A reduced basis approach for implementing thermodynamic phase-equilibria information in geophysical and geodynamic studies

Abstract:

We present a flexible, general and efficient approach for implementing thermodynamic phase equilibria information (in the form of sets of physical parameters) into geophysical and geodynamic studies.
The approach is based on multi-dimensional decomposition methods, which transform the original multi-dimensional discrete information into a dimensional-separated representation. This representation has the property of increasing the number of coefficients to be stored linearly with the number of dimensions (opposite to a full multi-dimensional cube requiring exponential storage depending on the number of dimensions). Thus, the amount of information to be stored in memory during a numerical simulation or geophysical inversion is drastically reduced. Accordingly, the amount and resolution of the thermodynamic information that can be used in a simulation or inversion increases substantially.
In addition, the method is independent of the actual software used to obtain the primary thermodynamic information, and therefore it can be used in conjunction with any thermodynamic modeling program and/or database. Also, the errors associated with the decomposition procedure are readily controlled by the user, depending on her/his actual needs (e.g. preliminary runs vs full resolution runs). We illustrate the benefits, generality and applicability of our approach with several examples of practical interest for both geodynamic modeling and geophysical inversion/modeling. Our results demonstrate that the proposed method is a competitive and attractive candidate for implementing thermodynamic constraints into a broad range of geophysical and geodynamic studies.