Modeling of mineralogical composition,density and elastic wave velocities in anhydrous magmatic rocks

We use the technique of direct minimization of the Gibbs free energy of the 8-component (K₂O-Na₂O-Fe₂O₃-FeO-CaO-MgO-Al₂O₃-SiO₂) multiphase system in order to determine the equilibrium mineral assemblages of rocks of different bulk chemical compositions equilibrated at various P-T conditions. The calculated modal compositions of rocks and experimental data on elastic moduli of single crystals are then used to calculate densities and isotropic elastic wave velocities of rocks together with their pressure and temperature derivatives. Sufficient accuracy of the calculations is confirmed by comparison with experimental data on the gabbro-eclogite transformation and precise ultrasonic measurements of elastic wave velocities in a number of magmatic and metamorphic rocks.We present calculated phase diagrams with isolines of density, elastic wave velocities, and their pressure and temperature derivatives for several anhydrous magmatic rocks, from granite to lherzolite. Density and elastic properties of rocks are controlled by their chemical compositions, especially the SiO₂ content, and by P-T of equilibration, and they increase with pressure due to mineral reactions changing mineral assemblages from plagioclase-bearing and garnet-free to garnetbearing and plagioclase-free. TheV_p-density correlation is high, and shows two clear trends: one for iron-poor ultramafic rocks and another for all the other rocks considered. Mineral reactions, which occur at high pressures, changeV_p and density of anhydrous magmatic rocks following the well-known Birch (or a similar) law.Felsic, intermediate and mafic rocks can be well distinguished in theV_p-V_p/V_s- diagram, although their values ofV_p can be close to one another. TheV_p-V_p/V_s-density diagrams together with calculated phase diagrams can serve as efficient instruments for petrologic interpretation of seismic velocities.