基于非线性贝叶斯理论的多模态界面波频散曲线反演研究
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摘要
海底探测和识别研究是海洋科学研究领域关注的课题之一,其研究方法和成果在海底资源勘探、海洋环境监测、海洋工程建设以及海洋军事活动等方面均具有极为重要的应用价值。界面波频散曲线反演技术是研究海底地质构造和勘探海底资源的主要手段,通过反演可以获取诸如剪切波速度剖面结构等重要的海底地质属性,剪切波速度不仅可为海底岩土工程应用提供重要的刚度指标,而且在声传播模型的建立以及声纳性能预测中具有重要作用。
界面波频散曲线的提取精度是反演成败的关键因素。传统界面波频散曲线反演方法是基于天然或人工激发的地震波在海底沉积层中传播的频散特性来反演海底沉积层属性。但传统的界面波频散曲线提取的分辨率受到地震分布和台站位置的影响。此外,界面波频散曲线反演是一个典型的高度非线性、多参数、多极值的海洋地球物理反演问题和最优化控制问题。由于正演模拟计算和测量误差等因素的存在,通常反演结果并没有唯一的“最优解”,而现有的非线性反演方法虽然不依赖于初始模型的选取,具有全局寻优和非线性映射能力,但参数的反演结果仅仅是一组最大后验概率意义下的最优解。本文旨在发展一种不依赖于震源、高分辨率的界面波频散曲线提取方法和一种既能满足局部和全局收敛条件,又能对参数反演结果的不确定性进行定量和定性分析的反演方法。
本文从海底地震仪记录的海底环境噪声数据中提取出高分辨率的多模态界面波频散曲线,基于新近发展的非线性贝叶斯反演理论,对基阶模态和多模态界面波频散曲线进行反演研究。论文主要工作包括传统反演理论和方法分析、基于海洋环境噪声提取界面波频散曲线、界面波频散曲线正演模型、非线性贝叶斯反演理论以及多模态界面波频散曲线反演研究等内容。
论文的主要研究成果包括:
1.提出了一种从海洋环境噪声中提取界面波频散曲线的方法。阐述了互相关、格林函数以及时频分析方法的基本原理,归纳了界面波提取的一般流程。海底地震环境噪声的源具有随机性,经多次散射的影响,具有与地震界面波相似的频散特性,其分辨率不依赖于震源信息,采样方向均匀,精度更高。通过对实测海洋环境噪声数据进行分析处理,获得界面波频散曲线的多模态特征,验证了该方法的可行性和有效性。
2.实现了多模态界面波频散曲线正演模型的建立与求解。正演是反演的前提,是提高反演精度和速度的关键因素。给出了各向同性均匀平面波的弹性波动方程,采用数值模拟实例实现并验证了Thompson-Haskill矩阵算法的有效性,该方法表达形式简单、物理意义明确,且易于编程实现。
3.完善了非线性贝叶斯反演方法。将反演问题的解转化为参数后验概率密度(PPD)的求解,首先利用非线性全局优化算法——自适应单纯形模拟退火法(ASSA)求解最大后验概率(MAP)模型,然后基于贝叶斯信息准则法(BIC)进行模型选择,对最优模型利用非线性数值积分方法——Metropolis-Hasting采样法(MHS)求解参数PPD和相关特征量,进而分析反演结果。与传统的单点估计法不同,非线性贝叶斯反演方法不仅可以有效地估计MAP模型,而且可以从统计角度对参数反演结果的不确定性进行定性和定量分析,通过一个数值算例来说明该算法的有效性。
4.探讨了多模态界面波频散曲线联合反演的机理。传统的界面波频散曲线反演研究认为,基阶模态的能量在波场中占主导地位,在反演中通常忽略高阶模态的影响。然而,在某些频段,如高频或中频段,基阶模态将不再占据主要地位,此时高阶模态界面波对反演结果的影响应予考虑。分析了不同海底分层和常见海底剪切波速度剖面模型,分别对基阶模态和多模态界面波频散曲线进行反演计算。结果表明,多模态界面波较基阶模态界面波对海底地质结构敏感性更强,利用多模态界面波频散曲线可以获得更多的海底分层结构,特别是近海底低速层信息,提高了反演精度。
论文在基于海洋环境噪声实现界面波频散曲线精确提取,以及利用多模态界面波频散曲线联合反演研究海底剪切波速度剖面结构方面具有创新性。
The detection and recognition study of seafloor is one of the most active front fields of the marine sciences research, which has an important academic significance and application value in the exploration and exploitation of seabed recourses, ocean environment monitoring, marine engineering construction and military operations. The inversion of interface wave dispersion curves is one of the most effective techniques to study the seabed structures and detect the seafloor resources. Recently, interface-wave inversion work has been getting more and more attention to estimate the shear-wave velocity profile structures. Shear-wave velocity provides a good indicator of sediment rigidity for seafloor geotechnical applications and shear-wave transition in shallow seabed can represent an important ocean acoustic loss mechanism which must be considered in propagation modeling and sonar performance predictions.
The extraction resolution of interface-wave dispersion curves is a key of success or failure in inversion. The dispersion curves were extracted normally from the seismic interface-wave propagating in seabed sediments by a mean of a natural or artificial earthquake focus. The resolution of dispersion curves is affected by the distributions of source and stations. It is very important to develop a high accuracy and resolution method independent of the seismic focus to obtain the interface-wave dispersion curves and the sediment parameters are estimated by inverting the dispersion curves. In additional, inversion of interface-wave dispersion curves is typically a highly nonlinear, multi-parameter, and multi-optima inversion problem, as well as most other marine geophysical optimization problems. Usually there is not an only optimal solution due to the measurement and calculation errors. The inversion results of traditional linear search methods depend on the choice of a starting model and the accuracy of the partial derivatives, which are prone to being trapped by local minima. The available nonlinear inversion techniques such as genetic algorithm (GA) and simulated annealing (SA), have proven to be quite useful for global optimization problems, but these techniques can only determine the best-fit model and slower convergence and not provide quantitatively nonlinear uncertainty estimation of model parameters. It is necessary to develop a quantitative nonlinear uncertainty estimation approach combined global and local optimization to seabed interface-wave dispersion inversion in a rigorous manner.
This paper applies a dataset of ocean seismic ambient noise data recorded by ocean bottom seismic cable to extract multi-mode interface-wave dispersion curves. The nonlinear Bayesian inversion is applied to estimate seabed sediment parameters and their uncertainties from interface-wave dispersion curves. The main contents of this paper include analysis of tranditional inversion theory and methods, interface-wave dispersion curves extracting from the seismic ambient noise data, the expressions and computional method of dispersion equations, nonlinear Bayesian inversion formulation and the study of multi-mode interface-wave dispersion curves inversion.
The main contributions are as follows:
1.A high accuracy and resolution approach to extract the interface-wave dispersion curves are applied from the ocean seismic ambient noise data. The fundamental principles of the cross-correlation, Green’s function and time-frequency analysis are illustrated and the general process to extract the interface-wave dispersion curves is summarized. The ambient noise has the dispersion characteristics because of its random sources and the effects of multiple scattering, so the resolution of dispersion is independent of the seismic sources. The multi-mode interface-wave dispersion curves are obtained by processing the noise signals recorded by an ocean bottom seismic.
2.An appropriate forward model is built and resolved to obtain the phase velocity dispersion of interface-wave on multilayered media. The forward model is a prerequisite for inversion and determines the precision and reliability of inversion. The Thompson-Haskill matrix formalism are used to compute the phase velocity dispersion equations for elastic plane waves propagated in a semi-infinite media with n parallel, homogeneous, istropic layers. The numerical case is applied to certify the effective of this method and illustrate this method has relative simple forms, obvious physical meanings of parameters, and the advantages of easy computing and programming.
3.A nonlinear Bayesian inversion approach is applied in this paper. In a Bayesian formulation, the multi-dimensional PPD represents the general solution to an inversion problem. The maximum a posterior (MAP) estimates are determined by minimizing misfit function numerically using adaptive simplex simulated annealing (ASSA), an effective hybrid optimization algorithm that combines the local downhill-simplex method with a very fast simulated annealing global search. The Bayesian information criterion (BIC) is applied to determine the optimal model that fully explains the observed data by the different parameterizations. An efficient and complete Metropolis Hastings sampling (MHS) algorithm is applied for computing 1-D and 2-D parameter marginal probability distributions. Bayesian inversion technique not only provides the MAP estimation, but also estimates the uncertainties of unkown parameters.
4.The mechanism of multi-mode interface-wave dispersion curves is studied and analyzed. It is usually considered that the fundamental mode of interface-wave dominates the recorded wavefield and higher modes can be ignored. However, the higher modes contribute significant amounts of energy at higher frequencies and the higher modes of interface wave can be applied to improve the accuracy of the inverted shear-wave velocity profiles. In this paper, inversion studies are carried out for both the fundamental mode alone and for the first three modes to determine the best parameterization for the shear-wave velocity profiles considering the different parameterizations. The results show that the multi-mode of interface-wave is more sensitive to the seabed sediment structures than the fundamental mode. The multi-mode interface-wave dispersion curves inversion can obtain more shear-wave velocity profile structures, especially the near-interface structures with low-velocities layers; improve the resolution and reliability of shear-wave velocities.
The innovation of the dissertation is appling nonlinear Bayesion inversion to estimate seabed shear-wave velocity profiles and their uncertainties using multi-mode interface wave dispersion curves extracted from ocean ambient noise data.
界面波频散曲线的提取精度是反演成败的关键因素。传统界面波频散曲线反演方法是基于天然或人工激发的地震波在海底沉积层中传播的频散特性来反演海底沉积层属性。但传统的界面波频散曲线提取的分辨率受到地震分布和台站位置的影响。此外,界面波频散曲线反演是一个典型的高度非线性、多参数、多极值的海洋地球物理反演问题和最优化控制问题。由于正演模拟计算和测量误差等因素的存在,通常反演结果并没有唯一的“最优解”,而现有的非线性反演方法虽然不依赖于初始模型的选取,具有全局寻优和非线性映射能力,但参数的反演结果仅仅是一组最大后验概率意义下的最优解。本文旨在发展一种不依赖于震源、高分辨率的界面波频散曲线提取方法和一种既能满足局部和全局收敛条件,又能对参数反演结果的不确定性进行定量和定性分析的反演方法。
本文从海底地震仪记录的海底环境噪声数据中提取出高分辨率的多模态界面波频散曲线,基于新近发展的非线性贝叶斯反演理论,对基阶模态和多模态界面波频散曲线进行反演研究。论文主要工作包括传统反演理论和方法分析、基于海洋环境噪声提取界面波频散曲线、界面波频散曲线正演模型、非线性贝叶斯反演理论以及多模态界面波频散曲线反演研究等内容。
论文的主要研究成果包括:
1.提出了一种从海洋环境噪声中提取界面波频散曲线的方法。阐述了互相关、格林函数以及时频分析方法的基本原理,归纳了界面波提取的一般流程。海底地震环境噪声的源具有随机性,经多次散射的影响,具有与地震界面波相似的频散特性,其分辨率不依赖于震源信息,采样方向均匀,精度更高。通过对实测海洋环境噪声数据进行分析处理,获得界面波频散曲线的多模态特征,验证了该方法的可行性和有效性。
2.实现了多模态界面波频散曲线正演模型的建立与求解。正演是反演的前提,是提高反演精度和速度的关键因素。给出了各向同性均匀平面波的弹性波动方程,采用数值模拟实例实现并验证了Thompson-Haskill矩阵算法的有效性,该方法表达形式简单、物理意义明确,且易于编程实现。
3.完善了非线性贝叶斯反演方法。将反演问题的解转化为参数后验概率密度(PPD)的求解,首先利用非线性全局优化算法——自适应单纯形模拟退火法(ASSA)求解最大后验概率(MAP)模型,然后基于贝叶斯信息准则法(BIC)进行模型选择,对最优模型利用非线性数值积分方法——Metropolis-Hasting采样法(MHS)求解参数PPD和相关特征量,进而分析反演结果。与传统的单点估计法不同,非线性贝叶斯反演方法不仅可以有效地估计MAP模型,而且可以从统计角度对参数反演结果的不确定性进行定性和定量分析,通过一个数值算例来说明该算法的有效性。
4.探讨了多模态界面波频散曲线联合反演的机理。传统的界面波频散曲线反演研究认为,基阶模态的能量在波场中占主导地位,在反演中通常忽略高阶模态的影响。然而,在某些频段,如高频或中频段,基阶模态将不再占据主要地位,此时高阶模态界面波对反演结果的影响应予考虑。分析了不同海底分层和常见海底剪切波速度剖面模型,分别对基阶模态和多模态界面波频散曲线进行反演计算。结果表明,多模态界面波较基阶模态界面波对海底地质结构敏感性更强,利用多模态界面波频散曲线可以获得更多的海底分层结构,特别是近海底低速层信息,提高了反演精度。
论文在基于海洋环境噪声实现界面波频散曲线精确提取,以及利用多模态界面波频散曲线联合反演研究海底剪切波速度剖面结构方面具有创新性。
The detection and recognition study of seafloor is one of the most active front fields of the marine sciences research, which has an important academic significance and application value in the exploration and exploitation of seabed recourses, ocean environment monitoring, marine engineering construction and military operations. The inversion of interface wave dispersion curves is one of the most effective techniques to study the seabed structures and detect the seafloor resources. Recently, interface-wave inversion work has been getting more and more attention to estimate the shear-wave velocity profile structures. Shear-wave velocity provides a good indicator of sediment rigidity for seafloor geotechnical applications and shear-wave transition in shallow seabed can represent an important ocean acoustic loss mechanism which must be considered in propagation modeling and sonar performance predictions.
The extraction resolution of interface-wave dispersion curves is a key of success or failure in inversion. The dispersion curves were extracted normally from the seismic interface-wave propagating in seabed sediments by a mean of a natural or artificial earthquake focus. The resolution of dispersion curves is affected by the distributions of source and stations. It is very important to develop a high accuracy and resolution method independent of the seismic focus to obtain the interface-wave dispersion curves and the sediment parameters are estimated by inverting the dispersion curves. In additional, inversion of interface-wave dispersion curves is typically a highly nonlinear, multi-parameter, and multi-optima inversion problem, as well as most other marine geophysical optimization problems. Usually there is not an only optimal solution due to the measurement and calculation errors. The inversion results of traditional linear search methods depend on the choice of a starting model and the accuracy of the partial derivatives, which are prone to being trapped by local minima. The available nonlinear inversion techniques such as genetic algorithm (GA) and simulated annealing (SA), have proven to be quite useful for global optimization problems, but these techniques can only determine the best-fit model and slower convergence and not provide quantitatively nonlinear uncertainty estimation of model parameters. It is necessary to develop a quantitative nonlinear uncertainty estimation approach combined global and local optimization to seabed interface-wave dispersion inversion in a rigorous manner.
This paper applies a dataset of ocean seismic ambient noise data recorded by ocean bottom seismic cable to extract multi-mode interface-wave dispersion curves. The nonlinear Bayesian inversion is applied to estimate seabed sediment parameters and their uncertainties from interface-wave dispersion curves. The main contents of this paper include analysis of tranditional inversion theory and methods, interface-wave dispersion curves extracting from the seismic ambient noise data, the expressions and computional method of dispersion equations, nonlinear Bayesian inversion formulation and the study of multi-mode interface-wave dispersion curves inversion.
The main contributions are as follows:
1.A high accuracy and resolution approach to extract the interface-wave dispersion curves are applied from the ocean seismic ambient noise data. The fundamental principles of the cross-correlation, Green’s function and time-frequency analysis are illustrated and the general process to extract the interface-wave dispersion curves is summarized. The ambient noise has the dispersion characteristics because of its random sources and the effects of multiple scattering, so the resolution of dispersion is independent of the seismic sources. The multi-mode interface-wave dispersion curves are obtained by processing the noise signals recorded by an ocean bottom seismic.
2.An appropriate forward model is built and resolved to obtain the phase velocity dispersion of interface-wave on multilayered media. The forward model is a prerequisite for inversion and determines the precision and reliability of inversion. The Thompson-Haskill matrix formalism are used to compute the phase velocity dispersion equations for elastic plane waves propagated in a semi-infinite media with n parallel, homogeneous, istropic layers. The numerical case is applied to certify the effective of this method and illustrate this method has relative simple forms, obvious physical meanings of parameters, and the advantages of easy computing and programming.
3.A nonlinear Bayesian inversion approach is applied in this paper. In a Bayesian formulation, the multi-dimensional PPD represents the general solution to an inversion problem. The maximum a posterior (MAP) estimates are determined by minimizing misfit function numerically using adaptive simplex simulated annealing (ASSA), an effective hybrid optimization algorithm that combines the local downhill-simplex method with a very fast simulated annealing global search. The Bayesian information criterion (BIC) is applied to determine the optimal model that fully explains the observed data by the different parameterizations. An efficient and complete Metropolis Hastings sampling (MHS) algorithm is applied for computing 1-D and 2-D parameter marginal probability distributions. Bayesian inversion technique not only provides the MAP estimation, but also estimates the uncertainties of unkown parameters.
4.The mechanism of multi-mode interface-wave dispersion curves is studied and analyzed. It is usually considered that the fundamental mode of interface-wave dominates the recorded wavefield and higher modes can be ignored. However, the higher modes contribute significant amounts of energy at higher frequencies and the higher modes of interface wave can be applied to improve the accuracy of the inverted shear-wave velocity profiles. In this paper, inversion studies are carried out for both the fundamental mode alone and for the first three modes to determine the best parameterization for the shear-wave velocity profiles considering the different parameterizations. The results show that the multi-mode of interface-wave is more sensitive to the seabed sediment structures than the fundamental mode. The multi-mode interface-wave dispersion curves inversion can obtain more shear-wave velocity profile structures, especially the near-interface structures with low-velocities layers; improve the resolution and reliability of shear-wave velocities.
The innovation of the dissertation is appling nonlinear Bayesion inversion to estimate seabed shear-wave velocity profiles and their uncertainties using multi-mode interface wave dispersion curves extracted from ocean ambient noise data.
引文
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