Inverting geophysical data for geological parameters or lithology

A remote, deterministic method for estimating at least lithology of a subsurface region, comprising:

• obtaining at least one type of remote geophysical survey data representing the sub surface region;
• identifying a plurality of possible lithology classes, each class being associated with a value of the discrete valued model 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, porosity, and water saturation, wherein the model subdivides the subsurface region into discrete cells in which the lithology is represented as a value of the discrete valued model parameter;
• using a computer to perform an inversion that inverts the at least one type of remote geophysical survey data to obtain at least the lithology, the porosity, and the water saturation of the subsurface region with the one or more deterministic rock physics equations that provide a mapping between the at least one type of remote geophysical survey data and the lithology, the porosity, and the water saturation of the subsurface region,
• wherein the inversion finds a best-fitting value of the lithology, the porosity, and the water saturation for each cell in the model by minimizing a misfit between the at least one type of remote geophysical survey data and simulated data generated by the computer from the model of the subsurface region;
• and
• drilling a well into the subsurface region based at least partly on the lithology, the porosity and the water saturation determined from the inversion.