This paper aims to provide a method for obtaining physically sound temperature fields to be used in geophysical inversions in the presence of immersed essential conditions.
The method produces a thermal field in agreement with a given location of the interface between the Lithosphere and Asthenosphere. It leverages the known location of the interface to enforce the location of a given isotherm while relaxing other constraints known with less precision. The method splits the domain: in the Lithosphere the solution is immediately obtained by standard procedures, while in the Asthenosphere a minimization problem is solved to fulfill continuity of temperatures (strongly imposed) and fluxes at the interface (weakly imposed).
The numerical methodology, based on the relaxation of the bottom fluxes, correctly recovers the thermal field in the complete domain. To obtain bottom fluxes following geophysical expected values, a constrained minimization strategy is required. The sensitivity of the method could be improved by relaxing other quantities such as lateral fluxes or mantle velocities.
A statement of the energy balance problem in terms of a known immersed condition is presented. A novel numerical procedure based on a domain-splitting strategy allows the solution of the problem. The procedure is tailored to be used within geophysical inversions and provides physically sound solutions.
