Adaptive reweighted Tikhonov inversion of gravity-gradient data for salt-boundary imaging.

Bibliographic Details
Title:	Adaptive reweighted Tikhonov inversion of gravity-gradient data for salt-boundary imaging.
Authors:	Shui, Yinqi¹ (AUTHOR), Guo, Hua² (AUTHOR) hyguohua@126.com, Zhang, Yu¹ (AUTHOR), Xu, Zheng-wei¹ (AUTHOR), Xian, Ming-hao¹ (AUTHOR)
Source:	Applied Geophysics: Bulletin of Chinese Geophysical Society. Aug2026, p1-22. 22p.
Subject Terms:	Tikhonov regularization, Inversion (Geophysics), Geological modeling, Imaging systems in geophysics, Deep learning, Mathematical regularization
Abstract:	Three-dimensional physical-property inversion is central to processing and interpreting gravity potential-field data because it provides quantitative estimates of the geometry and parameters of subsurface anomalous bodies. Yet gravity inversion remains fundamentally ill posed: limited observations and complex geology promote non-uniqueness and instability, and the skin effect can bias recovered models toward shallow structure, obscuring the true boundaries of complex bodies. Classical Tikhonov regularization—and common refinements such as depth- and structure-weighting—can partially suppress the skin effect, but typically lack spatial adaptivity and cannot self-adjust in response to the evolving geological image. Approaches based on stabilizing functionals often introduce additional mathematical tuning that can lead to sensitive parameters and fragile convergence. Conversely, purely data-driven deep-learning inversions, when used without physical constraints, may depart from plausible geological mechanisms and show limited robustness to interference and domain shift. Here we propose a Deep-Focus-Based Reweighted Regularization gravity inversion method (DFRI) that couples physics-based stability with data-driven structural guidance. Within a Tikhonov framework, we construct a deep-focus weighting matrix guided by a trained neural network: the network rapidly predicts a density model from observed gravity data, and the reciprocal of this prediction is used to form a spatially varying weight matrix Wc, which is embedded directly into the regularization objective. This hybrid framework fully retains the advantages of traditional regularized inversion, namely stable convergence and strong physical interpretability. By virtue of the constructed Wc, spatially differentiated regularization penalties are implemented across the model domain. It weakens regular constraints in underground anomalous areas to restore real structural morphology, and strengthens constraints in surrounding rock background areas to suppress artifacts, effectively mitigating the skin effect, and achieving an organic integration of the stability of physical regularization and the structural extraction capability of deep learning. Experiments with synthetic models and verifications through practical cases demonstrate that the proposed method can significantly improve the resolution of gravity inversion. Compared with the traditional minimum support weighting scheme and the improved depth weighting scheme, the average relative error of the model density of the method in this paper is reduced by 41.2% and 32.7% respectively, and the tailing artifacts beneath anomalous bodies can be largely eliminated and strengthens the delineation of complex anomalous-body boundaries, providing an effective pathway for gravity imaging in challenging geological settings.. [ABSTRACT FROM AUTHOR]
Database:	Academic Search Index

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Header	DbId: asx DbLabel: Academic Search Index An: 196505418 RelevancyScore: 1452 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1452.42541503906
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Items	– Name: Title Label: Title Group: Ti Data: Adaptive reweighted Tikhonov inversion of gravity-gradient data for salt-boundary imaging. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Shui%2C+Yinqi%22">Shui, Yinqi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Guo%2C+Hua%22">Guo, Hua</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> hyguohua@126.com</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Yu%22">Zhang, Yu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Xu%2C+Zheng-wei%22">Xu, Zheng-wei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Xian%2C+Ming-hao%22">Xian, Ming-hao</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Geophysics%3A+Bulletin+of+Chinese+Geophysical+Society%22">Applied Geophysics: Bulletin of Chinese Geophysical Society</searchLink>. Aug2026, p1-22. 22p. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Tikhonov+regularization%22">Tikhonov regularization</searchLink><br /><searchLink fieldCode="DE" term="%22Inversion+%28Geophysics%29%22">Inversion (Geophysics)</searchLink><br /><searchLink fieldCode="DE" term="%22Geological+modeling%22">Geological modeling</searchLink><br /><searchLink fieldCode="DE" term="%22Imaging+systems+in+geophysics%22">Imaging systems in geophysics</searchLink><br /><searchLink fieldCode="DE" term="%22Deep+learning%22">Deep learning</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+regularization%22">Mathematical regularization</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Three-dimensional physical-property inversion is central to processing and interpreting gravity potential-field data because it provides quantitative estimates of the geometry and parameters of subsurface anomalous bodies. Yet gravity inversion remains fundamentally ill posed: limited observations and complex geology promote non-uniqueness and instability, and the skin effect can bias recovered models toward shallow structure, obscuring the true boundaries of complex bodies. Classical Tikhonov regularization—and common refinements such as depth- and structure-weighting—can partially suppress the skin effect, but typically lack spatial adaptivity and cannot self-adjust in response to the evolving geological image. Approaches based on stabilizing functionals often introduce additional mathematical tuning that can lead to sensitive parameters and fragile convergence. Conversely, purely data-driven deep-learning inversions, when used without physical constraints, may depart from plausible geological mechanisms and show limited robustness to interference and domain shift. Here we propose a Deep-Focus-Based Reweighted Regularization gravity inversion method (DFRI) that couples physics-based stability with data-driven structural guidance. Within a Tikhonov framework, we construct a deep-focus weighting matrix guided by a trained neural network: the network rapidly predicts a density model from observed gravity data, and the reciprocal of this prediction is used to form a spatially varying weight matrix <bold>W</bold><bold>c</bold>, which is embedded directly into the regularization objective. This hybrid framework fully retains the advantages of traditional regularized inversion, namely stable convergence and strong physical interpretability. By virtue of the constructed <bold>W</bold><bold>c</bold>, spatially differentiated regularization penalties are implemented across the model domain. It weakens regular constraints in underground anomalous areas to restore real structural morphology, and strengthens constraints in surrounding rock background areas to suppress artifacts, effectively mitigating the skin effect, and achieving an organic integration of the stability of physical regularization and the structural extraction capability of deep learning. Experiments with synthetic models and verifications through practical cases demonstrate that the proposed method can significantly improve the resolution of gravity inversion. Compared with the traditional minimum support weighting scheme and the improved depth weighting scheme, the average relative error of the model density of the method in this paper is reduced by 41.2% and 32.7% respectively, and the tailing artifacts beneath anomalous bodies can be largely eliminated and strengthens the delineation of complex anomalous-body boundaries, providing an effective pathway for gravity imaging in challenging geological settings.. [ABSTRACT FROM AUTHOR]
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RecordInfo	BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s11770-026-1521-z Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 1 Subjects: – SubjectFull: Tikhonov regularization Type: general – SubjectFull: Inversion (Geophysics) Type: general – SubjectFull: Geological modeling Type: general – SubjectFull: Imaging systems in geophysics Type: general – SubjectFull: Deep learning Type: general – SubjectFull: Mathematical regularization Type: general Titles: – TitleFull: Adaptive reweighted Tikhonov inversion of gravity-gradient data for salt-boundary imaging. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Shui, Yinqi – PersonEntity: Name: NameFull: Guo, Hua – PersonEntity: Name: NameFull: Zhang, Yu – PersonEntity: Name: NameFull: Xu, Zheng-wei – PersonEntity: Name: NameFull: Xian, Ming-hao IsPartOfRelationships: – BibEntity: Dates: – D: 28 M: 08 Text: Aug2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 16727975 Titles: – TitleFull: Applied Geophysics: Bulletin of Chinese Geophysical Society Type: main
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