Guanghui Han, Bing-Shout He, Huixing Zhang, Enjiang Wang
The viscoelastic wave equations based on the constant- Q (CQ) model can accurately describe the amplitude dissipation and phase distortion of waves in anelastic medium. However, only three velocity or displacement components can be obtained directly by solving such equations. Starting from the time-domain second-order displacement viscoelastic wave equation, we derived the decoupled P- and S-wave displacement vector viscoelastic wave equation by using the polarization difference of P- and S- waves propagation in isotropic media. The equation can be transformed into the velocity-dilatation-rotation viscoelastic wave equation containing the first-order temporal derivative and fractional Laplacian operators which can be solved directly by using the staggered-grid finite-difference and pseudo-spectral methods. We use the low-rank decomposition method to approximate the derived mixed space-wavenumber domain fractional Laplacian operators for modeling wave propagation in heterogeneous attenuating medium. We also demonstrated the precision of the proposed equation by comparing the numerical solutions with the analytical solutions. Furthermore, compared with the conventional velocity-stress viscoelastic wave equation, experimental results demonstrate that the proposed equation can separate the pure P- and S-waves from the mixed wavefield during wavefield continuation, but also be decoupled to the equation containing predominantly amplitude attenuation or phase distortion term.
基于常数 Q（CQ）模型的粘弹性波方程可以精确描述弹性介质中波的振幅耗散和相位畸变。然而，通过求解此类方程只能直接得到三个速度或位移分量。我们从时域二阶位移粘弹性波方程出发，利用 P 波和 S 波在各向同性介质中传播的极化差，推导出了解耦的 P 波和 S 波位移矢量粘弹性波方程。该方程可转化为包含一阶时间导数和分数拉普拉斯算子的速度-膨胀-旋转粘弹性波方程，并可通过交错网格有限差分法和伪谱法直接求解。我们使用低秩分解法来近似求得混合空间-文数域分数拉普拉斯算子，以模拟波在异质衰减介质中的传播。我们还通过比较数值解与分析解，证明了所提出方程的精确性。此外，与传统的速度-应力粘弹性波方程相比，实验结果表明，所提出的方程不仅能在波场延续过程中将纯 P 波和 S 波从混合波场中分离出来，而且还能与主要包含振幅衰减或相位畸变项的方程解耦。
{"title":"Fractional-order velocity-dilatation-rotation viscoelastic wave equation and numerical solution based on constant-Q model","authors":"Guanghui Han, Bing-Shout He, Huixing Zhang, Enjiang Wang","doi":"10.1190/geo2023-0290.1","DOIUrl":"https://doi.org/10.1190/geo2023-0290.1","url":null,"abstract":"The viscoelastic wave equations based on the constant- Q (CQ) model can accurately describe the amplitude dissipation and phase distortion of waves in anelastic medium. However, only three velocity or displacement components can be obtained directly by solving such equations. Starting from the time-domain second-order displacement viscoelastic wave equation, we derived the decoupled P- and S-wave displacement vector viscoelastic wave equation by using the polarization difference of P- and S- waves propagation in isotropic media. The equation can be transformed into the velocity-dilatation-rotation viscoelastic wave equation containing the first-order temporal derivative and fractional Laplacian operators which can be solved directly by using the staggered-grid finite-difference and pseudo-spectral methods. We use the low-rank decomposition method to approximate the derived mixed space-wavenumber domain fractional Laplacian operators for modeling wave propagation in heterogeneous attenuating medium. We also demonstrated the precision of the proposed equation by comparing the numerical solutions with the analytical solutions. Furthermore, compared with the conventional velocity-stress viscoelastic wave equation, experimental results demonstrate that the proposed equation can separate the pure P- and S-waves from the mixed wavefield during wavefield continuation, but also be decoupled to the equation containing predominantly amplitude attenuation or phase distortion term.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139608997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jin Li, Yucheng Luo, Guang Li, Yecheng Liu, Jingtian Tang
Audio magnetotelluric (AMT), as a commonly used passive geophysical technique, provides outstanding metal ore exploration capabilities based on the resistivity structure of the Earth. However, the accuracy of AMT in translating geoelectrical structures decreases when the data collected in mining areas are of poor data quality and contain complex anthropogenic noise, leading to distorted apparent resistivity-phase curves and posing significant challenges for mineral exploration. To effectively denoise AMT data, we propose a new denoising method that combines atom-profile updating dictionary learning (APrU) with nucleus sampling attention mechanism sparse coding (NSAM). First, we use APrU to accurately learn the characteristics of the noise in the AMT data; then, we apply the updated dictionary to perform sparse coding on the AMT data by NSAM to obtain the noise; finally, we subtract the noise from the original AMT data to obtain the denoised data. Our experimental results suggest that the proposed method can learn an over-complete dictionary via the to-be-processed AMT data, thereby enabling the sparse representation of the noise within the learned dictionary. We also demonstrate the efficacy of this method with a set of field data collected from the Lu-zong mining area, and the attained denoised data faithfully restores the geoelectrical structures with heightened accuracy. The findings confirm that the proposed method realizes the unsupervised learning of the AMT data and allows us to achieve precise denoising performance.
音频磁法（AMT）作为一种常用的被动地球物理技术，可根据地球的电阻率结构提供出色的金属矿勘探能力。然而，当矿区采集的数据质量较差且含有复杂的人为噪声时，AMT 转换地球电结构的精度就会下降，导致视电阻率-相位曲线失真，给矿产勘探带来巨大挑战。为了有效地对 AMT 数据进行去噪，我们提出了一种将原子轮廓更新字典学习（APrU）与核采样注意机制稀疏编码（NSAM）相结合的新型去噪方法。首先，我们使用 APrU 准确地学习 AMT 数据中的噪声特征；然后，我们应用更新后的字典，通过 NSAM 对 AMT 数据进行稀疏编码，得到噪声；最后，我们从原始 AMT 数据中减去噪声，得到去噪数据。我们的实验结果表明，所提出的方法可以通过待处理的 AMT 数据学习到超完全字典，从而在学习到的字典中对噪声进行稀疏表示。我们还用一组从鲁宗矿区采集的野外数据证明了该方法的有效性，所获得的去噪数据忠实地还原了地质电学结构，且精度更高。研究结果证实，所提出的方法实现了对 AMT 数据的无监督学习，使我们能够获得精确的去噪性能。
{"title":"APrU dictionary learning with NSAM sparse coding for audio magnetotelluric denoising","authors":"Jin Li, Yucheng Luo, Guang Li, Yecheng Liu, Jingtian Tang","doi":"10.1190/geo2023-0205.1","DOIUrl":"https://doi.org/10.1190/geo2023-0205.1","url":null,"abstract":"Audio magnetotelluric (AMT), as a commonly used passive geophysical technique, provides outstanding metal ore exploration capabilities based on the resistivity structure of the Earth. However, the accuracy of AMT in translating geoelectrical structures decreases when the data collected in mining areas are of poor data quality and contain complex anthropogenic noise, leading to distorted apparent resistivity-phase curves and posing significant challenges for mineral exploration. To effectively denoise AMT data, we propose a new denoising method that combines atom-profile updating dictionary learning (APrU) with nucleus sampling attention mechanism sparse coding (NSAM). First, we use APrU to accurately learn the characteristics of the noise in the AMT data; then, we apply the updated dictionary to perform sparse coding on the AMT data by NSAM to obtain the noise; finally, we subtract the noise from the original AMT data to obtain the denoised data. Our experimental results suggest that the proposed method can learn an over-complete dictionary via the to-be-processed AMT data, thereby enabling the sparse representation of the noise within the learned dictionary. We also demonstrate the efficacy of this method with a set of field data collected from the Lu-zong mining area, and the attained denoised data faithfully restores the geoelectrical structures with heightened accuracy. The findings confirm that the proposed method realizes the unsupervised learning of the AMT data and allows us to achieve precise denoising performance.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Guangtan Huang, Shuying Wei, Davide Gei, Tongtao Wang
Sparsity constraints have been widely adopted in the regularization of ill-posed problems to obtain subsurface properties with sparseness feature. However, the target parameters are generally not sparsely distributed, and sparsity constraints lead to results that are missing information. Besides, smooth constraints (e.g., ℓ2 norm) lead to insufficient resolution of the inversion results. To overcome this issue, an effective solution is to convert the target parameters to a sparse representation, which can then be solved with sparsity constraints. For the estimation of elastic parameters, a high-resolution and reliable seismic basis pursuit inversion is proposed based on the exact Zoeppritz equation. Furthermore, the ℓ1–2 norm is proposed as a constraint, where a regularized function is minimized with the alternating direction method of multipliers (ADMM) algorithm. Numerical examples and real data applications demonstrate that the proposed method can not only improve the accuracy of the inversion results, especially the S-wave velocity and density information, but also increase the resolution of the inversion results. Furthermore, the ℓ1–2-norm constraint has better noise suppression demonstrating great potential in practical applications.
稀疏性约束已被广泛应用于非确定问题的正则化，以获得具有稀疏性特征的地下属性。然而，目标参数通常不是稀疏分布的，稀疏约束会导致结果信息缺失。此外，平滑约束（如 ℓ2 norm）会导致反演结果的分辨率不足。为克服这一问题，有效的解决方案是将目标参数转换为稀疏表示，然后利用稀疏约束求解。为了估算弹性参数，基于精确的 Zoeppritz 方程，提出了一种高分辨率和可靠的地震基追随反演。此外，还提出了 ℓ1-2 准则作为约束条件，使用交替乘法（ADMM）算法最小化正则化函数。数值实例和实际数据应用表明，所提出的方法不仅能提高反演结果的精度，尤其是 S 波速度和密度信息，还能提高反演结果的分辨率。此外，ℓ1-2-norm 约束具有更好的噪声抑制效果，在实际应用中具有巨大潜力。
{"title":"ℓ1–2-norm regularized basis pursuit seismic inversion based on exact Zoeppritz equation","authors":"Guangtan Huang, Shuying Wei, Davide Gei, Tongtao Wang","doi":"10.1190/geo2022-0336.1","DOIUrl":"https://doi.org/10.1190/geo2022-0336.1","url":null,"abstract":"Sparsity constraints have been widely adopted in the regularization of ill-posed problems to obtain subsurface properties with sparseness feature. However, the target parameters are generally not sparsely distributed, and sparsity constraints lead to results that are missing information. Besides, smooth constraints (e.g., ℓ2 norm) lead to insufficient resolution of the inversion results. To overcome this issue, an effective solution is to convert the target parameters to a sparse representation, which can then be solved with sparsity constraints. For the estimation of elastic parameters, a high-resolution and reliable seismic basis pursuit inversion is proposed based on the exact Zoeppritz equation. Furthermore, the ℓ1–2 norm is proposed as a constraint, where a regularized function is minimized with the alternating direction method of multipliers (ADMM) algorithm. Numerical examples and real data applications demonstrate that the proposed method can not only improve the accuracy of the inversion results, especially the S-wave velocity and density information, but also increase the resolution of the inversion results. Furthermore, the ℓ1–2-norm constraint has better noise suppression demonstrating great potential in practical applications.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139526487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The ultimate goal of survey design is to find the acquisition parameters that enable acquiring high-quality data suitable for optimal imaging. This, while fulfilling budget, health, safety and environmental constraints. We propose a target-oriented acquisition design algorithm based on Full-Wavefield Migration. The algorithm optimizes a receiver density function that indicates the number of receivers per unit area required for obtaining the best possible image quality. The method makes use of available seismic data to create a reference model which is included in the proposed objective function. To make the design target-oriented, the objective function is multiplied with a mask that gives more weight to the target areas of interest. The results of the 2D and 3D implementations show an optimized receiver density function with higher values at the zones where more data is needed for improving image quality. The corresponding receiver geometries have more receivers placed at these areas. We validate the results by computing the images of the target zone using uniform and optimized geometries. The use of the latter shows an improvement in the image quality at the target zone. Additionally, we compute the number of receivers required for achieving a certain signal-to-noise ratio after imaging based on the optimized receiver density function.
{"title":"Target-oriented acquisition geometry design based on Full-Wavefield Migration","authors":"B. Revelo‐Obando, G. Blacquière","doi":"10.1190/geo2023-0578.1","DOIUrl":"https://doi.org/10.1190/geo2023-0578.1","url":null,"abstract":"The ultimate goal of survey design is to find the acquisition parameters that enable acquiring high-quality data suitable for optimal imaging. This, while fulfilling budget, health, safety and environmental constraints. We propose a target-oriented acquisition design algorithm based on Full-Wavefield Migration. The algorithm optimizes a receiver density function that indicates the number of receivers per unit area required for obtaining the best possible image quality. The method makes use of available seismic data to create a reference model which is included in the proposed objective function. To make the design target-oriented, the objective function is multiplied with a mask that gives more weight to the target areas of interest. The results of the 2D and 3D implementations show an optimized receiver density function with higher values at the zones where more data is needed for improving image quality. The corresponding receiver geometries have more receivers placed at these areas. We validate the results by computing the images of the target zone using uniform and optimized geometries. The use of the latter shows an improvement in the image quality at the target zone. Additionally, we compute the number of receivers required for achieving a certain signal-to-noise ratio after imaging based on the optimized receiver density function.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139615782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Darya Morozov, Cristina McLaughlin, Elliot D. Grunewald, Trevor Irons, David O. Walsh
In medical MRI, spatial localization (imaging) is based upon the application of controlled magnetic field gradients on top of the main magnetic field, to spatially modulate the frequency and/or phase of the NMR across the volume of investigation. In this work, we have applied similar physical principles to produce controlled magnetic field gradients during surface NMR-based groundwater investigations. In this approach a gradient pulse of variable amplitude or duration is applied immediately after the excitation pulse, to cause predictable phase encoding of the NMR signal as a function of depth. This approach is also applicable to emerging surface NMR detection methods that use a pre-polarization field with fast non-adiabatic turn off to generate detectable NMR signals from the shallow subsurface. In this case, the gradient pulse is applied after terminating the pre-polarization field and provides a heretofore unavailable means of localizing the NMR response as a function of depth. The application of gradients can also be combined with tip-angle based modulation to yield higher imaging resolution than can be achieved through either gradient- or tip-angle based imaging alone. We implemented this new gradient-based capability into a surface NMR gradient generation accessory that is compatible with the GMR-Flex instrument and developed surface NMR-specific forward modeling and linear inverse models. We validated the accuracy of this novel gradient-based sNMR technology using computer simulations, experiments using a small pool filled with a discrete layer of bulk water, and field experiments at well-characterized groundwater test sites along Ebey Island, WA, and Larned, KS. The gradient-based sNMR imaging observations were compared with high resolution direct push NMR results observed at these sites. The results of computer simulations and field experiments indicate improvements in both detection (signal-to-noise ratio) and spatial resolution of shallow surface water content using surface NMR, compared to traditional surface NMR imaging methods.
{"title":"Gradient-based surface NMR for groundwater investigation","authors":"Darya Morozov, Cristina McLaughlin, Elliot D. Grunewald, Trevor Irons, David O. Walsh","doi":"10.1190/geo2023-0311.1","DOIUrl":"https://doi.org/10.1190/geo2023-0311.1","url":null,"abstract":"In medical MRI, spatial localization (imaging) is based upon the application of controlled magnetic field gradients on top of the main magnetic field, to spatially modulate the frequency and/or phase of the NMR across the volume of investigation. In this work, we have applied similar physical principles to produce controlled magnetic field gradients during surface NMR-based groundwater investigations. In this approach a gradient pulse of variable amplitude or duration is applied immediately after the excitation pulse, to cause predictable phase encoding of the NMR signal as a function of depth. This approach is also applicable to emerging surface NMR detection methods that use a pre-polarization field with fast non-adiabatic turn off to generate detectable NMR signals from the shallow subsurface. In this case, the gradient pulse is applied after terminating the pre-polarization field and provides a heretofore unavailable means of localizing the NMR response as a function of depth. The application of gradients can also be combined with tip-angle based modulation to yield higher imaging resolution than can be achieved through either gradient- or tip-angle based imaging alone. We implemented this new gradient-based capability into a surface NMR gradient generation accessory that is compatible with the GMR-Flex instrument and developed surface NMR-specific forward modeling and linear inverse models. We validated the accuracy of this novel gradient-based sNMR technology using computer simulations, experiments using a small pool filled with a discrete layer of bulk water, and field experiments at well-characterized groundwater test sites along Ebey Island, WA, and Larned, KS. The gradient-based sNMR imaging observations were compared with high resolution direct push NMR results observed at these sites. The results of computer simulations and field experiments indicate improvements in both detection (signal-to-noise ratio) and spatial resolution of shallow surface water content using surface NMR, compared to traditional surface NMR imaging methods.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Distributed acoustic sensing (DAS) is an emerging seismic acquisition technique with great practical potential. However, various types of noise seriously corrupt DAS signals, making it difficult to recover signals, particularly in low SNR regions. Existing deep learning methods address this challenge by augmenting datasets or strengthening the complex architecture, which can cause over-denoising and a computational power burden. Hence, we propose the heterogeneous knowledge distillation (HKD) method to more efficiently address the signal reconstruction under low SNR. HKD employs ResNet 20 as the teacher and student model (T-S). It utilizes residual learning and skip connections to facilitate feature representation at deeper levels. The main contribution is the training of the T-S framework with different noise levels. The teacher model that was trained using slightly noisy data serves as a powerful feature extractor to capture more accurate signal features, since high quality data is easy to recover. By minimizing the difference between the outputs of T-S models, the student that was trained using severely noisy data can distill the absent signal features from the teacher to improve its own signal recovery, which enables heterogeneous feature distillation. Furthermore, simultaneous learning of negative and positive components (PNL) has been proposed to extract more useful features from the teacher, enabling the T-S framework to learn from both the predicted signal and noise during training. Consequently, a new loss function that combines student denoising loss and HKD loss weighted by PNL was developed to alleviate signal leakage. The experimental results demonstrate that the HKD achieves distinct and consistent signal recovery without increasing computational costs.
{"title":"Efficient SNR enhancement model for severely contaminated DAS seismic data based on heterogeneous knowledge distillation","authors":"Q. Feng, Shignag Wang, Yue Li","doi":"10.1190/geo2023-0382.1","DOIUrl":"https://doi.org/10.1190/geo2023-0382.1","url":null,"abstract":"Distributed acoustic sensing (DAS) is an emerging seismic acquisition technique with great practical potential. However, various types of noise seriously corrupt DAS signals, making it difficult to recover signals, particularly in low SNR regions. Existing deep learning methods address this challenge by augmenting datasets or strengthening the complex architecture, which can cause over-denoising and a computational power burden. Hence, we propose the heterogeneous knowledge distillation (HKD) method to more efficiently address the signal reconstruction under low SNR. HKD employs ResNet 20 as the teacher and student model (T-S). It utilizes residual learning and skip connections to facilitate feature representation at deeper levels. The main contribution is the training of the T-S framework with different noise levels. The teacher model that was trained using slightly noisy data serves as a powerful feature extractor to capture more accurate signal features, since high quality data is easy to recover. By minimizing the difference between the outputs of T-S models, the student that was trained using severely noisy data can distill the absent signal features from the teacher to improve its own signal recovery, which enables heterogeneous feature distillation. Furthermore, simultaneous learning of negative and positive components (PNL) has been proposed to extract more useful features from the teacher, enabling the T-S framework to learn from both the predicted signal and noise during training. Consequently, a new loss function that combines student denoising loss and HKD loss weighted by PNL was developed to alleviate signal leakage. The experimental results demonstrate that the HKD achieves distinct and consistent signal recovery without increasing computational costs.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139614234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Compressional and shear sonic transit-time logs (DTC and DTS, respectively) provide important petrophysical and geomechanical information for subsurface characterization. However, they are often not acquired in all wells because of cost limitations or borehole problems. We propose a method to estimate DTC and DTS simultaneously, from other commonly acquired well logs like gamma-ray, density, and neutron porosity. Our method consists of two consecutive models to predict the sonic logs and predict the seismic traces at well locations. The model predicting the seismic traces adds a spatial constraint to the model predicting sonic logs. Our method also quantifies uncertainties of the prediction, which come from uncertainties of neural network parameters and input data. We train the network on four wells from the Poseidon dataset located on the Australian shelf, in the Browse basin. We test the network on other two wells from Browse basin. The test results show better predictions of sonic logs when we add the seismic constraint.
{"title":"PREDICTING MISSING SONIC LOGS WITH SEISMIC CONSTRAINT","authors":"Nam Pham, Lei Fu, Weichang Li","doi":"10.1190/geo2023-0286.1","DOIUrl":"https://doi.org/10.1190/geo2023-0286.1","url":null,"abstract":"Compressional and shear sonic transit-time logs (DTC and DTS, respectively) provide important petrophysical and geomechanical information for subsurface characterization. However, they are often not acquired in all wells because of cost limitations or borehole problems. We propose a method to estimate DTC and DTS simultaneously, from other commonly acquired well logs like gamma-ray, density, and neutron porosity. Our method consists of two consecutive models to predict the sonic logs and predict the seismic traces at well locations. The model predicting the seismic traces adds a spatial constraint to the model predicting sonic logs. Our method also quantifies uncertainties of the prediction, which come from uncertainties of neural network parameters and input data. We train the network on four wells from the Poseidon dataset located on the Australian shelf, in the Browse basin. We test the network on other two wells from Browse basin. The test results show better predictions of sonic logs when we add the seismic constraint.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139614063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hanyang Li, Jiahui Li, Xuegui Li, Hongli Dong, Gang Xu, Mi Zhang
Data-driven velocity inversion has emerged as a prominent and challenging problem in seismic exploration. The complexity of the inversion problem and the limited data set make it difficult to ensure the stability and generalization of neural networks. To address these concerns, we propose a novel approach called multi-branch attention U-Net (MAU-Net) for velocity inversion. The key distinction of MAU-Net from previous data-driven approaches lies in its ability to not only learn information from the data domain, but also incorporate prior model domain information. MAU-Net consists of two branches: one branch uses seismic records as input to effectively learn the mapping relationship between the data and model domains, while the other branch employs a prior geological model as input to extract features from the model domain, thereby guiding MAU-Net’s learning process. Additionally, we introduce three major improvements in the model branching path to enhance MAU-Net’s utilization of seismic data and handle redundant information. We validate the effectiveness of each improvement through ablation experiments. The performance of MAU-Net is demonstrated with the Marmousi model and 2004 BP model, and it can also be combined with FWI to further improve the quality of the inversion result. MAU-Net exhibits robust performance on field data through the use of transfer learning techniques, further confirming its reliability and applicability.
{"title":"MAU-Net:a multi-branch attention U-Net for full-wavefom inversion","authors":"Hanyang Li, Jiahui Li, Xuegui Li, Hongli Dong, Gang Xu, Mi Zhang","doi":"10.1190/geo2023-0043.1","DOIUrl":"https://doi.org/10.1190/geo2023-0043.1","url":null,"abstract":"Data-driven velocity inversion has emerged as a prominent and challenging problem in seismic exploration. The complexity of the inversion problem and the limited data set make it difficult to ensure the stability and generalization of neural networks. To address these concerns, we propose a novel approach called multi-branch attention U-Net (MAU-Net) for velocity inversion. The key distinction of MAU-Net from previous data-driven approaches lies in its ability to not only learn information from the data domain, but also incorporate prior model domain information. MAU-Net consists of two branches: one branch uses seismic records as input to effectively learn the mapping relationship between the data and model domains, while the other branch employs a prior geological model as input to extract features from the model domain, thereby guiding MAU-Net’s learning process. Additionally, we introduce three major improvements in the model branching path to enhance MAU-Net’s utilization of seismic data and handle redundant information. We validate the effectiveness of each improvement through ablation experiments. The performance of MAU-Net is demonstrated with the Marmousi model and 2004 BP model, and it can also be combined with FWI to further improve the quality of the inversion result. MAU-Net exhibits robust performance on field data through the use of transfer learning techniques, further confirming its reliability and applicability.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139526498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The research in this paper is to realize the simultaneous AVO/AVA (amplitude variation with offset or angle) inversion of anisotropic parameters for the transversely isotropic media with vertical axis of symmetry (VTI media). First, we introduce a nonlinear PP-wave reflection coefficient approximation equation in terms of only P- and S-wave impedances for isotropic elastic media. Then by replacing the isotropic part of Rüger’s equation with this equation, we obtain a new PP-wave reflection coefficient approximation equation called the ASI Rüger equation for VTI media. To invert parameters for VTI media based on the ASI Rüger equation, we adopt the Bayesian generalized linear inversion method, a combination of generalized linear inversion and Bayesian linear inversion, in which the noise and model perturbation are assumed to conform to the zero mean Gaussian distribution. Compared with Rüger’s equation, the ASI Rüger equation lowers the trade-off between the parameters, and reduces the ill-posedness of the inverse problem. The synthetic and field data tests demonstrate the feasibility of the proposed method for inverting VTI media parameters (the vertical P-wave impedance, the vertical S-wave impedance, Thomsen’s parameters δ and ϵ).
本文的研究旨在实现对垂直对称轴横向各向同性介质（VTI 介质）各向异性参数的 AVO/AVA（随偏移或角度的振幅变化）同步反演。首先，我们只用各向同性弹性介质的 P 波和 S 波阻抗引入一个非线性 PP 波反射系数近似方程。然后，用该方程替换 Rüger 方程的各向同性部分，我们就得到了一个新的 PP 波反射系数近似方程，即 VTI 介质的 ASI Rüger 方程。为了根据 ASI Rüger 公式反演 VTI 介质参数，我们采用了贝叶斯广义线性反演方法，即广义线性反演和贝叶斯线性反演的结合，其中假定噪声和模型扰动符合零均值高斯分布。与 Rüger 方程相比，ASI Rüger 方程降低了参数之间的权衡，减少了反演问题的假定性。合成和现场数据测试证明了所提方法在反演 VTI 介质参数（垂直 P 波阻抗、垂直 S 波阻抗、汤姆森参数 δ 和 ϵ）方面的可行性。
{"title":"Seismic amplitude inversion based on a new PP-wave reflection coefficient approximation equation for VTI media","authors":"Xin Fu","doi":"10.1190/geo2023-0132.1","DOIUrl":"https://doi.org/10.1190/geo2023-0132.1","url":null,"abstract":"The research in this paper is to realize the simultaneous AVO/AVA (amplitude variation with offset or angle) inversion of anisotropic parameters for the transversely isotropic media with vertical axis of symmetry (VTI media). First, we introduce a nonlinear PP-wave reflection coefficient approximation equation in terms of only P- and S-wave impedances for isotropic elastic media. Then by replacing the isotropic part of Rüger’s equation with this equation, we obtain a new PP-wave reflection coefficient approximation equation called the ASI Rüger equation for VTI media. To invert parameters for VTI media based on the ASI Rüger equation, we adopt the Bayesian generalized linear inversion method, a combination of generalized linear inversion and Bayesian linear inversion, in which the noise and model perturbation are assumed to conform to the zero mean Gaussian distribution. Compared with Rüger’s equation, the ASI Rüger equation lowers the trade-off between the parameters, and reduces the ill-posedness of the inverse problem. The synthetic and field data tests demonstrate the feasibility of the proposed method for inverting VTI media parameters (the vertical P-wave impedance, the vertical S-wave impedance, Thomsen’s parameters δ and ϵ).","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139526558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Seismic data processing, specifically tasks like denoising and interpolation, often hinges on sparse solutions of linear systems. Group sparsity plays an essential role in this context by enhancing sparse inversion. It introduces more refined constraints, which preserve the inherent relationships within seismic data. To this end, we propose a robust Orthogonal Matching Pursuit algorithm, combined with Radon operators in the frequency-slowness f- p domain, to tackle the strong group-sparsity problem. This approach is vital for interpolating seismic data and attenuating erratic noise simultaneously. Our algorithm takes advantage of group sparsity by selecting the dominant slowness group in each iteration and fitting Radon coefficients with a robust ℓ1-ℓ1 norm by the alternating direction method of multipliers (ADMM) solver. Its ability to resist erratic noise, along with its superior performance in applications such as simultaneous source deblending and reconstruction of noisy onshore datasets, underscores the importance of group sparsity. Both synthetic and real comparative analyses further demonstrate that strong group sparsity inversion consistently outperforms corresponding traditional methods without the group sparsity constraint. These comparisons emphasize the necessity of integrating group sparsity in these applications, thereby showing its indispensable role in optimizing seismic data processing.
地震数据处理，特别是去噪和插值等任务，往往取决于线性系统的稀疏解。组稀疏性通过增强稀疏反演在这方面发挥着重要作用。它引入了更精细的约束条件，保留了地震数据中的固有关系。为此，我们提出了一种稳健的正交匹配追寻算法，结合频率-慢度 f- p 域中的拉顿算子，来解决强组稀疏性问题。这种方法对于同时插值地震数据和衰减不稳定噪声至关重要。我们的算法利用了组稀疏性的优势，在每次迭代中选择主要的慢度组，并通过交替方向乘法（ADMM）求解器以稳健的 ℓ1-ℓ1 准则拟合 Radon 系数。它能够抵御不稳定噪声，在同步源去耦和高噪声陆上数据集重建等应用中表现出色，突出了组稀疏性的重要性。合成和实际对比分析进一步证明，强组稀疏性反演始终优于没有组稀疏性约束的相应传统方法。这些比较强调了在这些应用中整合群稀疏性的必要性，从而显示了群稀疏性在优化地震数据处理中不可或缺的作用。
{"title":"Robust multi-dimensional reconstruction via Group Sparsity with Radon operators","authors":"Ji Li, Dawei Liu","doi":"10.1190/geo2023-0465.1","DOIUrl":"https://doi.org/10.1190/geo2023-0465.1","url":null,"abstract":"Seismic data processing, specifically tasks like denoising and interpolation, often hinges on sparse solutions of linear systems. Group sparsity plays an essential role in this context by enhancing sparse inversion. It introduces more refined constraints, which preserve the inherent relationships within seismic data. To this end, we propose a robust Orthogonal Matching Pursuit algorithm, combined with Radon operators in the frequency-slowness f- p domain, to tackle the strong group-sparsity problem. This approach is vital for interpolating seismic data and attenuating erratic noise simultaneously. Our algorithm takes advantage of group sparsity by selecting the dominant slowness group in each iteration and fitting Radon coefficients with a robust ℓ1-ℓ1 norm by the alternating direction method of multipliers (ADMM) solver. Its ability to resist erratic noise, along with its superior performance in applications such as simultaneous source deblending and reconstruction of noisy onshore datasets, underscores the importance of group sparsity. Both synthetic and real comparative analyses further demonstrate that strong group sparsity inversion consistently outperforms corresponding traditional methods without the group sparsity constraint. These comparisons emphasize the necessity of integrating group sparsity in these applications, thereby showing its indispensable role in optimizing seismic data processing.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139616195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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