Cristiano M. Martins

Simultaneous 3D depth-to-basement and density-contrast estimates using gravity data and depth control at few points

We have developed a gravity-inversion method for simultaneouslyestimatingthe3Dbasementreliefofasedimentary basin and the parameters defining a presumed parabolic decay of the density contrast with depth in a sedimentary pack, assumingpriorknowledgeaboutthebasementdepthatafew points.Thesedimentarypackisapproximatedbyagridof3D vertical prisms juxtaposed in both horizontal directions of a right-handed coordinate system. The prisms’ thicknesses representthedepthstothebasementandaretheparametersto be estimated from the gravity data. To estimate the parameters defining the parabolic decay of the density contrast with depthandtoproducestabledepth-to-basementestimates,we imposed smoothness on the basement depths and proximity between estimated and known depths at boreholes. We applied our method to synthetic data from a simulated complex 3D basement relief with two sedimentary sections having distinct parabolic laws describing the density-contrast variationwithdepth.Theresultsprovidegoodestimatesofthetrue parameters of the parabolic law of density-contrast decay with depth and of the basement relief. Inverting the gravity data from the onshore and part of the shallow offshore AlmadaBasinonBrazil’snortheasterncoastshowsgoodcorrelationwithknownstructuralfeatures.

Total variation regularization for depth-to-basement estimate: Part 2 — Physicogeologic meaning and comparisons with previous inversion methods

We applied the mathematical basis of the total variation (TV) regularization to analyze the physicogeologic meaning of the TV method and compared it with previous gravity inversion methods (weighted smoothness and entropic Regularization) to estimate discontinuous basements. In the second part, we analyze the physicogeologic meaning of the TV method and compare it with previous gravity inversion methods (weighted smoothness and entropic regularization) to estimate discontinuous basements. Presenting a mathematical review of these methods, we show that minimizing the TV stabilizing function favors discontinuous solutions because a smooth solution, to honor the data, must oscillate, and the presence of these oscillations increases the value of the TV stabilizing function. These three methods are applied to synthetic data produced by a simulated 2D graben bordered by step faults. TV regularization and weighted smoothness are also applied to the real anomaly of Steptoe Valley, Nevada, U.S.A. In all applications, the three methods perform similarly. TV regularization, however, has the advantage, compared with weighted smoothness, of requiring no a priori information about the maximum depth of the basin. As compared with entropic regularization, TV regularization is much simpler to use because it requires, in general, the tuning of just one regularization parameter.

Total‐variation regularization for depth‐to‐basement estimate

We present an inversion approach that estimates the basement relief of a fault-bounded sedimentary basin. We parameterize the Earth’s subsurface, containing the sedimentary pack, into prismatic cells, with known horizontal dimensions and known density contrast, and estimate their thicknesses, which represent the depths to the basement. To obtain depth-to-basement estimates we use the total-variation regularization as a stabilizing function that allows the estimation of a faulting basement relief. Tests on synthetic and on field data from Almada Basin, Brazil, and from Steptoe Valley, Nevada, confirmed the potential of our method in detecting and locating normal faults in the basement relief of a sedimentary basin.