A new method estimates the dependence of P and S velocities in rocks on elastic properties of the pore-filling material by going beyond Gassmann's relations and accounting for pore-filling materials with nonzero shear stiffness. The resulting estimates are in good agreement with experimental data and Gassmann's relations for values of velocity in water-saturated rocks predicted from velocity measured on dry rocks. The method successfully predicts the temperature dependence of velocity: (1) in frozen rocks at the ice-water phase transition, and (2) in rocks saturated with heavy hydrocarbon undergoing solid-liquid phase transition.

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