A remote, deterministic method for estimating at least lithology class of a subsurface region, comprising: obtaining at least one type of remote geophysical survey data representing the subsurface region; identifying a plurality of possible lithology classes, each class being associated with a value of a discrete lithology parameter, and each class being defined by one or more deterministic rock physics equations; developing a model of the subsurface region in terms of at least lithology class, wherein the model subdivides the subsurface region into discrete cells in which lithology class is represented as a value of the discrete lithology parameter, including at least one geological parameter or geophysical parameter in the model, the at least one geological parameter or geophysical parameter having continuous values, the at least one geological parameter being a parameter which directly describes the rock; and using a computer to invert the at least one type of remote geophysical survey data to obtain lithology class and the at least one geological parameter or geophysical parameter of the subsurface region, wherein the inversion is constrained by the one or more deterministic rock physics equations; wherein the inversion finds a best-fitting value of the discrete lithology parameter and of the at least one geological parameter or geophysical parameter for each cell in the model to determine at least lithology class. obtaining at least one type of remote geophysical survey data representing the subsurface region; identifying a plurality of possible lithology classes, each class being associated with a value of a discrete lithology parameter, and each class being defined by one or more deterministic rock physics equations; developing a model of the subsurface region in terms of at least lithology class, wherein the model subdivides the subsurface region into discrete cells in which lithology class is represented as a value of the discrete lithology parameter, including at least one geological parameter or geophysical parameter in the model, the at least one geological parameter or geophysical parameter having continuous values, the at least one geological parameter being a parameter which directly describes the rock; and using a computer to invert the at least one type of remote geophysical survey data to obtain lithology class and the at least one geological parameter or geophysical parameter of the subsurface region, wherein the inversion is constrained by the one or more deterministic rock physics equations; identifying a plurality of possible lithology classes, each class being associated with a value of a discrete lithology parameter, and each class being defined by one or more deterministic rock physics equations; developing a model of the subsurface region in terms of at least lithology class, wherein the model subdivides the subsurface region into discrete cells in which lithology class is represented as a value of the discrete lithology parameter, including at least one geological parameter or geophysical parameter in the model, the at least one geological parameter or geophysical parameter having continuous values, the at least one geological parameter being a parameter which directly describes the rock; and using a computer to invert the at least one type of remote geophysical survey data to obtain lithology class and the at least one geological parameter or geophysical parameter of the subsurface region, wherein the inversion is constrained by the one or more deterministic rock physics equations; wherein the inversion finds a best-fitting value of the discrete lithology parameter and of the at least one geological parameter or geophysical parameter for each cell in the model to determine at least lithology class.