The technological improvement has provided the acquisition of a large volume of geophysical data, which is why the work of interpretation of gravity anomalies and pet relief sedimentary basins increasingly demand innovation in computational and mathematical formulation that allows for such offer. In order to obtain effective and computationally efficient solutions propose two new methods that incorporate linear inversion procedure for the solution of a nonlinear inversion problem. The first proposed method approximates the solution of the nonlinear inversion by linear inversion procedures and applies corrections in iterations from the initial approach, obeyed until the convergence criterion. The second method proposed solution approximates the nonlinear inversion of the linear inversion procedures only on the first iteration, the second iteration from the additional iterations are applied for correction. The investments made in the two new methods and nonlinear inversion, are stabilized by Tikhonov regularization functional first order (smoothness). The observations are modeled by a set of 3D vertical rectangular prisms whose thicknesses are parameters that define discreetly relief estimated at some points. The realization of nonlinear inversion procedure was necessary to validate the estimated basement relief of sedimentary basins produced by the new proposed methods, this validation is given by comparing the results obtained by the procedures of linear inversion with the inversion of nonlinear . We also evaluate the efficiency and effectiveness of the proposed methods and nonlinear inversion from synthetic tests. The proposed methods have proved more efficient than the nonlinear inversion method, since reduced computational time required to recover virtually identical reliefs. As regards efficiency, we conclude that the proposed methods are as effective as the non-linear inversion, since the estimates of the basement relief scale and are equivalent to each other in shape.
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