A method for predicting lithologic properties and porosity of a subsurface formation from seismic data, acquired over said subsurface formation, comprising: (a) inverting the seismic data to obtain one or more bulk elastic properties of the subsurface formation; (b) constructing a rock physics model of the subterranean formation, said model relating the lithologic properties, porosity and fluid content to the bulk elastic properties of the formation rock, said model comprising the following two features: (i) compliances and densities of sand and clay mineral fractions of the rock are characterized independently with separate pore spaces, different pore aspect ratios, and potentially different fluid types, and (ii) effective bulk and shear elastic moduli are computed using a combination of differential effective medium theory and Gassman fluid substitution; (c) building a fluid fill model indicating the type of fluid present at each location in the subsurface; (d) computing in tabular form values of said one or more elastic properties as predicted by the rock physics model for a range of possible values for said porosity and lithology properties in each fluid type present in the model and then numerically computing corresponding tables of the derivatives of the elastic properties with respect to porosity and clay content; and (e) using the computed tables of the elastic properties and their derivatives, along with the fluid type information to minimize a pre-selected objective function and thereby invert the rock physics model to obtain the lithologic properties and the porosity from the bulk elastic properties and fluid content information for the formation. (a) inverting the seismic data to obtain one or more bulk elastic properties of the subsurface formation; (b) constructing a rock physics model of the subterranean formation, said model relating the lithologic properties, porosity and fluid content to the bulk elastic properties of the formation rock, said model comprising the following two features: (i) compliances and densities of sand and clay mineral fractions of the rock are characterized independently with separate pore spaces, different pore aspect ratios, and potentially different fluid types, and (ii) effective bulk and shear elastic moduli are computed using a combination of differential effective medium theory and Gassman fluid substitution; (c) building a fluid fill model indicating the type of fluid present at each location in the subsurface; (d) computing in tabular form values of said one or more elastic properties as predicted by the rock physics model for a range of possible values for said porosity and lithology properties in each fluid type present in the model and then numerically computing corresponding tables of the derivatives of the elastic properties with respect to porosity and clay content; and (e) using the computed tables of the elastic properties and their derivatives, along with the fluid type information to minimize a pre-selected objective function and thereby invert the rock physics model to obtain the lithologic properties and the porosity from the bulk elastic properties and fluid content information for the formation.