We develop an integrated workflow that uses deep learning (DL) based approaches for processing and inverting ATEM (Airborne Transient Electromagnetic Method) data. Our novel workflow automates these preprocessing steps and enables real-time inversion in the field. Thus, we present an entire inversion workflow using three DL networks that covers all steps from preprocessing to imaging. The preprocessing DL network performs interpolation to discard data that are severely noisecontaminated and suppress the effects of noise in late-time channel. We employ an inversion DL network and a depth of investigation (DOI) network to generate images of subsurface resistivities exclusively within the DOI range where reliable predictions can be made. To optimize the inversion process, our approach focuses on designing the inversion DL network to simultaneously minimize both data misfit and model misfit. By addressing these two aspects, we ensure a more robust outcome in the final resistivity images. The practical applicability of the workflow is verified by comparing the imaging results of field data to those of conventional inversion and geological interpretation. Each workflow is near -automatic and very fast; we expect that our workflow will contribute to the development of real-time imaging software of ATEM survey which expands the applications of ATEM survey in various fields.
{"title":"Deep learning-based airborne transient electromagnetic inversion providing the depth of investigation","authors":"Hyeonwoo Kang, M. Bang, S. Seol, J. Byun","doi":"10.1190/geo2022-0723.1","DOIUrl":"https://doi.org/10.1190/geo2022-0723.1","url":null,"abstract":"We develop an integrated workflow that uses deep learning (DL) based approaches for processing and inverting ATEM (Airborne Transient Electromagnetic Method) data. Our novel workflow automates these preprocessing steps and enables real-time inversion in the field. Thus, we present an entire inversion workflow using three DL networks that covers all steps from preprocessing to imaging. The preprocessing DL network performs interpolation to discard data that are severely noisecontaminated and suppress the effects of noise in late-time channel. We employ an inversion DL network and a depth of investigation (DOI) network to generate images of subsurface resistivities exclusively within the DOI range where reliable predictions can be made. To optimize the inversion process, our approach focuses on designing the inversion DL network to simultaneously minimize both data misfit and model misfit. By addressing these two aspects, we ensure a more robust outcome in the final resistivity images. The practical applicability of the workflow is verified by comparing the imaging results of field data to those of conventional inversion and geological interpretation. Each workflow is near -automatic and very fast; we expect that our workflow will contribute to the development of real-time imaging software of ATEM survey which expands the applications of ATEM survey in various fields.","PeriodicalId":55102,"journal":{"name":"Geophysics","volume":"308 1","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139252342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thin and highly conductive objects are challenging to model in 3D direct current (dc) problems since they often require excessive mesh refinement that leads to a significant increase in computational costs. RESnet is a novel algorithm that converts any 3D geo-electric simulation to solving an equivalent 3D resistor network circuit. Two features of RESnet make it an attractive choice in the dc modeling of thin and conductive objects. First, in addition to the conductivity with units of S/m defined at the cell centers (cell conductivity), RESnet allows conductive properties defined on mesh faces and edges as face conductivity with units of S and edge conductivity with units of S·m, respectively. Face conductivity is the thickness-integrated conductivity, which preserves the electric effect of sheet-like conductors without an explicit statement in the mesh. Similarly, edge conductivity is the product of the cross-sectional area and the intrinsic conductivity of a line-like conductive object. Modeling thin objects using face and edge conductivity can avoid extremely small mesh grids if the dc problem concerns electric field responses at a much larger scale. Second, once the original simulation is transformed into an equivalent resistor network, certain types of infrastructure, like above-ground metallic pipes, can be conveniently modeled by directly connecting the circuit nodes, which cannot interact with each other in conventional modeling programs. Bilingually implemented in Matlab and Python, the algorithm has been made open source to promote wide use in academia and industry. Three examples are provided to validate its numerical accuracy, demonstrate its capability in modeling steel well casings, and show how it can be used to simulate the effect of complex metallic infrastructure on dc resistivity data.
{"title":"RESnet: 3D direct current resistivity simulation using the equivalent resistor network circuit","authors":"Dikun Yang","doi":"10.1190/geo2023-0336.1","DOIUrl":"https://doi.org/10.1190/geo2023-0336.1","url":null,"abstract":"Thin and highly conductive objects are challenging to model in 3D direct current (dc) problems since they often require excessive mesh refinement that leads to a significant increase in computational costs. RESnet is a novel algorithm that converts any 3D geo-electric simulation to solving an equivalent 3D resistor network circuit. Two features of RESnet make it an attractive choice in the dc modeling of thin and conductive objects. First, in addition to the conductivity with units of S/m defined at the cell centers (cell conductivity), RESnet allows conductive properties defined on mesh faces and edges as face conductivity with units of S and edge conductivity with units of S·m, respectively. Face conductivity is the thickness-integrated conductivity, which preserves the electric effect of sheet-like conductors without an explicit statement in the mesh. Similarly, edge conductivity is the product of the cross-sectional area and the intrinsic conductivity of a line-like conductive object. Modeling thin objects using face and edge conductivity can avoid extremely small mesh grids if the dc problem concerns electric field responses at a much larger scale. Second, once the original simulation is transformed into an equivalent resistor network, certain types of infrastructure, like above-ground metallic pipes, can be conveniently modeled by directly connecting the circuit nodes, which cannot interact with each other in conventional modeling programs. Bilingually implemented in Matlab and Python, the algorithm has been made open source to promote wide use in academia and industry. Three examples are provided to validate its numerical accuracy, demonstrate its capability in modeling steel well casings, and show how it can be used to simulate the effect of complex metallic infrastructure on dc resistivity data.","PeriodicalId":55102,"journal":{"name":"Geophysics","volume":"160 4","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139257395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Acoustic impedance (AI) inversion plays a vital role in seismic interpretation because AI contains valuable information on lithology and contributes to reservoir characterization. However, the effect of anelastic attenuation dissipates the energy and distorts the phase of seismic waves during their propagation in the Earth. Such attenuation-induced effects will degrade the quality of AI inversion unless some preprocessing routines are performed in advance (e.g., inverse Q-filtering). In order to invert for AI from nonstationary seismic data directly and enhance the lateral continuity, we propose a robust Q-compensated multidimensional AI inversion method. We incorporate the Q-filtering operator into the conventional convolution model and solve the inverse problem iteratively, which can avoid some of the errors introduced by those compensation-related processing routines. Furthermore, we incorporate structural information into the inversion processing via seislet-domain nonlinear shaping regularization. Compared with the conventional nonstationary multichannel AI inversion method, our proposed method can accelerate the convergence rate during inversion and further improve lateral continuity and accuracy in the presence of noise. Finally, synthetic and field data are used to validate the effectiveness and robustness of the proposed method. The results demonstrate that the proposed method can retrieve AI from nonstationary seismic data directly with improved efficiency and remove possible artifacts caused by ambient noise.
声阻抗（AI）反演在地震解释中起着至关重要的作用，因为声阻抗包含宝贵的岩性信息，有助于储层特征描述。然而，地震波在地球上传播时，无弹性衰减效应会耗散地震波的能量并扭曲其相位。除非事先执行一些预处理程序（如反向 Q 滤波），否则这种衰减引起的效应会降低 AI 反演的质量。为了直接对非稳态地震数据进行人工影响反演，并增强横向连续性，我们提出了一种稳健的 Q 补偿多维人工影响反演方法。我们将 Q 滤波算子纳入传统卷积模型，并迭代求解反演问题，从而避免了补偿相关处理程序带来的一些误差。此外，我们还通过小震子域非线性整形正则化将结构信息纳入反演处理。与传统的非稳态多通道人工智能反演方法相比，我们提出的方法可以加快反演过程中的收敛速度，并进一步提高噪声存在时的横向连续性和精度。最后，利用合成数据和现场数据验证了所提方法的有效性和鲁棒性。结果表明，所提出的方法可以直接从非稳态地震数据中提取人工影响，提高了效率，并消除了环境噪声可能造成的假象。
{"title":"Robust Q-compensated multidimensional impedance inversion using seislet-domain shaping regularization","authors":"Chao Li, Guochang Liu, Zhiyong Wang, Lanting Shi, Qibin Wu","doi":"10.1190/geo2022-0717.1","DOIUrl":"https://doi.org/10.1190/geo2022-0717.1","url":null,"abstract":"Acoustic impedance (AI) inversion plays a vital role in seismic interpretation because AI contains valuable information on lithology and contributes to reservoir characterization. However, the effect of anelastic attenuation dissipates the energy and distorts the phase of seismic waves during their propagation in the Earth. Such attenuation-induced effects will degrade the quality of AI inversion unless some preprocessing routines are performed in advance (e.g., inverse Q-filtering). In order to invert for AI from nonstationary seismic data directly and enhance the lateral continuity, we propose a robust Q-compensated multidimensional AI inversion method. We incorporate the Q-filtering operator into the conventional convolution model and solve the inverse problem iteratively, which can avoid some of the errors introduced by those compensation-related processing routines. Furthermore, we incorporate structural information into the inversion processing via seislet-domain nonlinear shaping regularization. Compared with the conventional nonstationary multichannel AI inversion method, our proposed method can accelerate the convergence rate during inversion and further improve lateral continuity and accuracy in the presence of noise. Finally, synthetic and field data are used to validate the effectiveness and robustness of the proposed method. The results demonstrate that the proposed method can retrieve AI from nonstationary seismic data directly with improved efficiency and remove possible artifacts caused by ambient noise.","PeriodicalId":55102,"journal":{"name":"Geophysics","volume":"52 1","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139257060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The diffusive-viscous wave (DVW) equation is an effective model for analyzing seismic low-frequency anomalies and attenuation in porous media. To effectively simulate DVW wavefields, the finite-difference or finite-element method in the time domain is favored, but the time-domain approach proves less efficient with multiple shots or a few frequency components. The finite-difference frequency-domain (FDFD) method, featuring optimal or adaptive coefficients is favored in seismic simulations due to its high efficiency. Initially, we develop a real-valued adaptive-coefficient (RVAC) FDFD method for the DVW equation, which ignores the numerical attenuation error and is a generalization of the acoustic adaptive-coefficient FDFD method. To reduce the numerical attenuation error of the RVAC FDFD method, we introduce a complex-valued adaptive-coefficient (CVAC) FDFD method for the DVW equation. The CVAC FDFD method is constructed by incorporating correction terms into the conventional second-order FDFD method. The adaptive coefficients are related to the spatial sampling ratio, number of spatial grid points per wavelength, and diffusive and viscous attenuation coefficients in the DVW equation. Numerical dispersion and attenuation analysis confirm that, with a maximum dispersion error of 1% and a maximum attenuation error of 10%, the CVAC FDFD method only necessitates 2.5 spatial grid points per wavelength. Compared with the RVAC FDFD method, the CVAC FDFD method exhibits enhanced capability in suppressing the numerical attenuation during anelastic wavefield modeling. To validate the accuracy of our proposed method, we propose an analytical solution for the DVW equation in a homogeneous medium. Three numerical examples substantiate the high accuracy of the CVAC FDFD method when employing a small number of spatial grid points per wavelength, but this method demands computational time and computer memory similar to those required by the conventional second-order FDFD method. A fluid-saturated model featuring various layer thicknesses is used to characterize the propagation characteristics of DVW.
{"title":"Complex-valued adaptive-coefficient finite difference frequency domain method for wavefield modeling based on diffusive-viscous wave equation","authors":"Haixia Zhao, Shaoru Wang, Wenhao Xu, Jinghuai Gao","doi":"10.1190/geo2023-0271.1","DOIUrl":"https://doi.org/10.1190/geo2023-0271.1","url":null,"abstract":"The diffusive-viscous wave (DVW) equation is an effective model for analyzing seismic low-frequency anomalies and attenuation in porous media. To effectively simulate DVW wavefields, the finite-difference or finite-element method in the time domain is favored, but the time-domain approach proves less efficient with multiple shots or a few frequency components. The finite-difference frequency-domain (FDFD) method, featuring optimal or adaptive coefficients is favored in seismic simulations due to its high efficiency. Initially, we develop a real-valued adaptive-coefficient (RVAC) FDFD method for the DVW equation, which ignores the numerical attenuation error and is a generalization of the acoustic adaptive-coefficient FDFD method. To reduce the numerical attenuation error of the RVAC FDFD method, we introduce a complex-valued adaptive-coefficient (CVAC) FDFD method for the DVW equation. The CVAC FDFD method is constructed by incorporating correction terms into the conventional second-order FDFD method. The adaptive coefficients are related to the spatial sampling ratio, number of spatial grid points per wavelength, and diffusive and viscous attenuation coefficients in the DVW equation. Numerical dispersion and attenuation analysis confirm that, with a maximum dispersion error of 1% and a maximum attenuation error of 10%, the CVAC FDFD method only necessitates 2.5 spatial grid points per wavelength. Compared with the RVAC FDFD method, the CVAC FDFD method exhibits enhanced capability in suppressing the numerical attenuation during anelastic wavefield modeling. To validate the accuracy of our proposed method, we propose an analytical solution for the DVW equation in a homogeneous medium. Three numerical examples substantiate the high accuracy of the CVAC FDFD method when employing a small number of spatial grid points per wavelength, but this method demands computational time and computer memory similar to those required by the conventional second-order FDFD method. A fluid-saturated model featuring various layer thicknesses is used to characterize the propagation characteristics of DVW.","PeriodicalId":55102,"journal":{"name":"Geophysics","volume":"276 1","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139256575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jeferson de Souza, S. P. Oliveira, L. Szameitat, O. A. De Souza Filho, Francisco José Fonseca Ferreira
Vertical derivatives of non-potential fields are, intentionally or not, often performed in the Fourier domain producing nonphysical but interpretable results. Using the dike model, we prove that the vertical derivative of the squared Analytic Signal Amplitude calculated in the Fourier domain does not correspond to the true one. We derive an analytical expression for this pseudo-vertical derivative, providing a mathematical meaning for it. One significant difference between the pseudo and true vertical derivative is that the former possesses real roots, while the latter does not. Taking advantage of this attribute, we show using synthetic and field data that the pseudo-vertical derivative can be used for qualitative and quantitative interpretation of magnetic data, despite being nonphysical. As an example of the usefulness of this filter in the qualitative interpretation we convert the image of the pseudo-derivative to a binary image where the anomalies are treated as discrete objects. This allows us to morphologically enhance, disconnect, classify and filter them using tools of shape analysis and mathematical morphology. We also illustrate its usefulness in quantitative interpretation by deriving a formula for estimating the depths of magnetic thin dikes and infinite steps. Our outcomes were also corroborated by outcrops observation found by field surveys.
{"title":"Fourier domain vertical derivative of the non-potential squared analytical signal of dike and step magnetic anomalies: a case of serendipity","authors":"Jeferson de Souza, S. P. Oliveira, L. Szameitat, O. A. De Souza Filho, Francisco José Fonseca Ferreira","doi":"10.1190/geo2022-0760.1","DOIUrl":"https://doi.org/10.1190/geo2022-0760.1","url":null,"abstract":"Vertical derivatives of non-potential fields are, intentionally or not, often performed in the Fourier domain producing nonphysical but interpretable results. Using the dike model, we prove that the vertical derivative of the squared Analytic Signal Amplitude calculated in the Fourier domain does not correspond to the true one. We derive an analytical expression for this pseudo-vertical derivative, providing a mathematical meaning for it. One significant difference between the pseudo and true vertical derivative is that the former possesses real roots, while the latter does not. Taking advantage of this attribute, we show using synthetic and field data that the pseudo-vertical derivative can be used for qualitative and quantitative interpretation of magnetic data, despite being nonphysical. As an example of the usefulness of this filter in the qualitative interpretation we convert the image of the pseudo-derivative to a binary image where the anomalies are treated as discrete objects. This allows us to morphologically enhance, disconnect, classify and filter them using tools of shape analysis and mathematical morphology. We also illustrate its usefulness in quantitative interpretation by deriving a formula for estimating the depths of magnetic thin dikes and infinite steps. Our outcomes were also corroborated by outcrops observation found by field surveys.","PeriodicalId":55102,"journal":{"name":"Geophysics","volume":"6 3","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139271734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shuang Wang, Xiangbo Gong, Xingguo Huang, Jing Rao, Kristian Jensen, Li Han, Naijian Wang, Xuliang Zhang
Reverse time migration (RTM) has been proven capable of producing high-quality images of subsurface structures. However, limited subsurface illumination combined with inaccurate forward modeling and migration velocities all lead to uncertainty in the seismic images. We quantify the migration uncertainty of RTM using an iterative inversion method based on a Bayesian inference framework. The posterior covariance matrix, computed at the maximum a posteriori (MAP) model, provides the foundation for estimating uncertainty. In the Bayesian inference framework, we combine an explicit sensitivity matrix based on a Green's function representation with an iterative extended Kalman filter (IEKF) method. This enables us to determine the MAP solution of RTM as well as an estimate of its uncertainty. Numerical examples using synthetic data demonstrate how well the method can measure RTM uncertainty and produce reliable imaging results.
{"title":"Bayesian reverse time migration with quantified uncertainty","authors":"Shuang Wang, Xiangbo Gong, Xingguo Huang, Jing Rao, Kristian Jensen, Li Han, Naijian Wang, Xuliang Zhang","doi":"10.1190/geo2022-0721.1","DOIUrl":"https://doi.org/10.1190/geo2022-0721.1","url":null,"abstract":"Reverse time migration (RTM) has been proven capable of producing high-quality images of subsurface structures. However, limited subsurface illumination combined with inaccurate forward modeling and migration velocities all lead to uncertainty in the seismic images. We quantify the migration uncertainty of RTM using an iterative inversion method based on a Bayesian inference framework. The posterior covariance matrix, computed at the maximum a posteriori (MAP) model, provides the foundation for estimating uncertainty. In the Bayesian inference framework, we combine an explicit sensitivity matrix based on a Green's function representation with an iterative extended Kalman filter (IEKF) method. This enables us to determine the MAP solution of RTM as well as an estimate of its uncertainty. Numerical examples using synthetic data demonstrate how well the method can measure RTM uncertainty and produce reliable imaging results.","PeriodicalId":55102,"journal":{"name":"Geophysics","volume":"41 1","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139274658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Borehole sonic measurements acquired in high-angle wells in general do not exhibit axial symmetry in the vicinity of bed boundaries and thin layers, while sonic waveforms remain strongly affected by the corresponding contrast in elastic properties across bed boundaries. The latter conditions often demand sophisticated and time-consuming numerical modeling to reliably interpret borehole sonic measurements into rock elastic properties. We circumvent this problem by implementing the eikonal equation based on the fast-marching method to (a) calculate first-arrival times of borehole acoustic waveforms, and (b) trace ray paths between sonic transmitters and receivers in high-angle wells. Furthermore, first-arrival times of compressional and shear waves are calculated at different azimuthal receivers included in wireline borehole sonic instruments and are verified against waveforms obtained via three-dimensional (3D) finite-difference time-domain simulations (3D-FDTD). Calculations of travel times, wavefronts, and ray paths for challenging synthetic examples with effects due to formation anisotropy and different inclination angles show a transition from a head wave to a boundary-induced refracted wave as the borehole sonic instrument moves across bed boundaries. Apparent slownesses obtained from first-arrival times at receivers can be faster or slower than the actual slownesses of rock formations surrounding the borehole, depending on formation dip, azimuth, anisotropy, and bed boundaries. Differences in apparent acoustic slownesses measured by adjacent azimuthal receivers reflect the behavior of wave propagation within the borehole and across bed boundaries and can be used to estimate bed-boundary orientation and anisotropy. The high-frequency approximation of travel times obtained with the eikonal equation saves more than 99% of calculation time with acceptable numerical errors, with respect to rigorous time-domain numerical simulation of the wave equation, and is therefore amenable to inversion-based measurement interpretation. Apparent slownesses extracted from acoustic arrival times suggest a potential method for estimating formation elastic properties and inferring boundary geometries
{"title":"Numerical simulation and interpretation of sonic arrival times in high-angle wells using the eikonal equation","authors":"Jingxuan Liu, C. Torres‐Verdín","doi":"10.1190/geo2023-0303.1","DOIUrl":"https://doi.org/10.1190/geo2023-0303.1","url":null,"abstract":"Borehole sonic measurements acquired in high-angle wells in general do not exhibit axial symmetry in the vicinity of bed boundaries and thin layers, while sonic waveforms remain strongly affected by the corresponding contrast in elastic properties across bed boundaries. The latter conditions often demand sophisticated and time-consuming numerical modeling to reliably interpret borehole sonic measurements into rock elastic properties. We circumvent this problem by implementing the eikonal equation based on the fast-marching method to (a) calculate first-arrival times of borehole acoustic waveforms, and (b) trace ray paths between sonic transmitters and receivers in high-angle wells. Furthermore, first-arrival times of compressional and shear waves are calculated at different azimuthal receivers included in wireline borehole sonic instruments and are verified against waveforms obtained via three-dimensional (3D) finite-difference time-domain simulations (3D-FDTD). Calculations of travel times, wavefronts, and ray paths for challenging synthetic examples with effects due to formation anisotropy and different inclination angles show a transition from a head wave to a boundary-induced refracted wave as the borehole sonic instrument moves across bed boundaries. Apparent slownesses obtained from first-arrival times at receivers can be faster or slower than the actual slownesses of rock formations surrounding the borehole, depending on formation dip, azimuth, anisotropy, and bed boundaries. Differences in apparent acoustic slownesses measured by adjacent azimuthal receivers reflect the behavior of wave propagation within the borehole and across bed boundaries and can be used to estimate bed-boundary orientation and anisotropy. The high-frequency approximation of travel times obtained with the eikonal equation saves more than 99% of calculation time with acceptable numerical errors, with respect to rigorous time-domain numerical simulation of the wave equation, and is therefore amenable to inversion-based measurement interpretation. Apparent slownesses extracted from acoustic arrival times suggest a potential method for estimating formation elastic properties and inferring boundary geometries","PeriodicalId":55102,"journal":{"name":"Geophysics","volume":"63 3","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139273780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gassmann’s equations have been known for several decades and are widely used in geophysics. These equations are treated as exact if all the assumptions used in their derivation are fulfilled. However, a recent theoretical study claimed that Gassmann’s equations contain an error. Shortly after that, I performed a three-dimensional numerical calculation on a simple pore geometry that verifies the validity of Gassmann’s equations. This pore geometry was simpler than those in real rocks but arbitrary. Furthermore, the employed pore geometry did not contain any special features (among all possible geometries) that were tailored to make it consistent with Gassmann’s equations. In other recent studies, I also performed numerical calculations on several other more complex pore geometries that supported the validity of Gassmann’s equations. To further support the validity of these equations, I provide here one more convergence study using a more realistic geometry of the pore space. Given that there are several studies that rederive Gassmann’s equations using different methods and numerical studies that verify them for different pore geometries, it can be concluded that Gassmann’s equations can be used in geophysics without concern if their assumptions are fulfilled. MATLAB routines to reproduce the presented results are provided.
{"title":"Reply to discussion on numerical validation of Gassmann’s equations (Yury Alkhimenkov, 2023, Geophysics, 88, no. 4, A25–A29) by Leon Thomsen","authors":"Yury Alkhimenkov","doi":"10.1190/geo2023-0678.1","DOIUrl":"https://doi.org/10.1190/geo2023-0678.1","url":null,"abstract":"Gassmann’s equations have been known for several decades and are widely used in geophysics. These equations are treated as exact if all the assumptions used in their derivation are fulfilled. However, a recent theoretical study claimed that Gassmann’s equations contain an error. Shortly after that, I performed a three-dimensional numerical calculation on a simple pore geometry that verifies the validity of Gassmann’s equations. This pore geometry was simpler than those in real rocks but arbitrary. Furthermore, the employed pore geometry did not contain any special features (among all possible geometries) that were tailored to make it consistent with Gassmann’s equations. In other recent studies, I also performed numerical calculations on several other more complex pore geometries that supported the validity of Gassmann’s equations. To further support the validity of these equations, I provide here one more convergence study using a more realistic geometry of the pore space. Given that there are several studies that rederive Gassmann’s equations using different methods and numerical studies that verify them for different pore geometries, it can be concluded that Gassmann’s equations can be used in geophysics without concern if their assumptions are fulfilled. MATLAB routines to reproduce the presented results are provided.","PeriodicalId":55102,"journal":{"name":"Geophysics","volume":"4 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136283821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：