Inversion of Young’s modulus,Poisson’s ratio and density from pre-stack seismic data has been proved to be feasible and effective.However,the existing methods do not take full advantage of the prior information.With...Inversion of Young’s modulus,Poisson’s ratio and density from pre-stack seismic data has been proved to be feasible and effective.However,the existing methods do not take full advantage of the prior information.Without considering the lateral continuity of the inversion results,these methods need to invert the reflectivity first.In this paper,we propose multi-gather simultaneous inversion for pre-stack seismic data.Meanwhile,the total variation（TV）regularization,L1 norm regularization and initial model constraint are used.In order to solve the objective function contains L1norm,TV norm and L2 norm,we develop an algorithm based on split Bregman iteration.The main advantages of our method are as follows：（1）The elastic parameters are calculated directly from objective function rather than from their reflectivity,therefore the stability and accuracy of the inversion process can be ensured.（2）The inversion results are more in accordance with the prior geological information.（3）The lateral continuity of the inversion results are improved.The proposed method is illustrated by theoretical model data and experimented with a 2-D field data.展开更多
We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong...We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multiparameter regularization over the single parameter regularization.展开更多
The inverse problem of wave equation is the importance of study not only in seismic prospecting but also in applied mathematics. With the development of the research, the inverse methods of 1 - D wave equations have b...The inverse problem of wave equation is the importance of study not only in seismic prospecting but also in applied mathematics. With the development of the research, the inverse methods of 1 - D wave equations have been trending towards the multiple parameters inversion . We have obtained an inverse method with double -parameter, in which medium density and wave velocity can be derived simultaneously. In this paper, to increase the inverse accuracy, the method is improved as follows. Firstly, the formula in which the Green Function is omitted are derived and used. Secondly, the regularizing method is reasonable used by choosing the stable function. With the new method, we may derive elastic parameter and medium density or medium density and wave velocity. Thus, lithology parameters for seismic prospecting may be obtained.After comparing the derived values from the new method with that from previous method, we obtain the new method through which substantially improve the derived accuracy . The new method has been applied to real depths inversion for sedimentary strata and volcanic rock strata in Chaoyanggou Terrace of Songliao Basin in eastern China. According to the inverse results,the gas - bearing beds are determlned.展开更多
The existence and uniqueness of the solutions are proved for a class of fourth-order stochastic heat equations driven by multi-parameter fractional noises. Furthermore the regularity of the solutions is studied for th...The existence and uniqueness of the solutions are proved for a class of fourth-order stochastic heat equations driven by multi-parameter fractional noises. Furthermore the regularity of the solutions is studied for the stochastic equations and the existence of the density of the law of the solution is obtained.展开更多
基金supported by the National Natural Science Foundation of China (Nos.61775030,61571096,41301460,61362018,and 41274127)the key projects of Hunan Provincial Department of Education (No.16A174)
文摘Inversion of Young’s modulus,Poisson’s ratio and density from pre-stack seismic data has been proved to be feasible and effective.However,the existing methods do not take full advantage of the prior information.Without considering the lateral continuity of the inversion results,these methods need to invert the reflectivity first.In this paper,we propose multi-gather simultaneous inversion for pre-stack seismic data.Meanwhile,the total variation（TV）regularization,L1 norm regularization and initial model constraint are used.In order to solve the objective function contains L1norm,TV norm and L2 norm,we develop an algorithm based on split Bregman iteration.The main advantages of our method are as follows：（1）The elastic parameters are calculated directly from objective function rather than from their reflectivity,therefore the stability and accuracy of the inversion process can be ensured.（2）The inversion results are more in accordance with the prior geological information.（3）The lateral continuity of the inversion results are improved.The proposed method is illustrated by theoretical model data and experimented with a 2-D field data.
基金supported in part by the Natural Science Foundation of China under grants 10371137the Foundation of Doctoral Program of National Higher Education of China under grant 20030558008+5 种基金Guangdong Provincial Natural Science Foundation of China under grant 05003308the Foundation of Zhongshan University Advanced Research Centersupported in part by the US National Science Foundation under grant CCR-0407476National Aeronautics and Space Administration under Cooperative Agreement NNX07AC37Athe Natural Science Foundation of China under grants 10371122 and 10631080the Education Ministry of the People's Republic of China under the Changjiang Scholar Chair Professorship Program through Zhongshan University
文摘We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multiparameter regularization over the single parameter regularization.
文摘The inverse problem of wave equation is the importance of study not only in seismic prospecting but also in applied mathematics. With the development of the research, the inverse methods of 1 - D wave equations have been trending towards the multiple parameters inversion . We have obtained an inverse method with double -parameter, in which medium density and wave velocity can be derived simultaneously. In this paper, to increase the inverse accuracy, the method is improved as follows. Firstly, the formula in which the Green Function is omitted are derived and used. Secondly, the regularizing method is reasonable used by choosing the stable function. With the new method, we may derive elastic parameter and medium density or medium density and wave velocity. Thus, lithology parameters for seismic prospecting may be obtained.After comparing the derived values from the new method with that from previous method, we obtain the new method through which substantially improve the derived accuracy . The new method has been applied to real depths inversion for sedimentary strata and volcanic rock strata in Chaoyanggou Terrace of Songliao Basin in eastern China. According to the inverse results,the gas - bearing beds are determlned.
基金Supported by the School of MathematicsLPMC at Nankai Universitythe NSF of China (Grant No. 10871103)
文摘The existence and uniqueness of the solutions are proved for a class of fourth-order stochastic heat equations driven by multi-parameter fractional noises. Furthermore the regularity of the solutions is studied for the stochastic equations and the existence of the density of the law of the solution is obtained.
文摘随着医学影像数据的不断发展,纵向数据分析逐渐成为了解和跟踪阿尔茨海默病(Alzheimer’s disease,AD)发病过程的重要研究方向。目前已经提出了许多纵向数据分析方法,其中多任务学习得到广泛应用,它能够集成多个时间点的影像数据,提高模型的泛化能力。大多数现有的方法能够识别不同时间点的共享特征,但这些特征中会包含一定的噪声。与此同时,不同时间点进展的潜在关联仍未得到充分的探索。本文提出了一种基于参数分解和关系诱导的多任务学习(Parameter decomposition and relation⁃induced multi⁃task learning,PDRIMTL)方法,以此从纵向数据中识别特征。该方法不仅能够识别去除噪声后的共享特征,提高共享特征的鲁棒性,而且能够对不同时间点的内在关联进行建模。结果表明,在不同时间点的结构磁共振成像(Structural magnetic resonance imaging,sMRI)数据上,该模型能够有效提高对AD鉴别的准确性。
