R. Beloborodov, James Gunning, M. Pervukhina, Juerg Hauser, M. B. Clennell, Alan Mur, Vladimir Li
While accurate litho-fluid and facies interpretation from wireline log data is critical for applications like joint facies and impedance inversion of seismic data, extracting this information manually is challenging due to the complexity and high dimensionality of the logs. Traditional clustering methods also struggle with litho-fluid type inference due to different depth trends in petrophysical rock properties due to compaction and diagenesis. We introduce a Rock Physics Machine Learning workflow that automates litho-fluid classification and property depth trend modeling to address these challenges. This workflow employs a maximum-likelihood approach, explicitly accounting for depth-related effects via Rock Physics models, to infer litho-fluid types from borehole data. It utilizes a robust Expectation-Maximization algorithm to associate each litho-fluid type with a specific Rock Physics model instance, constrained within physically reasonable bounds. The workflow directly outputs litho-fluid type proportions and type-specific Rock Physics models with associated uncertainties, providing essential prior information for seismic inversion.
{"title":"Automated litho-fluid and facies classification in well-logs: the Rock Physics perspective","authors":"R. Beloborodov, James Gunning, M. Pervukhina, Juerg Hauser, M. B. Clennell, Alan Mur, Vladimir Li","doi":"10.1190/geo2023-0533.1","DOIUrl":"https://doi.org/10.1190/geo2023-0533.1","url":null,"abstract":"While accurate litho-fluid and facies interpretation from wireline log data is critical for applications like joint facies and impedance inversion of seismic data, extracting this information manually is challenging due to the complexity and high dimensionality of the logs. Traditional clustering methods also struggle with litho-fluid type inference due to different depth trends in petrophysical rock properties due to compaction and diagenesis. We introduce a Rock Physics Machine Learning workflow that automates litho-fluid classification and property depth trend modeling to address these challenges. This workflow employs a maximum-likelihood approach, explicitly accounting for depth-related effects via Rock Physics models, to infer litho-fluid types from borehole data. It utilizes a robust Expectation-Maximization algorithm to associate each litho-fluid type with a specific Rock Physics model instance, constrained within physically reasonable bounds. The workflow directly outputs litho-fluid type proportions and type-specific Rock Physics models with associated uncertainties, providing essential prior information for seismic inversion.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140756467","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}
Separating wave modes on seismic records is an essential step in imaging of multicomponent seismic data. Viscoelastic anisotropic models provide a realistic description of subsurface formations that exhibit anisotropy of both velocity and attenuation. However, mode separation has not been extended to viscoelastic anisotropic media yet. Here, we propose an efficient approach to wavefield decomposition that takes both velocity and attenuation anisotropy into account. Our algorithm operates in the frequency-wavenumber domain and, therefore, is suitable for general dissipative models. We present exact equations for wavefield decomposition in arbitrarily anisotropic attenuative homogeneous media. Then the proposed approach is applied to viscoelastic constant- Q VTI (transversely isotropic with a vertical symmetry axis) models. Numerical examples demonstrate the accuracy and efficiency of our approach for piecewise-homogeneous media characterized by pronounced velocity and attenuation anisotropy.
{"title":"Wavefield decomposition for viscoelastic anisotropic media","authors":"Qi Hao, I. Tsvankin","doi":"10.1190/geo2023-0583.1","DOIUrl":"https://doi.org/10.1190/geo2023-0583.1","url":null,"abstract":"Separating wave modes on seismic records is an essential step in imaging of multicomponent seismic data. Viscoelastic anisotropic models provide a realistic description of subsurface formations that exhibit anisotropy of both velocity and attenuation. However, mode separation has not been extended to viscoelastic anisotropic media yet. Here, we propose an efficient approach to wavefield decomposition that takes both velocity and attenuation anisotropy into account. Our algorithm operates in the frequency-wavenumber domain and, therefore, is suitable for general dissipative models. We present exact equations for wavefield decomposition in arbitrarily anisotropic attenuative homogeneous media. Then the proposed approach is applied to viscoelastic constant- Q VTI (transversely isotropic with a vertical symmetry axis) models. Numerical examples demonstrate the accuracy and efficiency of our approach for piecewise-homogeneous media characterized by pronounced velocity and attenuation anisotropy.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140765394","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}
Diverse Monte Carlo methods have gained widespread use across a broad range of applications. However, the challenge of 3D Monte Carlo sampling remains due to the curse of dimensionality. To date, only a few works have been published regarding 3D Monte Carlo sampling. This study aims to develop an efficient 3D trans-dimensional Monte Carlo framework for reconstructing the spatial geometry of an anomalous body using gravity data. The proposed framework can also quantify the uncertainty of the shape of an anomalous body recovered from geophysical measurements. To improve the computational efficiency of 3D Monte Carlo sampling, we propose a sparse geometry parameterization strategy. This approach adequately approximates the shape of a complex 3D anomalous body using a set of simple geometries, such as an ellipsoid. Each ellipsoid can be characterized by a few parameters, including the centroid, axes, and orientations, significantly reducing the number of parameters to be sampled. During sampling, we randomly perturb the number, locations, sizes, and orientations of the ellipsoids. To impose prior structural constraints from other geophysical methods, such as seismic imaging, we design a new method by placing a fixed layer oriented along the top boundary of the anomalous body. The fixed layer is then connected to the randomly sampled ellipsoids using an alpha shape, allowing us to estimate the geometry of the anomalous source body. The current work focuses on the reconstruction of salt bodies. We start with a synthetic spherical salt model and then conduct a more realistic study using a simplified 3D SEG/EAGE salt model. Lastly, we apply our method to the Galveston Island salt dome, offshore Texas. The numerical results demonstrate that our framework can effectively recover the shape of an anomalous body and quantify the uncertainty of the reconstructed geometry.
{"title":"3D Monte Carlo geometry inversion using gravity data","authors":"Xiaolong Wei, Jiajia Sun, Mrinal Sen","doi":"10.1190/geo2023-0498.1","DOIUrl":"https://doi.org/10.1190/geo2023-0498.1","url":null,"abstract":"Diverse Monte Carlo methods have gained widespread use across a broad range of applications. However, the challenge of 3D Monte Carlo sampling remains due to the curse of dimensionality. To date, only a few works have been published regarding 3D Monte Carlo sampling. This study aims to develop an efficient 3D trans-dimensional Monte Carlo framework for reconstructing the spatial geometry of an anomalous body using gravity data. The proposed framework can also quantify the uncertainty of the shape of an anomalous body recovered from geophysical measurements. To improve the computational efficiency of 3D Monte Carlo sampling, we propose a sparse geometry parameterization strategy. This approach adequately approximates the shape of a complex 3D anomalous body using a set of simple geometries, such as an ellipsoid. Each ellipsoid can be characterized by a few parameters, including the centroid, axes, and orientations, significantly reducing the number of parameters to be sampled. During sampling, we randomly perturb the number, locations, sizes, and orientations of the ellipsoids. To impose prior structural constraints from other geophysical methods, such as seismic imaging, we design a new method by placing a fixed layer oriented along the top boundary of the anomalous body. The fixed layer is then connected to the randomly sampled ellipsoids using an alpha shape, allowing us to estimate the geometry of the anomalous source body. The current work focuses on the reconstruction of salt bodies. We start with a synthetic spherical salt model and then conduct a more realistic study using a simplified 3D SEG/EAGE salt model. Lastly, we apply our method to the Galveston Island salt dome, offshore Texas. The numerical results demonstrate that our framework can effectively recover the shape of an anomalous body and quantify the uncertainty of the reconstructed geometry.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835232","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}
Full waveform inversion (FWI) is a large-scale nonlinear ill-posed problem for which computationally expensive Newton-type methods can become trapped in undesirable local minima, particularly when the initial model lacks a low-wavenumber component and the recorded data lacks low-frequency content. A modification to the Gauss-Newton (GN) method is proposed to address these issues. The standard GN system for multisource multireceiver FWI is reformulated into an equivalent matrix equation form, with the solution becoming a diagonal matrix rather than a vector as in the standard system. The search direction is transformed from a vector to a matrix by relaxing the diagonality constraint, effectively adding a degree of freedom to the subsurface offset axis. The relaxed system can be explicitly solved with only the inversion of two small matrices that deblur the data residual matrix along the source and receiver dimensions, which simplifies the inversion of the Hessian matrix. When used to solve the extended source FWI objective function, the Extended GN (EGN) method integrates the benefits of both model and source extension. The EGN method effectively combines the computational effectiveness of the reduced FWI method with the robustness characteristics of extended formulations and offers a promising solution for addressing the challenges of FWI. It bridges the gap between these extended formulations and the reduced FWI method, enhancing inversion robustness while maintaining computational efficiency. The robustness and stability of the EGN algorithm for waveform inversion are demonstrated numerically.
{"title":"An extended Gauss-Newton method for full waveform inversion","authors":"Ali Gholami","doi":"10.1190/geo2022-0673.1","DOIUrl":"https://doi.org/10.1190/geo2022-0673.1","url":null,"abstract":"Full waveform inversion (FWI) is a large-scale nonlinear ill-posed problem for which computationally expensive Newton-type methods can become trapped in undesirable local minima, particularly when the initial model lacks a low-wavenumber component and the recorded data lacks low-frequency content. A modification to the Gauss-Newton (GN) method is proposed to address these issues. The standard GN system for multisource multireceiver FWI is reformulated into an equivalent matrix equation form, with the solution becoming a diagonal matrix rather than a vector as in the standard system. The search direction is transformed from a vector to a matrix by relaxing the diagonality constraint, effectively adding a degree of freedom to the subsurface offset axis. The relaxed system can be explicitly solved with only the inversion of two small matrices that deblur the data residual matrix along the source and receiver dimensions, which simplifies the inversion of the Hessian matrix. When used to solve the extended source FWI objective function, the Extended GN (EGN) method integrates the benefits of both model and source extension. The EGN method effectively combines the computational effectiveness of the reduced FWI method with the robustness characteristics of extended formulations and offers a promising solution for addressing the challenges of FWI. It bridges the gap between these extended formulations and the reduced FWI method, enhancing inversion robustness while maintaining computational efficiency. The robustness and stability of the EGN algorithm for waveform inversion are demonstrated numerically.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139834921","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}
Daria Olszowska, Gabriel Gallardo-Giozza, C. Torres‐Verdín
Laboratory and field measurements often fail to identify small-scale variations in rock elastic properties. Due to limited spatial resolution, conventional laboratory methods cannot properly describe rock formations exhibiting a high degree of heterogeneity, thereby masking differences between stiff and compliant layers. Continuous sample measurements can mitigate this problem but are not widely used by the industry. We build upon our previous work and apply laboratory angle-dependent ultrasonic reflection coefficient (ADURC) measurements to achieve detailed two-dimensional descriptions of the elastic properties of complex rock samples. This method successfully yields high-resolution information on P- and S-wave velocities, as well as bulk density, across the surface of rock samples. Elastic properties are estimated using a nonlinear inversion algorithm that matches laboratory measurements with numerical simulations. Angle-dependent ultrasonic reflection coefficient data acquired at various sample locations enable detailed rock descriptions, where the effective measurement area is determined by the size of the receiver, measurement frequency, and incidence angle. Consequently, the sampling area is smaller compared to triaxial loading and acoustic transmission tests, where the resolution is controlled by sample size. Measurements conducted on samples exhibiting different levels of spatial complexity validate the capability of the ADURC method to identify small-scale heterogeneities. For the reported experiments, variations in angle-dependent reflectivity give rise to corresponding variations in the estimated P- and S-wave velocities and density which can exceed 60%. These small-scale variations across heterogeneous rock samples are often overlooked by conventional laboratory methods.#xD;#xD;
实验室和实地测量往往无法确定岩石弹性特性的小尺度变化。由于空间分辨率有限，传统的实验室方法无法正确描述具有高度异质性的岩层，从而掩盖了坚硬层和顺应层之间的差异。连续样本测量可以缓解这一问题，但并未被业界广泛使用。我们在之前工作的基础上，应用实验室角度依赖性超声波反射系数（ADURC）测量方法，对复杂岩样的弹性特性进行了详细的二维描述。这种方法成功地获得了岩石样本表面 P 波和 S 波速度以及体积密度的高分辨率信息。使用非线性反演算法估算弹性特性，将实验室测量结果与数值模拟相匹配。在不同取样位置获取的与角度相关的超声波反射系数数据可对岩石进行详细描述，其中有效测量区域由接收器尺寸、测量频率和入射角度决定。因此，与三轴加载和声透射试验相比，取样面积较小，分辨率由样本大小控制。在具有不同空间复杂性的样品上进行的测量验证了 ADURC 方法识别小尺度异质性的能力。在报告的实验中，随角度变化的反射率会导致估算的 P 波和 S 波速度和密度出现相应的变化，变化率可超过 60%。传统的实验室方法往往会忽略这些异质岩石样本的小尺度变化；
{"title":"TWO-DIMENSIONAL IMAGING OF ELASTIC PROPERTIES OF ROCK CORE SAMPLES FROM MEASUREMENTS OF ANGLE-DEPENDENT ULTRASONIC REFLECTION COEFFICIENTS","authors":"Daria Olszowska, Gabriel Gallardo-Giozza, C. Torres‐Verdín","doi":"10.1190/geo2023-0505.1","DOIUrl":"https://doi.org/10.1190/geo2023-0505.1","url":null,"abstract":"Laboratory and field measurements often fail to identify small-scale variations in rock elastic properties. Due to limited spatial resolution, conventional laboratory methods cannot properly describe rock formations exhibiting a high degree of heterogeneity, thereby masking differences between stiff and compliant layers. Continuous sample measurements can mitigate this problem but are not widely used by the industry. We build upon our previous work and apply laboratory angle-dependent ultrasonic reflection coefficient (ADURC) measurements to achieve detailed two-dimensional descriptions of the elastic properties of complex rock samples. This method successfully yields high-resolution information on P- and S-wave velocities, as well as bulk density, across the surface of rock samples. Elastic properties are estimated using a nonlinear inversion algorithm that matches laboratory measurements with numerical simulations. Angle-dependent ultrasonic reflection coefficient data acquired at various sample locations enable detailed rock descriptions, where the effective measurement area is determined by the size of the receiver, measurement frequency, and incidence angle. Consequently, the sampling area is smaller compared to triaxial loading and acoustic transmission tests, where the resolution is controlled by sample size. Measurements conducted on samples exhibiting different levels of spatial complexity validate the capability of the ADURC method to identify small-scale heterogeneities. For the reported experiments, variations in angle-dependent reflectivity give rise to corresponding variations in the estimated P- and S-wave velocities and density which can exceed 60%. These small-scale variations across heterogeneous rock samples are often overlooked by conventional laboratory methods.#xD;#xD;","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835439","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}
Daria Olszowska, Gabriel Gallardo-Giozza, C. Torres‐Verdín
Laboratory and field measurements often fail to identify small-scale variations in rock elastic properties. Due to limited spatial resolution, conventional laboratory methods cannot properly describe rock formations exhibiting a high degree of heterogeneity, thereby masking differences between stiff and compliant layers. Continuous sample measurements can mitigate this problem but are not widely used by the industry. We build upon our previous work and apply laboratory angle-dependent ultrasonic reflection coefficient (ADURC) measurements to achieve detailed two-dimensional descriptions of the elastic properties of complex rock samples. This method successfully yields high-resolution information on P- and S-wave velocities, as well as bulk density, across the surface of rock samples. Elastic properties are estimated using a nonlinear inversion algorithm that matches laboratory measurements with numerical simulations. Angle-dependent ultrasonic reflection coefficient data acquired at various sample locations enable detailed rock descriptions, where the effective measurement area is determined by the size of the receiver, measurement frequency, and incidence angle. Consequently, the sampling area is smaller compared to triaxial loading and acoustic transmission tests, where the resolution is controlled by sample size. Measurements conducted on samples exhibiting different levels of spatial complexity validate the capability of the ADURC method to identify small-scale heterogeneities. For the reported experiments, variations in angle-dependent reflectivity give rise to corresponding variations in the estimated P- and S-wave velocities and density which can exceed 60%. These small-scale variations across heterogeneous rock samples are often overlooked by conventional laboratory methods.#xD;#xD;
实验室和实地测量往往无法确定岩石弹性特性的小尺度变化。由于空间分辨率有限，传统的实验室方法无法正确描述具有高度异质性的岩层，从而掩盖了坚硬层和顺应层之间的差异。连续样本测量可以缓解这一问题，但并未被业界广泛使用。我们在之前工作的基础上，应用实验室角度依赖性超声波反射系数（ADURC）测量方法，对复杂岩样的弹性特性进行了详细的二维描述。这种方法成功地获得了岩石样本表面 P 波和 S 波速度以及体积密度的高分辨率信息。使用非线性反演算法估算弹性特性，将实验室测量结果与数值模拟相匹配。在不同取样位置获取的与角度相关的超声波反射系数数据可对岩石进行详细描述，其中有效测量区域由接收器尺寸、测量频率和入射角度决定。因此，与三轴加载和声透射试验相比，取样面积较小，分辨率由样本大小控制。在具有不同空间复杂性的样品上进行的测量验证了 ADURC 方法识别小尺度异质性的能力。在报告的实验中，随角度变化的反射率会导致估算的 P 波和 S 波速度和密度出现相应的变化，变化率可超过 60%。传统的实验室方法往往会忽略这些异质岩石样本的小尺度变化；
{"title":"TWO-DIMENSIONAL IMAGING OF ELASTIC PROPERTIES OF ROCK CORE SAMPLES FROM MEASUREMENTS OF ANGLE-DEPENDENT ULTRASONIC REFLECTION COEFFICIENTS","authors":"Daria Olszowska, Gabriel Gallardo-Giozza, C. Torres‐Verdín","doi":"10.1190/geo2023-0505.1","DOIUrl":"https://doi.org/10.1190/geo2023-0505.1","url":null,"abstract":"Laboratory and field measurements often fail to identify small-scale variations in rock elastic properties. Due to limited spatial resolution, conventional laboratory methods cannot properly describe rock formations exhibiting a high degree of heterogeneity, thereby masking differences between stiff and compliant layers. Continuous sample measurements can mitigate this problem but are not widely used by the industry. We build upon our previous work and apply laboratory angle-dependent ultrasonic reflection coefficient (ADURC) measurements to achieve detailed two-dimensional descriptions of the elastic properties of complex rock samples. This method successfully yields high-resolution information on P- and S-wave velocities, as well as bulk density, across the surface of rock samples. Elastic properties are estimated using a nonlinear inversion algorithm that matches laboratory measurements with numerical simulations. Angle-dependent ultrasonic reflection coefficient data acquired at various sample locations enable detailed rock descriptions, where the effective measurement area is determined by the size of the receiver, measurement frequency, and incidence angle. Consequently, the sampling area is smaller compared to triaxial loading and acoustic transmission tests, where the resolution is controlled by sample size. Measurements conducted on samples exhibiting different levels of spatial complexity validate the capability of the ADURC method to identify small-scale heterogeneities. For the reported experiments, variations in angle-dependent reflectivity give rise to corresponding variations in the estimated P- and S-wave velocities and density which can exceed 60%. These small-scale variations across heterogeneous rock samples are often overlooked by conventional laboratory methods.#xD;#xD;","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775697","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}
Diverse Monte Carlo methods have gained widespread use across a broad range of applications. However, the challenge of 3D Monte Carlo sampling remains due to the curse of dimensionality. To date, only a few works have been published regarding 3D Monte Carlo sampling. This study aims to develop an efficient 3D trans-dimensional Monte Carlo framework for reconstructing the spatial geometry of an anomalous body using gravity data. The proposed framework can also quantify the uncertainty of the shape of an anomalous body recovered from geophysical measurements. To improve the computational efficiency of 3D Monte Carlo sampling, we propose a sparse geometry parameterization strategy. This approach adequately approximates the shape of a complex 3D anomalous body using a set of simple geometries, such as an ellipsoid. Each ellipsoid can be characterized by a few parameters, including the centroid, axes, and orientations, significantly reducing the number of parameters to be sampled. During sampling, we randomly perturb the number, locations, sizes, and orientations of the ellipsoids. To impose prior structural constraints from other geophysical methods, such as seismic imaging, we design a new method by placing a fixed layer oriented along the top boundary of the anomalous body. The fixed layer is then connected to the randomly sampled ellipsoids using an alpha shape, allowing us to estimate the geometry of the anomalous source body. The current work focuses on the reconstruction of salt bodies. We start with a synthetic spherical salt model and then conduct a more realistic study using a simplified 3D SEG/EAGE salt model. Lastly, we apply our method to the Galveston Island salt dome, offshore Texas. The numerical results demonstrate that our framework can effectively recover the shape of an anomalous body and quantify the uncertainty of the reconstructed geometry.
{"title":"3D Monte Carlo geometry inversion using gravity data","authors":"Xiaolong Wei, Jiajia Sun, Mrinal Sen","doi":"10.1190/geo2023-0498.1","DOIUrl":"https://doi.org/10.1190/geo2023-0498.1","url":null,"abstract":"Diverse Monte Carlo methods have gained widespread use across a broad range of applications. However, the challenge of 3D Monte Carlo sampling remains due to the curse of dimensionality. To date, only a few works have been published regarding 3D Monte Carlo sampling. This study aims to develop an efficient 3D trans-dimensional Monte Carlo framework for reconstructing the spatial geometry of an anomalous body using gravity data. The proposed framework can also quantify the uncertainty of the shape of an anomalous body recovered from geophysical measurements. To improve the computational efficiency of 3D Monte Carlo sampling, we propose a sparse geometry parameterization strategy. This approach adequately approximates the shape of a complex 3D anomalous body using a set of simple geometries, such as an ellipsoid. Each ellipsoid can be characterized by a few parameters, including the centroid, axes, and orientations, significantly reducing the number of parameters to be sampled. During sampling, we randomly perturb the number, locations, sizes, and orientations of the ellipsoids. To impose prior structural constraints from other geophysical methods, such as seismic imaging, we design a new method by placing a fixed layer oriented along the top boundary of the anomalous body. The fixed layer is then connected to the randomly sampled ellipsoids using an alpha shape, allowing us to estimate the geometry of the anomalous source body. The current work focuses on the reconstruction of salt bodies. We start with a synthetic spherical salt model and then conduct a more realistic study using a simplified 3D SEG/EAGE salt model. Lastly, we apply our method to the Galveston Island salt dome, offshore Texas. The numerical results demonstrate that our framework can effectively recover the shape of an anomalous body and quantify the uncertainty of the reconstructed geometry.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775712","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}
Full waveform inversion (FWI) is a large-scale nonlinear ill-posed problem for which computationally expensive Newton-type methods can become trapped in undesirable local minima, particularly when the initial model lacks a low-wavenumber component and the recorded data lacks low-frequency content. A modification to the Gauss-Newton (GN) method is proposed to address these issues. The standard GN system for multisource multireceiver FWI is reformulated into an equivalent matrix equation form, with the solution becoming a diagonal matrix rather than a vector as in the standard system. The search direction is transformed from a vector to a matrix by relaxing the diagonality constraint, effectively adding a degree of freedom to the subsurface offset axis. The relaxed system can be explicitly solved with only the inversion of two small matrices that deblur the data residual matrix along the source and receiver dimensions, which simplifies the inversion of the Hessian matrix. When used to solve the extended source FWI objective function, the Extended GN (EGN) method integrates the benefits of both model and source extension. The EGN method effectively combines the computational effectiveness of the reduced FWI method with the robustness characteristics of extended formulations and offers a promising solution for addressing the challenges of FWI. It bridges the gap between these extended formulations and the reduced FWI method, enhancing inversion robustness while maintaining computational efficiency. The robustness and stability of the EGN algorithm for waveform inversion are demonstrated numerically.
{"title":"An extended Gauss-Newton method for full waveform inversion","authors":"Ali Gholami","doi":"10.1190/geo2022-0673.1","DOIUrl":"https://doi.org/10.1190/geo2022-0673.1","url":null,"abstract":"Full waveform inversion (FWI) is a large-scale nonlinear ill-posed problem for which computationally expensive Newton-type methods can become trapped in undesirable local minima, particularly when the initial model lacks a low-wavenumber component and the recorded data lacks low-frequency content. A modification to the Gauss-Newton (GN) method is proposed to address these issues. The standard GN system for multisource multireceiver FWI is reformulated into an equivalent matrix equation form, with the solution becoming a diagonal matrix rather than a vector as in the standard system. The search direction is transformed from a vector to a matrix by relaxing the diagonality constraint, effectively adding a degree of freedom to the subsurface offset axis. The relaxed system can be explicitly solved with only the inversion of two small matrices that deblur the data residual matrix along the source and receiver dimensions, which simplifies the inversion of the Hessian matrix. When used to solve the extended source FWI objective function, the Extended GN (EGN) method integrates the benefits of both model and source extension. The EGN method effectively combines the computational effectiveness of the reduced FWI method with the robustness characteristics of extended formulations and offers a promising solution for addressing the challenges of FWI. It bridges the gap between these extended formulations and the reduced FWI method, enhancing inversion robustness while maintaining computational efficiency. The robustness and stability of the EGN algorithm for waveform inversion are demonstrated numerically.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775365","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}
Marine towed-streamer blended data are usually challenging to deblend because of the low dimensionality of the data. While the present ocean-bottom-cable (OBC) surveys produce well-sampled 3D receiver gathers, towed-streamer data have a lower sparsity in the transformed f - k domain. Here, we revisit two practical strategies to improve deblending performance. In the first strategy, we revisit applying 3D deblending to 2D surveys, which considers the shot domain as a sparsity-constrained domain. We compare the sparseness of the 2D and 3D FFT transformed domains by drawing the coefficients decaying curves. The 3D FFT transformed domain is much sparser than the 2D FFT transformed domain, according to the sparseness comparison. Thus, 3D deblending can obtain better performance than 2D deblending. In the second strategy, we revisit an improved deblending approach that combines traditional deblending and popcorn reconstruction, and other methods of coding sources. The popcorn shooting technique adds an extra level of constraint to the inversion because each source is coded with a different popcorn pattern. Thus, when deblending, convolution and deconvolution for each source with a predefined popcorn pattern will attenuate the interference that does not belong to the selected source. For both scenarios revisited here, we use both synthetic and field data examples with different complexity to demonstrate their superior performance.
由于数据维度较低，海洋拖曳流混合数据的去分层通常具有挑战性。目前的海洋底层电缆（OBC）勘测能产生采样良好的三维接收机采集数据，而拖曳流体数据在变换后的 f - k 域中具有较低的稀疏性。在此，我们重新探讨了两种提高去耦性能的实用策略。在第一种策略中，我们重新探讨了将三维排阻应用于二维勘测的问题，这种方法将射电域视为稀疏性受限域。我们通过绘制系数衰减曲线来比较二维和三维 FFT 变换域的稀疏性。根据稀疏性比较，三维 FFT 变换域比二维 FFT 变换域稀疏得多。因此，三维排阻可以获得比二维排阻更好的性能。在第二种策略中，我们重新探讨了一种改进的排错方法，它结合了传统排错和爆米花重构以及其他编码源方法。爆米花拍摄技术为反演增加了额外的限制，因为每个信号源都用不同的爆米花模式编码。因此，在进行去卷积时，用预定义的爆米花图案对每个信号源进行卷积和去卷积，就会减弱不属于所选信号源的干扰。对于本文重新讨论的这两种情况，我们使用了具有不同复杂性的合成和现场数据示例来证明它们的卓越性能。
{"title":"Revisiting two notable methods for improving the deblending performance of marine towed-streamer acquisition","authors":"Yangkang Chen, Min Zhou, Ray Abma","doi":"10.1190/geo2022-0621.1","DOIUrl":"https://doi.org/10.1190/geo2022-0621.1","url":null,"abstract":"Marine towed-streamer blended data are usually challenging to deblend because of the low dimensionality of the data. While the present ocean-bottom-cable (OBC) surveys produce well-sampled 3D receiver gathers, towed-streamer data have a lower sparsity in the transformed f - k domain. Here, we revisit two practical strategies to improve deblending performance. In the first strategy, we revisit applying 3D deblending to 2D surveys, which considers the shot domain as a sparsity-constrained domain. We compare the sparseness of the 2D and 3D FFT transformed domains by drawing the coefficients decaying curves. The 3D FFT transformed domain is much sparser than the 2D FFT transformed domain, according to the sparseness comparison. Thus, 3D deblending can obtain better performance than 2D deblending. In the second strategy, we revisit an improved deblending approach that combines traditional deblending and popcorn reconstruction, and other methods of coding sources. The popcorn shooting technique adds an extra level of constraint to the inversion because each source is coded with a different popcorn pattern. Thus, when deblending, convolution and deconvolution for each source with a predefined popcorn pattern will attenuate the interference that does not belong to the selected source. For both scenarios revisited here, we use both synthetic and field data examples with different complexity to demonstrate their superior performance.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139837584","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}
Marine towed-streamer blended data are usually challenging to deblend because of the low dimensionality of the data. While the present ocean-bottom-cable (OBC) surveys produce well-sampled 3D receiver gathers, towed-streamer data have a lower sparsity in the transformed f - k domain. Here, we revisit two practical strategies to improve deblending performance. In the first strategy, we revisit applying 3D deblending to 2D surveys, which considers the shot domain as a sparsity-constrained domain. We compare the sparseness of the 2D and 3D FFT transformed domains by drawing the coefficients decaying curves. The 3D FFT transformed domain is much sparser than the 2D FFT transformed domain, according to the sparseness comparison. Thus, 3D deblending can obtain better performance than 2D deblending. In the second strategy, we revisit an improved deblending approach that combines traditional deblending and popcorn reconstruction, and other methods of coding sources. The popcorn shooting technique adds an extra level of constraint to the inversion because each source is coded with a different popcorn pattern. Thus, when deblending, convolution and deconvolution for each source with a predefined popcorn pattern will attenuate the interference that does not belong to the selected source. For both scenarios revisited here, we use both synthetic and field data examples with different complexity to demonstrate their superior performance.
由于数据维度较低，海洋拖曳流混合数据的去分层通常具有挑战性。目前的海洋底层电缆（OBC）勘测能产生采样良好的三维接收机采集数据，而拖曳流体数据在变换后的 f - k 域中具有较低的稀疏性。在此，我们重新探讨了两种提高去耦性能的实用策略。在第一种策略中，我们重新探讨了将三维排阻应用于二维勘测的问题，这种方法将射电域视为稀疏性受限域。我们通过绘制系数衰减曲线来比较二维和三维 FFT 变换域的稀疏性。根据稀疏性比较，三维 FFT 变换域比二维 FFT 变换域稀疏得多。因此，三维排阻可以获得比二维排阻更好的性能。在第二种策略中，我们重新探讨了一种改进的排错方法，它结合了传统排错和爆米花重构以及其他编码源方法。爆米花拍摄技术为反演增加了额外的限制，因为每个信号源都用不同的爆米花模式编码。因此，在进行去卷积时，用预定义的爆米花图案对每个信号源进行卷积和去卷积，就会减弱不属于所选信号源的干扰。对于本文重新讨论的这两种情况，我们使用了具有不同复杂性的合成和现场数据示例来证明它们的卓越性能。
{"title":"Revisiting two notable methods for improving the deblending performance of marine towed-streamer acquisition","authors":"Yangkang Chen, Min Zhou, Ray Abma","doi":"10.1190/geo2022-0621.1","DOIUrl":"https://doi.org/10.1190/geo2022-0621.1","url":null,"abstract":"Marine towed-streamer blended data are usually challenging to deblend because of the low dimensionality of the data. While the present ocean-bottom-cable (OBC) surveys produce well-sampled 3D receiver gathers, towed-streamer data have a lower sparsity in the transformed f - k domain. Here, we revisit two practical strategies to improve deblending performance. In the first strategy, we revisit applying 3D deblending to 2D surveys, which considers the shot domain as a sparsity-constrained domain. We compare the sparseness of the 2D and 3D FFT transformed domains by drawing the coefficients decaying curves. The 3D FFT transformed domain is much sparser than the 2D FFT transformed domain, according to the sparseness comparison. Thus, 3D deblending can obtain better performance than 2D deblending. In the second strategy, we revisit an improved deblending approach that combines traditional deblending and popcorn reconstruction, and other methods of coding sources. The popcorn shooting technique adds an extra level of constraint to the inversion because each source is coded with a different popcorn pattern. Thus, when deblending, convolution and deconvolution for each source with a predefined popcorn pattern will attenuate the interference that does not belong to the selected source. For both scenarios revisited here, we use both synthetic and field data examples with different complexity to demonstrate their superior performance.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139777908","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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