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Abstract

We propose a new method of petrologic modeling allowing equilibrium mineral compositions, densities, and elastic properties of rocks to be calculated from their bulk chemical compositions and pressure-temperature (P-T equilibrium conditions. To calculate the mineral composition of a rock, the method of direct minimization of the Gibbs free energy is used applying to the eight-component (SiO2 - Al2O3 - Fe2O3 - FeO - MgO - CaO - Na2O - K2O) multiphase closed thermodynamic system. The density of rock, the isotropic VP, VS, and their P-T derivatives are computed on the actual mineral compositions, with the use of available experimental data on elastic moduli of minerals. Good accuracy of the computations is supported by comparison with experiments on the phase transitions gabbro/eclogite in rocks and with high-precision laboratory measurements of elastic wave velocities in samples of magmatic and metamorphic rocks. The calculated phase diagrams are given together with isolines of density, elastic wave velocities, and their pressure and temperature derivatives for some abundant anhydrous magmatic rocks ranging from granite to lherzolite. The density and elastic wave velocities noticeably increase with formation pressure of rock due to proceeding several mineral reactions resulting in the appearance and growth of garnet and disappearance of plagioclase. Character of the pressure dependence of VP and VS is determined by the bulk chemical composition of rock and can essentially be nonlinear. Rocks of different bulk compositions are well-distinguished on the plots of VP - VP/VS density. Such diagrams together with phase diagrams can be employed as efficient means for petrological interpretation of seismic data.