We present a gravity inversion method to reconstruct the discontinuous basement relief of a
sedimentary basin, whose density contrast between the basement and the sediments is constant, or
decreases monotonically with depth, and known. The solution is stabilized using the total variation
functional (VT), which does not impose smoothness on the solution. We compare the proposed
method with the global smoothness (SG), weighted smoothness (SP) and entropic regularization
(RE) methods using synthetic data produced by 2D and 3D basins presenting discontinuous relief.
The solutions obtained with the proposed method were better than those obtained with SG and
similar to the ones produced by SP and RE. Differently from SP, however, the proposed method
does not require a priori knowledge about the basin maximum depth. As compared with RE, the
present method is operationally simpler and requires the specification of just one regularization
parameter. The VT, SG, and SP methods were also applied to the following areas: Ponte do Poema
(UFPA), Steptoe Valley (Nevada, United States), San Jacinto Graben (California, United States)
and Büyük Menderes (Turkey). Almost all those areas are characterized by the presence of highangle
faults. In all cases, the VT produced basement relief estimates presenting sharp, high-angle
discontinuities, in accordance with the tectonic setting of the areas.
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