Parâmetros de regularização de operadores diferenciais no processamento de dados aeromagnéticos

Abstract

The evaluation of numerical derivatives is an essential tool in magnetic data processing, aiming to map structural lineaments and estimate the depth of the respective anomalous sources in the subsurface. Generally, directional derivatives are obtained through numerical methods based on the calculation of the Fourier transform, susceptible to noise amplification due to numerical instability. One way to improve stability in differentiation is to apply Tikhonov regularization to balance the oscillatory characteristics of the derivatives with the smoothing degree associated with the particular regularization parameter choice. This work proposes a graphical procedure to estimate regularization parameters for different potential field transformations that require first or second-order derivatives. This tool is based on normalizing the L 2 -norm of the respective transformed fields to a trial regularization parameters sequence, resulting in a characteristic function with a staircase format. This function has smooth and monotonic behavior, decreasing from 1 to 0 for increasing regularization values, in which the upper step (1) of the function is associated with non-regularized and sub-regularized transformations and the lower step (0) corresponds to over-regularized transformations. Synthetic tests simulating models with different noise levels or anomaly complexities illustrated that the well-suited regularization parameter selection for transformed fields depends on analyzing the distortions in the maps. Euler deconvolution processing applied to synthetic models showed that the appropriate regularization parameter choice is associated with the ascertaining of erroneous (overestimated) depth inferences. The applicability of the regularization procedure is evaluated on gridded aeromagnetic data covering two study areas in the Tocantins Province, central Brazil. In Area-I, covering the Anápolis-Itauçu Complex, transformations using first-order derivatives regularized with the intermediate ramp criterion were efficient in better mapping the continuity of magnetic lineaments with different directions and intersections, associated with shear zones, geological faults, and intrusive bodies. Applications in Area-II covering the Transbrasiliano tectonic corridor revealed the need for a low-dose regularization to obtain depth estimates consistent with the depths of the underlying basement of the Bananal Basin, according to available information from seismic lines and gravity models.Regularization tuned to the intermediate ramp criterion was sufficient for transformations with first-order derivatives to map the complex pattern of multiple linear structures. The results in Area-II showed that transformations based on second-order derivatives require a high degree of regularization to detect the contributions from subtle structural features.