An inverse modeling approach to obtain P–T conditions of metamorphic stages involving garnet growth and resorption

This contribution presents an approach and a computer program (GRTMOD) for numerical simulation of garnet evolution based on compositions of successive growth zones in natural samples. For each garnet growth stage, a new local effective bulk composition is optimized, allowing for resorption and/or fractionation of previously crystallized garnet. The successive minimizations are performed using the Nelder – Mead algorithm; a heuristic search method. An automated strategy including two optimization stages and one refinement stage is described and tested. This program is used to calculate pressure – temperature (P–T) conditions of crystal growth as archived in garnet from the Sesia Zone (Western Alps). The compositional variability of successive growth zones is characterized using standardized X-ray maps and the program XMapTools. The model suggests that Permian garnet cores crystallized under granulite-facies conditions at T>800°C and P = 6 kbar. During Alpine times, a first garnet rim grew at eclogite-facies conditions (650°C, 16 kbar) at the expense of the garnet core. A second rim was added at lower P (~1 kbar) and 630°C. In total, garnet resorption is modeled to amount to ~9 vol% during the Alpine evolution; this value is supported by our observations in X-ray compositional maps.