Subsurface anisotropy is commonly induced by shale layers, aligned cracks and fine bedding, and has a significant impact on seismic wave propagation. Ignoring anisotropic effects during seismic migration will degrade image quality. Therefore, we derive a pure qP-wave equation with high accuracy for modeling seismic wave propagation in tilted transversely isotropic (TTI) media. However, the derived pure qP-wave equation requires a computationally expensive spectral-based method for performing numerical simulations. This is unsuitable for large-scale industrial applications, particularly three-dimension applications. For numerical efficiency, we first decompose the newly derived wave equation into some fractional differential operators and spatial derivatives. The spatial derivatives can be directly solved by conventional finite-difference (FD) approaches. Then, we employ an asymptotic approximation to find an equivalent form of fractional differential operators, obtaining scalar operators that we can discretize with the FD method. Numerical tests show that the proposed TTI pure qP-wave equation with an FD discretization can produce accurate and highly efficient wavefield simulations in TTI media. We also use the proposed TTI pure qP-wave equation with an FD discretization as a forward engine to implement TTI reverse time migration (RTM). Synthetic examples and a field data test demonstrate that the proposed TTI RTM can effectively correct the anisotropic effects, providing high-quality imaging results while maintaining good computational efficiency.
{"title":"Efficient pure qP-wave modeling and reverse time migration in tilted transversely isotropic media calculated by a finite-difference approach","authors":"Qiang Mao, Jianping Huang, Xinru Mu, Yujian Zhang","doi":"10.1190/geo2023-0631.1","DOIUrl":"https://doi.org/10.1190/geo2023-0631.1","url":null,"abstract":"Subsurface anisotropy is commonly induced by shale layers, aligned cracks and fine bedding, and has a significant impact on seismic wave propagation. Ignoring anisotropic effects during seismic migration will degrade image quality. Therefore, we derive a pure qP-wave equation with high accuracy for modeling seismic wave propagation in tilted transversely isotropic (TTI) media. However, the derived pure qP-wave equation requires a computationally expensive spectral-based method for performing numerical simulations. This is unsuitable for large-scale industrial applications, particularly three-dimension applications. For numerical efficiency, we first decompose the newly derived wave equation into some fractional differential operators and spatial derivatives. The spatial derivatives can be directly solved by conventional finite-difference (FD) approaches. Then, we employ an asymptotic approximation to find an equivalent form of fractional differential operators, obtaining scalar operators that we can discretize with the FD method. Numerical tests show that the proposed TTI pure qP-wave equation with an FD discretization can produce accurate and highly efficient wavefield simulations in TTI media. We also use the proposed TTI pure qP-wave equation with an FD discretization as a forward engine to implement TTI reverse time migration (RTM). Synthetic examples and a field data test demonstrate that the proposed TTI RTM can effectively correct the anisotropic effects, providing high-quality imaging results while maintaining good computational efficiency.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141674126","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}
K. Luo, Zhaoyun Zong, Xingyao Yin, L. Ji, Yaming Yang
Compared with other sedimentary rocks, the strong elastic anisotropy of shale is extremely prominent, which is mainly caused by the preferred orientation and platy nature of its clay minerals. Especially in seismic reservoir characterization, a suitable and correct estimation of the shale elastic anisotropy can improve the accuracy of the shale seismic inversion and prediction. Due to the long-term compaction of shale and the rearrangement of minerals, its microstructure and macrostructure are more complex, resulting in obvious anisotropic characteristics of shale. Existing methods do not incorporate the impact of non-plate particles on clay platelets, or indirectly incorporate it through empirical formulas, resulting in poor applicability and errors in the rock physics models. To reveal the main causes of the anisotropy of clay minerals, a theoretical model incorporating the effect of compaction and non-plate particles on the preferred orientation of clay platelets is developed using experimental data and electronic scanning results. Based on theoretical analysis, an orientation distribution function (ODF) based on the effect of compaction and non-plate particles is derived, which not only incorporates the influence of compaction but also further incorporates the effect of other non-plate particles such as quartz, which makes the established shale anisotropic rock physics model more reasonable and accurate. Then, an improved anisotropic shale rock physics model is proposed using the compaction and non-plate particles based ODF. The prediction results show that the presence of non-plate particles has an inhibitory effect on the preferred orientation of clay platelets, which is verified by the measured experimental data and indicates that the proposed method is reliable and effective.
{"title":"Shale anisotropic rock physics model incorporating the effect of compaction and non-plate mixtures on clay preferred orientation","authors":"K. Luo, Zhaoyun Zong, Xingyao Yin, L. Ji, Yaming Yang","doi":"10.1190/geo2023-0591.1","DOIUrl":"https://doi.org/10.1190/geo2023-0591.1","url":null,"abstract":"Compared with other sedimentary rocks, the strong elastic anisotropy of shale is extremely prominent, which is mainly caused by the preferred orientation and platy nature of its clay minerals. Especially in seismic reservoir characterization, a suitable and correct estimation of the shale elastic anisotropy can improve the accuracy of the shale seismic inversion and prediction. Due to the long-term compaction of shale and the rearrangement of minerals, its microstructure and macrostructure are more complex, resulting in obvious anisotropic characteristics of shale. Existing methods do not incorporate the impact of non-plate particles on clay platelets, or indirectly incorporate it through empirical formulas, resulting in poor applicability and errors in the rock physics models. To reveal the main causes of the anisotropy of clay minerals, a theoretical model incorporating the effect of compaction and non-plate particles on the preferred orientation of clay platelets is developed using experimental data and electronic scanning results. Based on theoretical analysis, an orientation distribution function (ODF) based on the effect of compaction and non-plate particles is derived, which not only incorporates the influence of compaction but also further incorporates the effect of other non-plate particles such as quartz, which makes the established shale anisotropic rock physics model more reasonable and accurate. Then, an improved anisotropic shale rock physics model is proposed using the compaction and non-plate particles based ODF. The prediction results show that the presence of non-plate particles has an inhibitory effect on the preferred orientation of clay platelets, which is verified by the measured experimental data and indicates that the proposed method is reliable and effective.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141673523","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}
Ray-tracing in anisotropic media is pivotal for interpreting observed seismic data and creating high-resolution images of subsurface structures, which are crucial in exploration geophysics. Elliptical anisotropy, a simplified model that approximates a transversely isotropic medium, is particularly relevant for geologic settings like shale formations or stressed sedimentary layers where directional dependencies of seismic velocities are pronounced. This paper presents an analytical solution of the ray-tracing equations for a two-dimensional inhomogeneous and anisotropic medium, where velocities depend elliptically on direction and increase linearly with depth – a scenario frequently encountered in stratified geologic formations. Unlike previous studies that assume constant ellipticity throughout the medium, our approach allows for variations in ellipticity, providing a more flexible and realistic representation of subsurface anisotropy. The phase velocities along the x- and z-axis are not necessarily multiples of each other at every point, offering a generalized version of the elliptical anisotropy. This enhancement may enable more accurate predictions and interpretations of observed seismic data, particularly in complex exploration scenarios. The analytical solution yields expressions for both the ray paths and the wavefront normals. By setting the normals of the wavefront at the seismic source point and the location of the seismic source as the initial conditions in phase space, we explore the evolution of these wavefront normal curves across different types of the elliptical anisotropy. Our innovative approach includes plotting the evolution of wavefront normal curves on the generalized momentum coordinate plane of the phase space – that commonly overlooked in traditional models focused only on position coordinates.
各向异性介质中的射线追踪对于解释观测到的地震数据和绘制地下结构的高分辨率图像至关重要，这在勘探地球物理中至关重要。椭圆各向异性是一种近似横向各向同性介质的简化模型，尤其适用于页岩地层或受压沉积层等地震速度具有明显方向依赖性的地质环境。本文提出了二维非均质和各向异性介质的射线追踪方程的解析解，在这种介质中，速度与方向成椭圆关系，并随深度线性增加--这是在层状地质构造中经常遇到的情况。与以往假设整个介质椭圆度恒定的研究不同，我们的方法允许椭圆度的变化，从而更灵活、更真实地反映了地下各向异性。沿 x 轴和 z 轴的相速度不一定是每一点的倍数，从而提供了椭圆各向异性的广义版本。这种改进可以更准确地预测和解释观测到的地震数据，尤其是在复杂的勘探情况下。解析解可以得到射线路径和波前法线的表达式。通过将震源点的波面法线和震源位置作为相空间的初始条件，我们探索了这些波面法线曲线在不同类型的椭圆各向异性中的演变。我们的创新方法包括在相空间的广义动量坐标平面上绘制波前法线曲线的演变图--传统模型通常只关注位置坐标，而忽略了这一点。
{"title":"Analytical Solutions of Ray-Tracing Equations in Generalized Elliptical Anisotropy","authors":"Çaðrý Diner, A. Beyaz","doi":"10.1190/geo2023-0464.1","DOIUrl":"https://doi.org/10.1190/geo2023-0464.1","url":null,"abstract":"Ray-tracing in anisotropic media is pivotal for interpreting observed seismic data and creating high-resolution images of subsurface structures, which are crucial in exploration geophysics. Elliptical anisotropy, a simplified model that approximates a transversely isotropic medium, is particularly relevant for geologic settings like shale formations or stressed sedimentary layers where directional dependencies of seismic velocities are pronounced. This paper presents an analytical solution of the ray-tracing equations for a two-dimensional inhomogeneous and anisotropic medium, where velocities depend elliptically on direction and increase linearly with depth – a scenario frequently encountered in stratified geologic formations. Unlike previous studies that assume constant ellipticity throughout the medium, our approach allows for variations in ellipticity, providing a more flexible and realistic representation of subsurface anisotropy. The phase velocities along the x- and z-axis are not necessarily multiples of each other at every point, offering a generalized version of the elliptical anisotropy. This enhancement may enable more accurate predictions and interpretations of observed seismic data, particularly in complex exploration scenarios. The analytical solution yields expressions for both the ray paths and the wavefront normals. By setting the normals of the wavefront at the seismic source point and the location of the seismic source as the initial conditions in phase space, we explore the evolution of these wavefront normal curves across different types of the elliptical anisotropy. Our innovative approach includes plotting the evolution of wavefront normal curves on the generalized momentum coordinate plane of the phase space – that commonly overlooked in traditional models focused only on position coordinates.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141676833","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}
Julia Correa, S. Glubokovskikh, Avinash Nayak, Linqing Luo, T. Wood, Xiaoyu Zhu, Jonathan Ajo-Franklin, B. Freifeld
Understanding hydraulic fracturing is crucial to improving the stimulation of unconventional reservoirs and increasing fluid production. This study proposes a novel seismic monitoring technology, using distributed acoustic sensing (DAS) and surface orbital vibrators (SOV), to capture fracture seismic response and mechanical properties at high temporal intervals. We analyze continuous time-lapse Vertical Seismic Profiling (VSP) data acquired every hour during the first nine days of treatment of an unconventional reservoir in the Austin Chalk/Eagle Ford Shale Laboratory. The VSP data contains clear seismic signals scattered from the activated fractures. The spatiotemporal changes of the fracture reflectivity revealed by the SOV/DAS data correlate well with the observations of fracture locations inferred from low-frequency DAS data. These results capture the fracture opening and closure processes, as well as highlighting potential pre-stage activations of the fractures due to hydraulic connectivity with pre-existing fracture systems. Therefore, analysis of the presented data set provides a unique opportunity to understand fracture initiation and subsequent evolution, not only in the context of unconventional resources, but also in enhanced geothermal systems.
了解水力压裂对改善非常规储层的激励和提高液体产量至关重要。本研究提出了一种新型地震监测技术，利用分布式声学传感（DAS）和表面轨道振动器（SOV），以高时间间隔捕捉压裂地震响应和机械特性。我们分析了在奥斯汀白垩纪/鹰滩页岩实验室处理非常规储层的前九天中每小时采集的连续延时垂直地震剖面（VSP）数据。VSP 数据包含从激活的裂缝中散射出的清晰地震信号。SOV/DAS 数据显示的裂缝反射率时空变化与低频 DAS 数据推断的裂缝位置观测结果非常吻合。这些结果捕捉到了裂缝的打开和闭合过程，并突出显示了由于与原有裂缝系统的水力连接而可能导致的裂缝前期激活。因此，对所提供的数据集进行分析，不仅为了解非常规资源，而且为了解增强地热系统中的断裂起始和后续演化提供了一个独特的机会。
{"title":"Continuous seismic monitoring of hydraulic fracturing reveals complex subsurface dynamics: observations using distributed acoustic sensing and surface orbital vibrators","authors":"Julia Correa, S. Glubokovskikh, Avinash Nayak, Linqing Luo, T. Wood, Xiaoyu Zhu, Jonathan Ajo-Franklin, B. Freifeld","doi":"10.1190/geo2023-0785.1","DOIUrl":"https://doi.org/10.1190/geo2023-0785.1","url":null,"abstract":"Understanding hydraulic fracturing is crucial to improving the stimulation of unconventional reservoirs and increasing fluid production. This study proposes a novel seismic monitoring technology, using distributed acoustic sensing (DAS) and surface orbital vibrators (SOV), to capture fracture seismic response and mechanical properties at high temporal intervals. We analyze continuous time-lapse Vertical Seismic Profiling (VSP) data acquired every hour during the first nine days of treatment of an unconventional reservoir in the Austin Chalk/Eagle Ford Shale Laboratory. The VSP data contains clear seismic signals scattered from the activated fractures. The spatiotemporal changes of the fracture reflectivity revealed by the SOV/DAS data correlate well with the observations of fracture locations inferred from low-frequency DAS data. These results capture the fracture opening and closure processes, as well as highlighting potential pre-stage activations of the fractures due to hydraulic connectivity with pre-existing fracture systems. Therefore, analysis of the presented data set provides a unique opportunity to understand fracture initiation and subsequent evolution, not only in the context of unconventional resources, but also in enhanced geothermal systems.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141681269","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}
Changxiao Sun, Alison Malcolm, Rajiv Kumar, Weijian Mao
In order to maximize the utility of seismic imaging and inversion results, we need to compute not only a final image but also quantify the uncertainty in that image. While the most thorough approach to quantify the uncertainty is to use a method such as Markov chain Monte Carlo (MCMC), which systematically samples the entire posterior distribution, this is often inefficient and not all applications require a full representation of the posterior. We use normalizing flows (NF), a machine learning technique to perform uncertainty quantification (UQ) in full waveform inversion (FWI), specifically for time-lapse data. As with any machine learning algorithm, the NF learns only the mapping from the part of the prior spanned by the training data to the distribution of final models spanned by the training data. Here we make use of this property to perform UQ efficiently by learning a mapping from the prior to the distribution that really characterizes the model perturbations within a specific range. Our approach involves using a range of starting models, paired with final models from a standard FWI as training data. While this does not capture the full posterior of the FWI problem, it enables us to quantify the uncertainties associated with updating from an initial to a final model. Since our target is to perform UQ for time-lapse imaging, we use a local wave-equation solver that allows us to solve the wave equation in a small subset of our entire model, thereby keeping computational costs low. Numerical examples demonstrate that incorporating the training step for NF provides a distribution of model perturbations, which is dependent on a designated prior, to quantify the uncertainty of FWI results.
{"title":"Enabling Uncertainty Quantification in a standard Full Waveform Inversion method using Normalizing Flows","authors":"Changxiao Sun, Alison Malcolm, Rajiv Kumar, Weijian Mao","doi":"10.1190/geo2023-0755.1","DOIUrl":"https://doi.org/10.1190/geo2023-0755.1","url":null,"abstract":"In order to maximize the utility of seismic imaging and inversion results, we need to compute not only a final image but also quantify the uncertainty in that image. While the most thorough approach to quantify the uncertainty is to use a method such as Markov chain Monte Carlo (MCMC), which systematically samples the entire posterior distribution, this is often inefficient and not all applications require a full representation of the posterior. We use normalizing flows (NF), a machine learning technique to perform uncertainty quantification (UQ) in full waveform inversion (FWI), specifically for time-lapse data. As with any machine learning algorithm, the NF learns only the mapping from the part of the prior spanned by the training data to the distribution of final models spanned by the training data. Here we make use of this property to perform UQ efficiently by learning a mapping from the prior to the distribution that really characterizes the model perturbations within a specific range. Our approach involves using a range of starting models, paired with final models from a standard FWI as training data. While this does not capture the full posterior of the FWI problem, it enables us to quantify the uncertainties associated with updating from an initial to a final model. Since our target is to perform UQ for time-lapse imaging, we use a local wave-equation solver that allows us to solve the wave equation in a small subset of our entire model, thereby keeping computational costs low. Numerical examples demonstrate that incorporating the training step for NF provides a distribution of model perturbations, which is dependent on a designated prior, to quantify the uncertainty of FWI results.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141682529","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}
Wei Zhang, Xuebao Guo, Matteo Ravasi, Jinghuai Gao, Wenbo Sun
Image-domain least-squares migration (IDLSM) is an established approach to recover high-fidelity seismic images of subsurface reflectors; this is achieved by removing the blurring effects of the Hessian operator in the standard migration approach with the help of so-called point spread functions (PSFs). However, most of the existing IDLSM approaches recover an angle-independent image of the subsurface reflectors, which is not suitable for subsequent amplitude versus angle (AVA) analysis. To overcome this limitation, we have developed an angle-dependent IDLSM approach, denoted as AD-IDLSM, which can recover a high-fidelity and high-resolution angle-dependent reflectivity image of subsurface reflectors. The problem is formulated here as an angle-dependent image-domain inversion with PSFs computed by means of full-wave Green's function. More specifically, we derive an analytical expression to compute angle-dependent PSFs by means of a wave-equation-based Kirchhoff migration (WEBKM) engine, where a localization assumption is made in both spatial directions to decrease the computational cost and memory overhead. The amplitude and traveltime of the Green's functions involved in the WEBKM approach are estimated by the excitation-amplitude and excitation-time of the full-wave wavefield. The scattering angle is then approximately estimated from the Poynting vector of the excitation-time field. To stabilize the solution of AD-IDLSM, we utilize a regularization scheme that applies a second derivative along the direction of the reflection angle of angle-domain common-image gathers (ADCIGs) to ensure continuity in the amplitude variations versus angle and suppress migration artifacts. We demonstrate the effectiveness of the AD-IDLSM approach through two synthetic data and a field marine dataset; the presented results confirm that AD-IDLSM can create ADCIGs with higher spatial resolution, better amplitude-fidelity, and fewer migration artifacts, compared to those obtained by its migration counterpart. Moreover, AD-IDLSM amplitude variations with angle are shown to closely resemble the theoretical AVA curve of the reflectors.
{"title":"Angle-dependent image-domain least-squares migration through analytical point spread functions","authors":"Wei Zhang, Xuebao Guo, Matteo Ravasi, Jinghuai Gao, Wenbo Sun","doi":"10.1190/geo2023-0499.1","DOIUrl":"https://doi.org/10.1190/geo2023-0499.1","url":null,"abstract":"Image-domain least-squares migration (IDLSM) is an established approach to recover high-fidelity seismic images of subsurface reflectors; this is achieved by removing the blurring effects of the Hessian operator in the standard migration approach with the help of so-called point spread functions (PSFs). However, most of the existing IDLSM approaches recover an angle-independent image of the subsurface reflectors, which is not suitable for subsequent amplitude versus angle (AVA) analysis. To overcome this limitation, we have developed an angle-dependent IDLSM approach, denoted as AD-IDLSM, which can recover a high-fidelity and high-resolution angle-dependent reflectivity image of subsurface reflectors. The problem is formulated here as an angle-dependent image-domain inversion with PSFs computed by means of full-wave Green's function. More specifically, we derive an analytical expression to compute angle-dependent PSFs by means of a wave-equation-based Kirchhoff migration (WEBKM) engine, where a localization assumption is made in both spatial directions to decrease the computational cost and memory overhead. The amplitude and traveltime of the Green's functions involved in the WEBKM approach are estimated by the excitation-amplitude and excitation-time of the full-wave wavefield. The scattering angle is then approximately estimated from the Poynting vector of the excitation-time field. To stabilize the solution of AD-IDLSM, we utilize a regularization scheme that applies a second derivative along the direction of the reflection angle of angle-domain common-image gathers (ADCIGs) to ensure continuity in the amplitude variations versus angle and suppress migration artifacts. We demonstrate the effectiveness of the AD-IDLSM approach through two synthetic data and a field marine dataset; the presented results confirm that AD-IDLSM can create ADCIGs with higher spatial resolution, better amplitude-fidelity, and fewer migration artifacts, compared to those obtained by its migration counterpart. Moreover, AD-IDLSM amplitude variations with angle are shown to closely resemble the theoretical AVA curve of the reflectors.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141688350","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 quality proves pivotal to its interpretation, necessitating the reduction of noise and the enhancement of resolution. Both traditional and deep learning-based solutions have achieved varying degrees of success on low-dimensional seismic data. In this paper, we develop a deep generative solution for high-dimensional seismic data denoising and super-resolution through the innovative application of denoising diffusion probabilistic models (DDPMs), which we refer to as MD Diffusion. MD Diffusion treats degraded seismic data as a conditional prior that guides the generative process, enhancing the capability to recover data from complex noise. By iteratively training an implicit probability model, we achieve a sampling speed ten times faster than the original DDPM. Extensive training allows us to explicitly model complex seismic data distributions in synthetic datasets to transfer this knowledge to the process of recovering field data with unknown noise levels, thereby attenuating noise and enhancing resolution in an unsupervised manner. Quantitative metrics and qualitative results for 3D synthetic and field data demonstrate that MD Diffusion exhibits superior performance in high-dimensional seismic data denoising and super-resolution compared to the UNet and Seismic Super-Resolution methods, especially in enhancing thin-layer structures and preserving fault features, and shows the potential for application to higher-dimensional data.
{"title":"Diffusion Models for Multidimensional Seismic Noise Attenuation and Super-Resolution","authors":"Yuan Xiao, Kewen Li, Yimin Dou, Wentao Li, Zhixuan Yang, Xinyuan Zhu","doi":"10.1190/geo2023-0676.1","DOIUrl":"https://doi.org/10.1190/geo2023-0676.1","url":null,"abstract":"Seismic data quality proves pivotal to its interpretation, necessitating the reduction of noise and the enhancement of resolution. Both traditional and deep learning-based solutions have achieved varying degrees of success on low-dimensional seismic data. In this paper, we develop a deep generative solution for high-dimensional seismic data denoising and super-resolution through the innovative application of denoising diffusion probabilistic models (DDPMs), which we refer to as MD Diffusion. MD Diffusion treats degraded seismic data as a conditional prior that guides the generative process, enhancing the capability to recover data from complex noise. By iteratively training an implicit probability model, we achieve a sampling speed ten times faster than the original DDPM. Extensive training allows us to explicitly model complex seismic data distributions in synthetic datasets to transfer this knowledge to the process of recovering field data with unknown noise levels, thereby attenuating noise and enhancing resolution in an unsupervised manner. Quantitative metrics and qualitative results for 3D synthetic and field data demonstrate that MD Diffusion exhibits superior performance in high-dimensional seismic data denoising and super-resolution compared to the UNet and Seismic Super-Resolution methods, especially in enhancing thin-layer structures and preserving fault features, and shows the potential for application to higher-dimensional data.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141685271","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}
Debao Guo, Jinlai Bian, Yunqiu Song, Yong Yang, Zailin Yang
The development of tunnels or the laying of underground pipelines are essential engineering projects in modern society, and in canyon tunnels and underground pipeline projects, the surface motion and cavity edge motion have been topics of concern in ground vibration problems. In this paper, we investigate the wave scattering problem in an elastic half-space anisotropic medium containing a semicircular canyon and a subsurface movable cylindrical cavity by using the wave function expansion method, the complex function method and the mirror method. By deriving the governing equation and transforming it into the standard form of the Helmholtz equation satisfying the zero-stress boundary condition, we solve the corresponding displacement functions. Introducing a position correction coefficient, the scattered wave field in a half-space anisotropic medium is constructed by the mirror method, which improves the problem of scattered wave source singularity in anisotropic half-space medium. Then, combining the free boundary conditions with a Fourier series expansion method we solve for the unknown coefficients in the equations. The correctness of the method is verified by degenerating it to a classical analytic solution. Finally, using frequency and time domain analysis, we investigate the effects of the relevant parameters on the surface motion| w1|( w), the dynamic stress concentration factor (DSCF) and the displacement amplitude| w2|. The results show that rock anisotropy and the presence of semicircular canyons have a significant effect on the dynamic response of subsurface structures. This not only provides a theoretical basis for practical unlined tunnels or pipeline projects, but can also provide a basis for seismic design of underground structures.
{"title":"Response of Semicircular Canyons and Movable Cylindrical Cavities to SH Waves in Anisotropic Half-space Geology","authors":"Debao Guo, Jinlai Bian, Yunqiu Song, Yong Yang, Zailin Yang","doi":"10.1190/geo2023-0598.1","DOIUrl":"https://doi.org/10.1190/geo2023-0598.1","url":null,"abstract":"The development of tunnels or the laying of underground pipelines are essential engineering projects in modern society, and in canyon tunnels and underground pipeline projects, the surface motion and cavity edge motion have been topics of concern in ground vibration problems. In this paper, we investigate the wave scattering problem in an elastic half-space anisotropic medium containing a semicircular canyon and a subsurface movable cylindrical cavity by using the wave function expansion method, the complex function method and the mirror method. By deriving the governing equation and transforming it into the standard form of the Helmholtz equation satisfying the zero-stress boundary condition, we solve the corresponding displacement functions. Introducing a position correction coefficient, the scattered wave field in a half-space anisotropic medium is constructed by the mirror method, which improves the problem of scattered wave source singularity in anisotropic half-space medium. Then, combining the free boundary conditions with a Fourier series expansion method we solve for the unknown coefficients in the equations. The correctness of the method is verified by degenerating it to a classical analytic solution. Finally, using frequency and time domain analysis, we investigate the effects of the relevant parameters on the surface motion| w1|( w), the dynamic stress concentration factor (DSCF) and the displacement amplitude| w2|. The results show that rock anisotropy and the presence of semicircular canyons have a significant effect on the dynamic response of subsurface structures. This not only provides a theoretical basis for practical unlined tunnels or pipeline projects, but can also provide a basis for seismic design of underground structures.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141102119","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}
Despite additional availability of laboratory data from water-saturated sandstone at seismic frequencies, measurements of rock samples saturated with high viscous fluids, particularly at partial saturation, are still rare. To quantify the effects of fluid viscosity and saturation levels on seismic dispersion and attenuation characteristics, we conducted two comparative forced-oscillation measurements in partially saturated sandstone with varying fluid viscosity (e.g., water, glycerin) at seismic frequencies (2-400 Hz). The results demonstrate that both fluid viscosity and saturation levels substantially influence the dispersion and attenuation characteristics at the measured frequencies. Significant dispersion and attenuation are observed in the presence of a relatively small amount of gas (∼6% - 8%) for both glycerin and water saturation cases but vary in their magnitudes and characteristic frequencies. Specifically, the maximum extensional attenuation (∼0.024) occurs at approximately 200 Hz for water-saturated rock at 94% saturation, while at around 30 Hz with a peak of 0.032 for glycerin-saturated rock at 92% saturation. Based on theoretical modeling analysis, we suggest that mesoscopic fluid flow might be a dominant mechanism accounting for the observed attenuation in partial water or glycerin saturation, while the microscopic (squirt) flow mechanism possibly dominates the fully saturated cases.
{"title":"Effects of fluid saturation and viscosity on seismic dispersion characteristics in Berea sandstone","authors":"Qianqian Wei, De-hua Han, Hui Li, Jianhua Wang, Yang Wang, Jianjun Chen","doi":"10.1190/geo2023-0350.1","DOIUrl":"https://doi.org/10.1190/geo2023-0350.1","url":null,"abstract":"Despite additional availability of laboratory data from water-saturated sandstone at seismic frequencies, measurements of rock samples saturated with high viscous fluids, particularly at partial saturation, are still rare. To quantify the effects of fluid viscosity and saturation levels on seismic dispersion and attenuation characteristics, we conducted two comparative forced-oscillation measurements in partially saturated sandstone with varying fluid viscosity (e.g., water, glycerin) at seismic frequencies (2-400 Hz). The results demonstrate that both fluid viscosity and saturation levels substantially influence the dispersion and attenuation characteristics at the measured frequencies. Significant dispersion and attenuation are observed in the presence of a relatively small amount of gas (∼6% - 8%) for both glycerin and water saturation cases but vary in their magnitudes and characteristic frequencies. Specifically, the maximum extensional attenuation (∼0.024) occurs at approximately 200 Hz for water-saturated rock at 94% saturation, while at around 30 Hz with a peak of 0.032 for glycerin-saturated rock at 92% saturation. Based on theoretical modeling analysis, we suggest that mesoscopic fluid flow might be a dominant mechanism accounting for the observed attenuation in partial water or glycerin saturation, while the microscopic (squirt) flow mechanism possibly dominates the fully saturated cases.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141098938","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}
We develop a modified fluid-saturated thermoporoelastic model by introducing two temperature equations to account for the temperature differences between the solid skeleton and the pore filling. The modified two-temperature-generalized thermoporoelastic (TTG) equation is an extension of the classical single-temperature (ST) Lord-Shulman (LS), Green-Lindsay (GL) and generalized LS theories. It predicts four compressional waves and one shear wave based on the analysis of inhomogeneous plane waves. We study the exact reflection and transmission coefficients (R/T) at the interface separating two thermoporoelastic half-spaces and develop an amplitude-variation-with-offset (AVO) approximation. Comparison with the Biot poroelastic case of the water/oil contact shows that the TTG model reproduces the exact R/T results. The AVO response of oil, gas, and real CO2 geosequestration reservoirs illustrates the practical applicability of the proposed model and provides the theoretical basis for the exploration of high-temperature resources.
{"title":"Reflection, transmission and AVO response of inhomogeneous plane waves in thermoporoelastic media with two-temperature equations of heat conduction","authors":"W. Hou, Li-Yun Fu, J. Carcione","doi":"10.1190/geo2023-0625.1","DOIUrl":"https://doi.org/10.1190/geo2023-0625.1","url":null,"abstract":"We develop a modified fluid-saturated thermoporoelastic model by introducing two temperature equations to account for the temperature differences between the solid skeleton and the pore filling. The modified two-temperature-generalized thermoporoelastic (TTG) equation is an extension of the classical single-temperature (ST) Lord-Shulman (LS), Green-Lindsay (GL) and generalized LS theories. It predicts four compressional waves and one shear wave based on the analysis of inhomogeneous plane waves. We study the exact reflection and transmission coefficients (R/T) at the interface separating two thermoporoelastic half-spaces and develop an amplitude-variation-with-offset (AVO) approximation. Comparison with the Biot poroelastic case of the water/oil contact shows that the TTG model reproduces the exact R/T results. The AVO response of oil, gas, and real CO2 geosequestration reservoirs illustrates the practical applicability of the proposed model and provides the theoretical basis for the exploration of high-temperature resources.","PeriodicalId":509604,"journal":{"name":"GEOPHYSICS","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141105711","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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