Full-Waveform Inversion of Two-Parameter Ground-Penetrating Radar Based on Quadratic Wasserstein Distance
Full-waveform inversion (FWI) is one of the most promising techniques in current ground-penetrating radar (GPR) inversion methods. The least-squares method is usually used, minimizing the mismatch between the observed signal and the simulated signal. However, the cycle-skipping problem has become an...
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MDPI AG
2024-11-01
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| author | Kai Lu Yibo Wang Heting Han Shichao Zhong Yikang Zheng |
| author_facet | Kai Lu Yibo Wang Heting Han Shichao Zhong Yikang Zheng |
| author_sort | Kai Lu |
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| description | Full-waveform inversion (FWI) is one of the most promising techniques in current ground-penetrating radar (GPR) inversion methods. The least-squares method is usually used, minimizing the mismatch between the observed signal and the simulated signal. However, the cycle-skipping problem has become an urgent focus of this method because of the nonlinearity of the inversion problem. To mitigate the issue of local minima, the optimal transport problem has been introduced into full-waveform inversion in this study. The Wasserstein distance derived from the optimal transport problem is defined as the mismatch function in the FWI objective function, replacing the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> norm. In this study, the Wasserstein distance is computed by using entropy regularization and the Sinkhorn algorithm to reduce computational complexity and improve efficiency. Additionally, this study presents the objective function for dual-parameter full-waveform inversion of ground-penetrating radar, with the Wasserstein distance as the mismatch function. By normalizing with the Softplus function, the electromagnetic wave signals are adjusted to meet the non-negativity and mass conservation assumptions of the Wasserstein distance, and the convexity of the method has been proven. A multi-scale frequency-domain Wasserstein distance full-waveform inversion method based on the Softplus normalization approach is proposed, enabling the simultaneous inversion of relative permittivity and conductivity from ground-penetrating radar data. Numerical simulation cases demonstrate that this method has low initial model dependency and low noise sensitivity, allowing for high-precision inversion of relative permittivity and conductivity. The inversion results show that it, in particular, significantly improves the accuracy of conductivity inversion. |
| format | Article |
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| institution | Kabale University |
| issn | 2072-4292 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Remote Sensing |
| spelling | doaj-art-fb98d2e8f84e43368e1ccbc6a45e659d2024-11-26T18:19:43ZengMDPI AGRemote Sensing2072-42922024-11-011622414610.3390/rs16224146Full-Waveform Inversion of Two-Parameter Ground-Penetrating Radar Based on Quadratic Wasserstein DistanceKai Lu0Yibo Wang1Heting Han2Shichao Zhong3Yikang Zheng4MNR Key Laboratory of Polar Science, Polar Research Institute of China, Shanghai 200062, ChinaKey Laboratory of Petroleum Resource Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, ChinaKey Laboratory of Petroleum Resource Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, ChinaYangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing 314019, ChinaKey Laboratory of Petroleum Resource Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, ChinaFull-waveform inversion (FWI) is one of the most promising techniques in current ground-penetrating radar (GPR) inversion methods. The least-squares method is usually used, minimizing the mismatch between the observed signal and the simulated signal. However, the cycle-skipping problem has become an urgent focus of this method because of the nonlinearity of the inversion problem. To mitigate the issue of local minima, the optimal transport problem has been introduced into full-waveform inversion in this study. The Wasserstein distance derived from the optimal transport problem is defined as the mismatch function in the FWI objective function, replacing the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> norm. In this study, the Wasserstein distance is computed by using entropy regularization and the Sinkhorn algorithm to reduce computational complexity and improve efficiency. Additionally, this study presents the objective function for dual-parameter full-waveform inversion of ground-penetrating radar, with the Wasserstein distance as the mismatch function. By normalizing with the Softplus function, the electromagnetic wave signals are adjusted to meet the non-negativity and mass conservation assumptions of the Wasserstein distance, and the convexity of the method has been proven. A multi-scale frequency-domain Wasserstein distance full-waveform inversion method based on the Softplus normalization approach is proposed, enabling the simultaneous inversion of relative permittivity and conductivity from ground-penetrating radar data. Numerical simulation cases demonstrate that this method has low initial model dependency and low noise sensitivity, allowing for high-precision inversion of relative permittivity and conductivity. The inversion results show that it, in particular, significantly improves the accuracy of conductivity inversion.https://www.mdpi.com/2072-4292/16/22/4146Wasserstein distanceoptimal transport distancerelative permittivity and conductivityfull-waveform inversion |
| spellingShingle | Kai Lu Yibo Wang Heting Han Shichao Zhong Yikang Zheng Full-Waveform Inversion of Two-Parameter Ground-Penetrating Radar Based on Quadratic Wasserstein Distance Remote Sensing Wasserstein distance optimal transport distance relative permittivity and conductivity full-waveform inversion |
| title | Full-Waveform Inversion of Two-Parameter Ground-Penetrating Radar Based on Quadratic Wasserstein Distance |
| title_full | Full-Waveform Inversion of Two-Parameter Ground-Penetrating Radar Based on Quadratic Wasserstein Distance |
| title_fullStr | Full-Waveform Inversion of Two-Parameter Ground-Penetrating Radar Based on Quadratic Wasserstein Distance |
| title_full_unstemmed | Full-Waveform Inversion of Two-Parameter Ground-Penetrating Radar Based on Quadratic Wasserstein Distance |
| title_short | Full-Waveform Inversion of Two-Parameter Ground-Penetrating Radar Based on Quadratic Wasserstein Distance |
| title_sort | full waveform inversion of two parameter ground penetrating radar based on quadratic wasserstein distance |
| topic | Wasserstein distance optimal transport distance relative permittivity and conductivity full-waveform inversion |
| url | https://www.mdpi.com/2072-4292/16/22/4146 |
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