Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain
Multiple reflection is a common interference wave in offshore petroleum and gas exploration, and the Radon-based filtering method is a frequently used approach for multiple removal. However, the filtering parameter setting is crucial in multiple suppression and relies heavily on the experience of pr...
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| Format: | Article |
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MDPI AG
2023-10-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/19/11041 |
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| author | An Ma Jianguo Song Yufei Su Caijun Hu |
| author_facet | An Ma Jianguo Song Yufei Su Caijun Hu |
| author_sort | An Ma |
| collection | DOAJ |
| description | Multiple reflection is a common interference wave in offshore petroleum and gas exploration, and the Radon-based filtering method is a frequently used approach for multiple removal. However, the filtering parameter setting is crucial in multiple suppression and relies heavily on the experience of processors. To reduce the dependence on human intervention, we introduce the geometric mode decomposition (GMD) and develop a novel processing flow that can automatically separate primaries and multiples, and then accomplish the suppression of multiples. GMD leverages the principle of the Wiener filtering to iteratively decompose the data into modes with varying curvature and intercept. By exploiting the differences in curvature, GMD can separate primary modes and multiple modes. Then, we propose a novel sparse Radon transform (RT) constrained with the elastic half (EH) norm. The EH norm contains a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>l</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> norm and a scaled <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>l</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> norm, which is added to overcome the numerical oscillation problem of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>l</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> norm. With the help of the EH norm, the estimated Radon model can reach a remarkable level of sparsity. To solve the optimization problem of the proposed sparse RT, an efficient alternating multiplier iteration algorithm is employed. Leveraging the high sparsity of the Radon model obtained from the proposed transform, we improve the GMD-based multiple removal framework. The high-sparsity Radon model obtained from the proposed Radon transform can not only simplify the separation of primary and multiple modes but also accelerate the convergence of GMD, thus improving the processing efficiency of the GMD method. The performance of the proposed GMD-based framework in multiple elimination is validated through synthetic and field data tests. |
| first_indexed | 2024-03-10T21:48:32Z |
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| institution | Directory Open Access Journal |
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| last_indexed | 2024-03-10T21:48:32Z |
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| spelling | doaj.art-53092105359742e58e0054a623867da72023-11-19T14:07:49ZengMDPI AGApplied Sciences2076-34172023-10-0113191104110.3390/app131911041Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon DomainAn Ma0Jianguo Song1Yufei Su2Caijun Hu3National Key Laboratory of Deep Oil and Gas, School of Geosciences, China University of Petroleum (East China), Qingdao 266580, ChinaNational Key Laboratory of Deep Oil and Gas, School of Geosciences, China University of Petroleum (East China), Qingdao 266580, ChinaNational Key Laboratory of Deep Oil and Gas, School of Geosciences, China University of Petroleum (East China), Qingdao 266580, ChinaNational Key Laboratory of Deep Oil and Gas, School of Geosciences, China University of Petroleum (East China), Qingdao 266580, ChinaMultiple reflection is a common interference wave in offshore petroleum and gas exploration, and the Radon-based filtering method is a frequently used approach for multiple removal. However, the filtering parameter setting is crucial in multiple suppression and relies heavily on the experience of processors. To reduce the dependence on human intervention, we introduce the geometric mode decomposition (GMD) and develop a novel processing flow that can automatically separate primaries and multiples, and then accomplish the suppression of multiples. GMD leverages the principle of the Wiener filtering to iteratively decompose the data into modes with varying curvature and intercept. By exploiting the differences in curvature, GMD can separate primary modes and multiple modes. Then, we propose a novel sparse Radon transform (RT) constrained with the elastic half (EH) norm. The EH norm contains a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>l</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> norm and a scaled <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>l</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> norm, which is added to overcome the numerical oscillation problem of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>l</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> norm. With the help of the EH norm, the estimated Radon model can reach a remarkable level of sparsity. To solve the optimization problem of the proposed sparse RT, an efficient alternating multiplier iteration algorithm is employed. Leveraging the high sparsity of the Radon model obtained from the proposed transform, we improve the GMD-based multiple removal framework. The high-sparsity Radon model obtained from the proposed Radon transform can not only simplify the separation of primary and multiple modes but also accelerate the convergence of GMD, thus improving the processing efficiency of the GMD method. The performance of the proposed GMD-based framework in multiple elimination is validated through synthetic and field data tests.https://www.mdpi.com/2076-3417/13/19/11041multiple removalsparse radon transformmode decompositionsparse inversion |
| spellingShingle | An Ma Jianguo Song Yufei Su Caijun Hu Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain Applied Sciences multiple removal sparse radon transform mode decomposition sparse inversion |
| title | Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain |
| title_full | Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain |
| title_fullStr | Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain |
| title_full_unstemmed | Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain |
| title_short | Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain |
| title_sort | multiple elimination based on mode decomposition in the elastic half norm constrained radon domain |
| topic | multiple removal sparse radon transform mode decomposition sparse inversion |
| url | https://www.mdpi.com/2076-3417/13/19/11041 |
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