{"title":"Robust Estimation of Structural Orientation Parameters and 2D/3D Local Anisotropic Tikhonov Regularization","authors":"Ali Gholami, Silvia Gazzola","doi":"arxiv-2409.05754","DOIUrl":null,"url":null,"abstract":"Understanding the orientation of geological structures is crucial for\nanalyzing the complexity of the Earths' subsurface. For instance, information\nabout geological structure orientation can be incorporated into local\nanisotropic regularization methods as a valuable tool to stabilize the solution\nof inverse problems and produce geologically plausible solutions. We introduce\na new variational method that employs the alternating direction method of\nmultipliers within an alternating minimization scheme to jointly estimate\norientation and model parameters in both 2D and 3D inverse problems.\nSpecifically, the proposed approach adaptively integrates recovered information\nabout structural orientation, enhancing the effectiveness of anisotropic\nTikhonov regularization in recovering geophysical parameters. The paper also\ndiscusses the automatic tuning of algorithmic parameters to maximize the new\nmethod's performance. The proposed algorithm is tested across diverse 2D and 3D\nexamples, including structure-oriented denoising and trace interpolation. The\nresults show that the algorithm is robust in solving the considered large and\nchallenging problems, alongside efficiently estimating the associated tilt\nfield in 2D cases and the dip, strike, and tilt fields in 3D cases. Synthetic\nand field examples show that the proposed anisotropic regularization method\nproduces a model with enhanced resolution and provides a more accurate\nrepresentation of the true structures.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Geophysics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05754","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.