结构方向参数的鲁棒估计和二维/三维局部各向异性提霍诺夫正则化

Ali Gholami, Silvia Gazzola
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引用次数: 0

摘要

了解地质结构的走向对于分析地球地下的复杂性至关重要。例如,地质结构方位信息可被纳入局部各向异性正则化方法,作为稳定逆问题求解并产生地质可信解的重要工具。我们介绍了一种新的变分方法,该方法在交替最小化方案中采用了交替方向乘数法,以联合估计二维和三维反演问题中的方向和模型参数。论文还讨论了算法参数的自动调整,以最大限度地提高新方法的性能。对所提出的算法进行了各种二维和三维实例测试,包括面向结构的去噪和轨迹插值。结果表明,该算法能稳健地解决所考虑的大型挑战性问题,在二维情况下能有效估计相关的倾斜场,在三维情况下能有效估计倾角、走向和倾斜场。合成和野外实例表明,所提出的各向异性正则化方法生成的模型具有更高的分辨率,并能更准确地反映真实结构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Robust Estimation of Structural Orientation Parameters and 2D/3D Local Anisotropic Tikhonov Regularization
Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic regularization methods as a valuable tool to stabilize the solution of inverse problems and produce geologically plausible solutions. We introduce a new variational method that employs the alternating direction method of multipliers within an alternating minimization scheme to jointly estimate orientation and model parameters in both 2D and 3D inverse problems. Specifically, the proposed approach adaptively integrates recovered information about structural orientation, enhancing the effectiveness of anisotropic Tikhonov regularization in recovering geophysical parameters. The paper also discusses the automatic tuning of algorithmic parameters to maximize the new method's performance. The proposed algorithm is tested across diverse 2D and 3D examples, including structure-oriented denoising and trace interpolation. The results show that the algorithm is robust in solving the considered large and challenging problems, alongside efficiently estimating the associated tilt field in 2D cases and the dip, strike, and tilt fields in 3D cases. Synthetic and field examples show that the proposed anisotropic regularization method produces a model with enhanced resolution and provides a more accurate representation of the true structures.
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