We present a new gravity inversion method, which estimates the basement relief of a sedimentary basin, whose sediments may present a constant or a decreasing density contrast with depth
relative to the basement. The method combines the minimization of the first-order entropy
measure with the maximization of the zeroth-order entropy measure of the solution vector (depths
to the basement). The interpretation model consists of a set of rectangular juxtaposed vertical
prisms with known density contrasts and whose thicknesses represent the depths to the basement
relief and are the parameters to be estimated. The minimization of the first-order entropy favors
solutions presenting abrupt discontinuities, and the maximization of the zeroth-order entropy is
employed just to prevent its excessive minimization. We applied our method to synthetic data
simulating: (i) intracratonic basins with smooth or discontinuous relief, and (ii) faulted marginal
basins. In the case of a smooth basement relief, it was well delineated by the entropic
regularization, and by the global and weighted smoothness. In the case of a faulted basement,
either in intracratonic or marginal basins, the entropic regularization and the weighted
smoothness delineated the basement relief with good precision, differently from the global
smoothness. The entropic regularization, however, did not require the knowledge of the basin’s
maximum depth. We applied our method to four sets of real Bouguer anomalies. The first one
comes from a profile across a bridge located in the campus of the Federal University of Pará,
Belém. The solution delineated the known, discontinuous topography below the bridge. The
second set comes from the northern portion of Steptoe Valley, Nevada. The solution delineated a
discontinuous basement relief in accordance with the known geological setting of the area. The
third set comes from the San Jacinto graben, situated in California, United States. The solution
indicated an asymmetric graben, as already reported by other authors. The fourth data set comes
from the Büyük Menderes graben, western Turkey. The solutions presented large vertical
displacements on the northern border, which is confirmed by geological information.
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