Two-dimensional numerical modeling of pressure-temperature-time paths for the exhumation of some granulite facies terrains in the Precambrian

Pressure (P)-temperature (T) paths accurately record movement of metamorphic rocks within the Earthʹs crust. 1D geodynamic modeling of P-T-time paths of regional metamorphism have explained many important features of the P-T evolution of metamorphic rocks. Further progress may be achieved using 2D numerical geodynamic modeling. Different types of P-T paths obtained for some granulites allow their 2D numerical modeling in terms of a theory of gravitational redistribution of material within the Earthʹs crust. This modeling was done using the finite differences method for a Newtonian incompressible fluid. The P-T paths obtained geothermobarometrically for metapelites from the Limpopo granulite complex were compared with the P-T-time paths calculated numerically by monitoring the movement of different `samplesʹ in the thermal and gravitational field. The results of this monitoring support a hypothesis of isobaric cooling of granulites during the thermal interaction between rising hot granulites and sinking cool cratonic rocks. Effective viscosities of the rocks were gradually adjusted during the modeling by using the shape of the P-T paths. The calculated average viscosity of 1019 Pa s for the granulites, supports an idea that the lower crust is a weak layer between upper crust (1021 Pa s) and the Upper Mantle. The average rate of exhumation of granulites during the gravitational redistribution process is estimated at about 2.5 mm per year. This suggests exhumation of granulites from depths of about 30 km during approximately 10 Myr. The results of numerical modeling successfully explain the presence of two types of P-T paths observed in metapelites of the Limpopo granulite complex emplaced between the >3 Ga Kaapvaal and Zimbabwe cratons at ~2.65 Ga.