The invention is a method for determining a parameter of interest of a region of interest of the earth using tensor data. At least one component of potential fields data 401 is measured at a plurality of locations over a region of interest including a subterranean formation of interest. The potential fields data are selected 405 from magnetic data and gravity data. An initial geophysical model 403 is determined for the region including the subterranean formation of interest. For the model, geophysical tensor data is updated using a forward model 410 at a plurality of locations using an interior method for constrained optimization. A difference between the estimated model value and the measured value of the potential field measurements are determined 405 at the plurality of locations. Based on the this difference the geophysical model is updated 409. The model is iteratively updated and compared to the measured data until the differences reach an acceptable level and the parameter of interest has been determined 411.
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