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 (∼11 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.