop simplified parameterizations from the complete thermodynamic models (e.g., using machine learning tools). That, however, requires recalibration for different scenarios, and gives up some of the predictive power of the models, such as the chemistry of the stable mineral assemblage or seismic velocities, unless the system was trained on that.

We therefore developed a new approach in which we dynamically update a database of precomputed points that only performs new thermodynamic calculations for points that do not yet exist in the database. We only store the minimum required information per point, with which we can reconstruct all derived thermodynamic quantities without having to redo the minimization. This significantly reduces the computational effort and allows coupling thermodynamic simulations with thermo-mechanical simulations in a self-consistent manner.  We illustrate the power of the method with 2D/3D thermo-kinematic simulations of magmatic systems, as well as by reactive two-phase flow calculations applied to small-scale magma transfer processes in lower crustal migmatites.

[1] https://github.com/ComputationalThermodynamics/MAGEMin

[2] https://github.com/ComputationalThermodynamics/MAGEMin_C.jl

[3] https://github.com/ComputationalThermodynamics/MAGEMinApp.jl