The application of multidimensional wavelets to unveiling multi-phase diagrams and in situ physical properties of rocks

Calculation of phase diagrams for terrestrial and planetary materials exerts a growing impact in geosciences today. In this work, we demonstrate the feasibility of efficient delineation and visualization of complicated realistic multi-phase diagrams and related in situ physical properties of rocks by using discontinuous second generation wavelets, allowing a representation of both isotropic and anisotropic properties with arbitrary resolution. This is done by combining adaptive wavelet-based meshing technology with recently developed efficient “phase diagram function” designed as a Gibbs free energy minimization. The proposed automated strategy allows one to obtain an efficient delineation of physical properties using a uniform set of wavelet nodes regardless of whether these variables are continuous or discontinuous functions of pressure, temperature, or composition. The use of this strategy captures very small details of phase diagram morphology allowing both acceleration of the calculations and compression of results on the order of 102 by comparison to uniform grids of the same effective resolution. The web-based application of the proposed methodology for phase diagram visualization with interactive zooming capabilities is also discussed.