A computer-implemented method is provided for determining properties of a formation traversed by a well or wellbore. A formation model describing formation properties at an interval-of-interest within the well or wellbore is derived from measured sonic data, resistivity data, and density data for the interval-of-interest. The formation model is used as input to a plurality of petrophysical transforms and corresponding tool response simulators that derive simulated sonic data, resistivity data, and density data for the interval-of-interest. The measured sonic data, resistivity data, and density data for the interval-of-interest and the simulated sonic data, resistivity data, and density data for the interval-of-interest are used by an inversion process to refine the formation model and determine properties of the formation at the interval-of-interest. In embodiments, properties of the formation may be radial profiles for porosity, water saturation, gas or oil saturation, or pore aspect ratio.