We present a new gravity inversion method, which produces an apparent density contrast mapping on the horizontal plane by combining the minimization of the first-order entropy with the maximization of the zero-order entropy of the estimated density contrasts. The interpretation model consists of a grid of vertical, juxtaposed prisms in both horizontal directions. The top and the bottom of the gravity sources are assumed to be flat and horizontal, and the parameters to be estimated are the prism density contrasts. The maximization of the zero-order entropy is similar to the global smoothness constraint whereas the minimization of the first-order entropy favors solutions presenting sharp borders, so a judicious combination of both constrains may lead to solutions characterized by regions where the estimated density contrasts are virtually constant (in the case of homogeneous bodies), separated by sharp discontinuities. The method has been applied to synthetic data simulating the presence of intrusive bodies in sediments. The comparison of the results with those obtained with the global smoothness constraint method shows that both methods produce good and equivalent locations of the source positions, but the entropic regularization delineates the contour of the bodies with greater resolution, even in the case of 100 m wide bodies separated by a distance as small as 50 m. In the case that the depth to the top of the causative sources is neither flat nor horizontal, both method produced similar results. Both the proposed and the global smoothness methods have been applied to two sets of real data produced by igneous intrusions into metamorphic rocks. The first one is from the Matsitama region, northeast of Botswana. The application of both methods to this data set lead to similar results, indicating that depth to the sources top is neither flat nor horizontal. The second set is from the Cornuália region, England. The results produced by both methods in this case are reasonably different, indicating that the gravity source present an approximately flat and horizontal top. This is confirmed by the available geological information.
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