Títol de la Tesi: Numerical techniques for the solution of thermal problems in the context of geophysical inversions
Directors:: Dr. Pedro Díez / Dr. Sergio Zlotnik
Programa de doctorat en Enginyeria Civil
The thermal structure of the Earth’s interior contains key information for the understanding of geodynamic processes, including plate tectonics, mantle convection, and the Earth’s overall thermal evolution. In particular, it is relevant to describe the geometry of the Lithosphere-Asthenosphere Boundary (LAB), separating the rigid Lithosphere from the ductile Asthenosphere. Accurately characterising this interface is key for the understanding of the thermal and mechanical structure of the Earth.
Most models used in practice involve a formulation that is not physically sound, at least, in some part of the domain. These models involve smearing out regions or empirical estimations that do not fulfil the energy equilibrium equations. These estimates are useful in practice, but a formulation that respects physical principles would be preferable.
This thesis focuses on developing forward solvers that allow for the computation of physically sound temperature fields within an inversion problem. The structure of the forward problem is altered by imposing the location of the LAB on the interior of the domain. The mathematical statement of this problem is presented in two versions and numerical methods to obtain solutions are developed and tested. The first solver enforces the isotherm condition by splitting the domain into Lithosphere and Asthenosphere, such that the LAB is a boundary to both, and explicitly adds equations to impose the condition. The second solver finds a mantle velocity field that enforces the isotherm condition indirectly. While the first solver needs to restore flux continuity by adding conditions, the second needs a velocity field that complies with the isotherm condition, both providing valuable information to improve geophysical understanding.
The methodologies are tested across different scenarios and LAB geometries, using synthetic and non-synthetic temperatures to assess their performance in geophysical inversions. Results demonstrate that the domain-splitting solver reliably and efficiently recovers the LAB geometry, making it suitable for large-scale applications. The second solver, although computationally expensive and sensitive to parameter choices, also constitutes a robust solver.
This thesis contributes to advance in the geophysics field by providing robust tools for thermal modelling. The tools have the potential to improve our understanding by solving partial differential equations providing insights into the thermal and mechanical properties of the Earth.