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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