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prestack Seismic inversion via Global Optimization With an Accurate Hessian Matrix and the Three-Variable Cauchy Distribution for Exact Zoeppritz Equations

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2025年 63卷

作者： Xu, Zihe Peng, Suping Cui, Xiaoqin Lu, Yongxu Jin, Chao Lin, Peng China Univ Min & Technol Beijing State Key Lab Fine Explorat & Intelligent Dev Coal Beijing 100083 Peoples R China Khalifa Univ Dept Earth Sci Abu Dhabi U Arab Emirates

prestack inversion is typically based on the Zoeppritz equation combined with gradient-based optimization of objective functions. To address the limitations of traditional gradient-based algorithms that heavily rely on initial models, researchers have introduced intelligent optimization algorithms, such as particle swarm optimization (PSO), into prestack inversion to improve inversion accuracy. However, these global optimization algorithms often exhibit low computational efficiency due to insufficient consideration of gradients and the Hessian matrix. In this study, we introduce the exact Zoeppritz gradient-based global optimization (EZGBO) method, which integrates an accurate gradient and the Hessian matrix under a Bayesian framework with a three-variable Cauchy prior into the gradient-based global optimizer (GBO) to enhance inversion accuracy and efficiency. The proposed method combines the advantages of traditional Newton-like algorithms and global intelligent optimization algorithms by incorporating the accurate gradient and the Hessian matrix of the objective function into the global optimization process. This approach achieves better inversion results with fewer particles and iterations, thus enhancing computational efficiency. To ensure the stability of the stochastic global inversion, we employ adaptive edge-preserving smoothing (Ad-EPS) to facilitate optimal positioning of the population particles. Finally, we validate the proposed method using both synthetic and field data. Specifically, we compared the proposed method with quantum PSO (Q) and traditional approaches. The results show that our method excels in accuracy, stability, efficiency, and resolution, offering a novel solution to global optimization in prestack inversion.

关键词： Optimization Mathematical models Accuracy Particle swarm optimization Linear programming Bayes methods Reflection coefficient Stability criteria Newton method Data mining Accurate Hessian matrix gradient-based global optimizer (GBO) prestack inversion three-variable Cauchy distribution

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prestack inversion based on anisotropic Markov random field-maximum posterior probability inversion and its application to identify shale gas sweet spots

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Applied Geophysics 2015年第4期12卷 533-544,628页

作者：王康宁孙赞东董宁中国石油大学地质地球物理综合研究中心北京102249 中国石油化工股份有限公司石油勘探开发研究院北京100083 中国石油集团东方地球物理勘探有限责任公司河北涿州072751

Economic shale gas production requires hydraulic fracture stimulation to increase the formation permeability. Hydraulic fracturing strongly depends on geomechanical parameters such as Young＇s modulus and Poisson＇s ratio. Fracture-prone sweet spots can be predicted by prestack inversion, which is an ill-posed problem; thus, regularization is needed to obtain unique and stable solutions. To characterize gas-bearing shale sedimentary bodies, elastic parameter variations are regarded as an anisotropic Markov random field. Bayesian statistics are adopted for transforming prestack inversion to the maximum posterior probability. Two energy functions for the lateral and vertical directions are used to describe the distribution, and the expectation-maximization algorithm is used to estimate the hyperparameters of the prior probability of elastic parameters. Finally, the inversion yields clear geological boundaries, high vertical resolution, and reasonable lateral continuity using the conjugate gradient method to minimize the objective function. Antinoise and imaging ability of the method were tested using synthetic and real data.

关键词： shale gas/oil sweet spot prestack inversion Markov random field

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Zoeppritz equation-based prestack inversion and its application in fluid identification

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Applied Geophysics 2015年第2期12卷 199-211,275页

作者：黄捍东王彦超郭飞张生纪永祯刘承汉油气资源与探测国家重点实验室(中国石油大学(北京)) 北京102249 中国石油大学提高采收率研究院北京102249 中海石油深圳分公司研究院广州510240 长江大学地球物理与石油资源学院湖北武汉430100

prestack seismic inversion methods adopt approximations of the Zoeppritz equations to describe the relation between reflection coefficients and P-wave velocity, S-wave velocity, and density. However, the error in these approximations increases with increasing angle of incidence and variation of the elastic parameters, which increases the number of inversion solutions and minimizes the inversion accuracy. In this study, we explore a method for solving the reflection coefficients by using the Zoeppritz equations. To increase the accuracy of prestack inversion, the simultaneous inversion of P-wave velocity, S-wave velocity, and density by using prestack large-angle seismic data is proposed based on generalized linear inversion theory. Moreover, we reduce the ill posedness and increase the convergence of prestack inversion by using the regularization constraint damping factor and the conjugate gradient algorithm. The proposed prestack inversion method uses prestack large-angle seismic data to obtain accurate seismic elastic parameters that conform to prestack seismic data and are consistent with logging data from wells.

关键词： prestack inversion Zoeppritz equation simultaneous inversion fluid identification

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Global Optimizing prestack Seismic inversion Approach Using an Accurate Hessian Matrix Based on Exact Zoeppritz Equations

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2024年 62卷 1页

作者： Xu, Pengyu Zhou, Huailai Liu, Xingye Zhou, Jie Yang, Yuyong Chengdu Univ Technol Coll Geophys Key Lab Earth Explorat & Informat Technol Minist Educ Chengdu 610059 Peoples R China

To increase the accuracy and vertical resolution of seismic inversion for exploratory purposes, a new method was developed for P-wave velocity, S-wave velocity, and density inversion using prestack seismic data based on the mayfly optimization algorithm (MA), exact Zoeppritz equations, and Bayesian framework. A new form of an accurate Hessian matrix was successfully derived. We innovatively used the MA nonlinear amplitude variation with angle (AVA) inversion based on the accurate Hessian matrix (MANAI-Hessian) method for prestack seismic inversion and highlighted two main challenges for the first time. The popular and recent whale optimization algorithm (WOA) and a conventional Levenberg-Marquardt (LM) method were introduced to demonstrate the existence of these two challenges. Comprehensive partial derivative tests were well designed to verify the existence of the second-order partial derivatives of the P-wave reflection coefficients. A 3-D special wedge model was introduced to test the accuracy and vertical resolution of the new method. Next, we applied the proposed method to the field data of deep carbonate rock from a study area in China. Compared with the conventional LM method and the accurate Jacobian matrix-based nonlinear AVA inversion method, which provides foundational approaches to address the two main challenges, the proposed approach shows superior performance in terms of accuracy and vertical resolution.

关键词： Jacobian matrices Mathematical models Reflection coefficient Reflection Linear programming Rocks Matrix converters Accurate Hessian matrix exact Zoeppritz equations mayfly optimization algorithm (MA) prestack inversion

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Hybrid-Driven High-Resolution prestack Seismic inversion

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IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING 2023年 16卷 9875-9885页

作者： Zhang, Jian Zhao, Xiaoyan Sun, Hui Li, Jingye Chen, Xiaohong Southwest Jiaotong Univ Fac Geosci & Environm Engn Chengdu 611756 Peoples R China Southwest Jiaotong Univ MOE Key Lab High Speed Railway Engn Chengdu 610036 Peoples R China China Univ Petr State Key Lab Petr Resources & Prospecting Natl Engn Lab Offshore Oil Explorat Beijing 102249 Peoples R China

prestack seismic inversion is considered among the most frequently utilized techniques for reservoir characterization. However, the resolution of the inverted parameters, such as P-, S-wave velocity, and density, is low due to the limited bandwidth and side-lobe interference of the seismic wavelet. To address this issue, a hybrid two-step strategy that combines data-driven and model-driven methods is proposed to enable higher resolution and accuracy of the inverted results. We first construct a three-layer fully connected network to implement the mapping of seismic data to reflection coefficients. The method does not require exact seismic wavelet to be known and intensive human-computer interaction. It estimates reflectivity based on the extracted features from training data, which gives more accurate results compared with traditional sparse inversion methods. Then, the model-driven method (i.e., amplitude variation with offset/angle inversion method) is adopted to reconstruct P-wave velocity, S-wave velocity, and density from the estimated reflection coefficients. The performance of the hybrid-driven strategy is checked using synthetic model and real data. The results indicate that the proposed method provides more accurate and higher resolution inversion results for seismic reservoir characterization.

关键词： Training Reflectivity Reflection coefficient Reservoirs Mathematical models Linear programming Artificial neural networks Data-driven model-driven prestack inversion reservoir characterization

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Regularisation parameter adaptive selection and its application in the prestack AVO inversion

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EXPLORATION GEOPHYSICS 2018年第3期49卷 323-335页

作者： Huang, Guangtan Li, Jingye Luo, Cong Chen, Xiaohong China Univ Petr State Key Lab Petr Resources & Prospecting Beijing 102249 Peoples R China China Univ Petr Natl Engn Lab Offshore Oil Explorat Beijing 102249 Peoples R China

The numerical solution of the inverse problem is usually obtained by solving a set of linear algebraic equations, while the system of equations may suffer from ill-posedness due to insufficient data. Regularisation is a technique for making the estimation problems well posed by adding indirect constraints on the estimated model, but the regularisation parameter selection is difficult. In geophysics, without explicit calculation methods and quantitative evaluation criteria, it is usually based on the experience of the inversion engineers to try to achieve the best inversion results by continuously modifying the regularisation parameter. For prestack amplitude variation with offset (AVO) inversion for real seismic data, fixed regularisation parameters cannot satisfy the optimisation conditions in the seismic data with different signal-to-noise (SNR) in one area. Besides, fixed regularisation parameter may cause that the model constraint misfit is too large or too small compared to data misfit, which may guide the inversion to generate undesirable results. Therefore, adaptive selection of regularisation parameter according to the seismic data can help guarantee a good inversion result. Based on the traditional L-curve criterion, we derive the theoretical formula of the adaptive computation of the regularisation parameter, which can be applied to any norm constraint. We proposed the application of this selection scheme in prestack AVO inversion. Model tests show that the improved L-curve method has better stability than its main competitor, the generalised cross-validation (GCV) method. prestack AVO inversion on logging data and real seismic data demonstrate that the proposed method can improve the accuracy of the inversion, and it is more immune to strong noise.

关键词： generalised cross-validation L-curve prestack inversion regularisation parameter sparse constraint condition

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Block sparse Bayesian learning-based prestack seismic inversion with the correlation of velocities and density

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ACTA GEOPHYSICA 2023年第1期71卷 261-274页

作者： Ma, Ming Zhang, Rui Changan Univ Sch Geol Engn & Geomat Xian Peoples R China Univ Louisiana Lafayette Sch Geosci Lafayette LA 70504 USA

prestack seismic inversion has been widely used around the seismic exploration. It can precisely output the elastic properties of layers in subsurface, e.g., P-wave velocity (V-p), S-wave velocity (V-s), and density (rho). These are utilized further to extract many reservoir properties, like saturation and porosity, which are very helpful for the successful oil field development. The accuracy of prestack inversion result could play a critical role for the evaluation of reservoir characterization and the quantitative interpretation. It has been observed the existing relationships among velocities and density (V-p, V-s, and rho) lead to the correlations of three reflectivities (R-p, R-s, and R-rho). In this paper, we establish a new formulation for amplitude-versus-angle (AVA) inversion incorporating these correlations. A machine learning technique-block sparse Bayesian learning, has been implemented as the inversion engine to solve R-p, R-s, and R-rho and to estimate the correlations described as the covariance matrix automatically. Due to the contribution of relationship between velocities and density, the performance of proposed AVA inversion is superior to the conventional technique in denoising and highlighting small-scale reflections. Three reflectivities are finally converted into velocities and density via an optimal multi-trace algorithm L-BFGS, which can mighty mitigate the lateral discontinuity of inverted results. The proposed approach has been tested on the synthetic examples. It shows a good consistence between inverted and true elastic properties. Field data test with the seismic profiles in Ordos basin area has demonstrated its high feasibility and efficiency for practical applications.

关键词： prestack inversion bSBL Correlation of elastic parameters

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Direct reservoir property estimation based on prestack seismic inversion

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2018年 171卷 1475-1486页

作者： Liu, Qian Dong, Ning Ji, Yuxin Chen, Tiansheng SINOPEC Petr Explorat & Prod Res Inst Beijing Peoples R China

Reservoir property estimation is an essential part for reservoir characterization. Most commonly-used estimation methods are implemented in two steps, seismic inversion and rock physics inversion. However, these indirect methods may increase the uncertainty and reduce the accuracy of estimation results. In this work, we propose a Bayesian inversion approach to estimate reservoir properties directly from prestack seismic data. Firstly, by combining the reflection coefficient equation and rock physics model, we derive a P-wave reflection approximation in terms of reservoir parameters, which establishes a direct link between seismic data and reservoir properties. Model examples illustrate the accuracy of the approximation comparing to the exact reflection coefficient equation, which satisfies the requirements of the prestack seismic inversion. Then in the framework of Bayesian inversion theory, a novel inversion method is presented to estimate porosity, mineral volume and water saturation directly from prestack seismic angle gathers. Direct estimation increases the stability and decreases the uncertainty. The synthetic test demonstrates the advantage of the proposed method on the accuracy and stability over indirect methods. The real data example verifies the feasibility of the proposed method in direct reservoir property estimation.

关键词： Reservoir property Direct estimation Rock physics model prestack inversion Bayesian theory

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Effect of inaccurate wavelet phase on prestack waveform inversion

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Applied Geophysics 2014年第4期11卷 479-488,511页

作者：骆春妹王尚旭袁三一中国石油大学(北京)油气资源与探测国家重点实验室北京102249 中国石油大学(北京)CNPC物探重点实验室北京102249

Wavelets are critical to inversion methods. Incorrect phase estimation will affect the objective function and cause convergence to local minima, and thus produce biased or incorrect results. Based on two simple models and ignoring all other factors, we studied the variation of the wavelet phase as a function of frequency and its effect on the prestack waveform inversion. Numerical experiments show that an incorrect phase may result in large deviations from the real solution, even if there is a high similarity between the model and real wavelets. The precision of the inversion slightly improves by using the constant-phase rotation; however, the effect of phase inaccuracy is not eliminated, which limits the precision of prestack inversion.

关键词： wavelet phase prestack inversion

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Bayesian prestack seismic inversion with a self-adaptive Huber-Markov random-field edge protection scheme

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Applied Geophysics 2013年第4期10卷 453-460,512页

作者：田玉昆周辉陈汉明邹雅铭关守军中国石油大学(北京)油气资源与探测国家重点实验室 CNPC物探重点实验室北京102249

Seismic inversion is a highly ill-posed problem, due to many factors such as the limited seismic frequency bandwidth and inappropriate forward modeling. To obtain a unique solution, some smoothing constraints, e.g., the Tikhonov regularization are usually applied. The Tikhonov method can maintain a global smooth solution, but cause a fuzzy structure edge. In this paper we use Huber-Markov random-field edge protection method in the procedure of inverting three parameters, P-velocity, S-velocity and density. The method can avoid blurring the structure edge and resist noise. For the parameter to be inverted, the Huber- Markov random-field constructs a neighborhood system, which further acts as the vertical and lateral constraints. We use a quadratic Huber edge penalty function within the layer to suppress noise and a linear one on the edges to avoid a fuzzy result. The effectiveness of our method is proved by inverting the synthetic data without and with noises. The relationship between the adopted constraints and the inversion results is analyzed as well.

关键词： Huber edge punishment function markov random-field bayesian framework prestack inversion

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