Methods and systems are provided characterizing a formation traversed by a wellbore, wherein the formation includes at least a flushed zone and an uninvaded zone, which involve obtaining well log data based on plurality of different well log measurements of the formation at multiple depths in the wellbore. The well log data is used to a computational model that solves for a set of petrophysical parameters that characterize a portion of the formation corresponding to the multiple depths in the wellbore, wherein the set of petrophysical parameters include a cementation exponent, a saturation exponent, and a flushed zone water resistivity. The solved-for set of petrophysical parameters can be used to determine a value of water saturation of the uninvaded zone for the portion of the formation corresponding to the multiple depths in the wellbore.