Viscosity Formulations and the Effect of Uncertain Parameters

Abstract:

The development of detailed models of the interior of the Earth and other terrestrial planets is frequently hampered by poorly constrained compositional parameters, namely Activation Energy and Volume, which are necessary to define Arrhenius viscosity. This results in the values of said parameters varying considerably to suit the needs of individual investigations. A computational exploration of the effects of Activation Energy and Volume on the Earth's mantle was thus conducted, with a view to developing a robust and versatile method for obtaining a first-degree approximation for the parameter values, and providing some context for future studies.

A wide range of plausible mantle configurations was examined in both one and two dimensions, with the latter case utilising the modelling program ASPECT to generate a series of simple Earth-like planets which were allowed to evolve until a steady state was achieved. A comprehensive statistical analysis was then performed, allowing for suitable parameter values to be more effectively constrained for numerous given viscosity formulations. Activation Energy was seen to exhibit considerable influence over the bulk magnitude of viscosity values, while Activation Volume heavily impacted the viscosity contrast between the upper and lower mantle. This behaviour stems from the parameters controlling the temperature and pressure dependency of viscosity within the calculation. Results were found to be highly dependent on the minimum and maximum values imposed on the viscosity, reinforcing the need for a fuller understanding of the formulation.

A notable impact on stress profiles, and hence tectonic regime, was also observed. As such similar calculations were performed on directly scaled Super-Earths, with the intention of providing some insight into scenarios conducive to particular tectonic regimes in planets outside our solar system.