在磁倾斜导数和梯度强度数据处理中应用正则化导数的Python程序:选择正则化参数的图形程序

IF 2.6 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Janaína Anjos Melo, Carlos Alberto Mendonça, Yara Regina Marangoni
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引用次数: 0

摘要

Tikhonov正则化参数是控制正则化未知解的平滑度和振荡的关键参数。通常确定适当参数的方法(例如l -曲线或差异原理)并不容易适用于正则化导数的求值,因为该公式没有明确说明实现这些方法所必需的一组模型参数。我们开发了一种确定正则化参数的程序,该程序基于与一组试验正则化参数的正则化导数的l2范数相关联的特征“阶梯”函数的图形构造。该函数与模型参数无关,呈平滑单调变化。“阶梯”函数的上一阶的正则化参数(低值)提供了与非正则化导数等效的结果,下一阶的参数(高值)导致了过度平滑的导数。对于评估的数据集,适当的正则化参数位于连接楼梯曲线的两个平坦端部的斜率上,从而平衡了变换场中的噪声放大和幅度损失。给出了一组Python程序来评估由多个(大块和细长)磁源组成的著名综合模型中的正则化过程。该数值方法还应用于巴西中部Tocantins省Brasília褶皱带中部Anápolis-Itauçu杂岩的网格化航磁数据,该杂岩具有多个不同方向和交汇的磁线,与剪切带、地质断层和侵入体有关。正则化处理的结果表明,该方法可以有效地改进滤波后的磁场图,更好地跟踪磁线的连续性和一般地质趋势。在Brasília褶皱带的应用结果增强了高应变皮里内斯带的重要性和更广泛的覆盖范围。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Python programs to apply regularized derivatives in the magnetic tilt derivative and gradient intensity data processing: A graphical procedure to choose the regularization parameter

The Tikhonov regularization parameter is a key parameter controlling the smoothness degree and oscillations of a regularized unknown solution. Usual methods to determine a proper parameter (L-curve or the discrepancy principle, for example) are not readily applicable to the evaluation of regularized derivatives, since this formulation does not make explicit a set of model parameters that are necessary to implement these methods. We develop a procedure for the determination of the regularization parameter based on the graphical construction of a characteristic “staircase” function associated with the L2-norm of the regularized derivatives for a set of trial regularization parameters. This function is independent of model parameters and presents a smooth and monotonic variation. The regularization parameters at the upper step (low values) of the ''staircase'' function provide equivalent results to the non-regularized derivative, the parameters at the lower step (high values) leading to over-smoothed derivatives. For the evaluated data sets, the proper regularization parameter is located in the slope connecting these two flat end-members of the staircase curve, thus balancing noise amplification against the amplitude loss in the transformed fields. A set of Python programs are presented to evaluate the regularization procedure in a well-known synthetic model composed of multiple (bulk and elongated) magnetic sources. This numerical approach also is applied in gridded aeromagnetic data covering high-grade metamorphic terrains of the Anápolis-Itauçu Complex in the Brasília Fold Belt central portion of Tocantins Province, central Brazil, characterized by multiple magnetic lineaments with different directions and intersections which are associated with shear zones, geologic faults, and intrusive bodies. The results obtained from the regularization procedure show efficiency in improving the maps of filtered fields, better tracking the continuity of magnetic lineaments and general geological trends. The results from the application in the Brasília Fold Belt enhance the importance and broader coverage of the Pirineus Zone of High Strain.

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来源期刊
Applied Computing and Geosciences
Applied Computing and Geosciences Computer Science-General Computer Science
CiteScore
5.50
自引率
0.00%
发文量
23
审稿时长
5 weeks
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