| 瑞雷波多阶模式频散曲线稀疏正则化反演方法研究 |
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| 引用本文： | 崔岩,王彦飞.瑞雷波多阶模式频散曲线稀疏正则化反演方法研究[J].地球物理学报,2022,65(3):1086-1095. |
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| 作者姓名： | 崔岩 王彦飞 |
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| 作者单位： | 山东科技大学地球科学与工程学院,青岛 266590;河北地质大学,京津冀城市群地下空间智能探测与装备重点实验室,石家庄050031,中国科学院地质与地球物理研究所,中国科学院油气资源研究重点实验室,北京 100029;中国科学院大学,北京100049;中国科学院地球科学研究院,北京 100029 |
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| 基金项目： | 国家自然科学基金(12171455);中国科学院创新项目(ZDBS-LY-DQC003)资助。 |
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| 摘 要： | 目前瑞雷波多阶模式频散曲线反演中仅考虑数据的拟合,缺乏对模型的约束,不能很好地刻画地层间断面的问题,针对此问题,研究了瑞雷波多阶模式频散曲线稀疏正则化反演方法.正演模拟基于广义反射-透射系数法,数值计算上采用一种快速求根方法,与二等分方法相比,能够在很短的时间内达到最优的收敛效果;反演建模时采用L1范数正则化方法对模型进行稀疏性刻画,使反演结果更加符合地质实际;在反问题的数值实现上,针对稀疏正则化模型提出一种隐式迭代正则化算法,其迭代算子具有非膨胀特性,可以收敛到极小化问题的解.数值实验结果表明,新的反演方案具有计算效率高,模型"逐块"光滑的特性刻画好,对非高斯噪声鲁棒性强的特点.
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| 关 键 词： | 瑞雷波 多阶模式频散曲线 稀疏正则化反演 速度结构 |
Sparse regularization inversion of Rayleigh wave multiple mode dispersion curve |
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| CUI Yan,WANG YanFei.Sparse regularization inversion of Rayleigh wave multiple mode dispersion curve[J].Chinese Journal of Geophysics,2022,65(3):1086-1095. |
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| Authors: | CUI Yan WANG YanFei |
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| Institution: | (Shandong University of Science and Technology,College of Earth Science and Engineering,Qingdao 266590,China;Key Laboratory of Intelligent Detection and Equipment for Underground Space of Beijing-Tianjin-Hebei Urban Agglomeration,Ministry of Natural Resources,Hebei GEO University,Shijiazhuang 050031,China;Key Laboratory of Petroleum Resources Research,Chinese Academy of Sciences,Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China;University of Chinese Academy of Sciences,Beijing 100049,China;Innovation Academy for Earth Science,Chinese Academy of Sciences,Beijing 100029,China) |
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| Abstract: | The common Rayleigh wave multi-mode dispersion curve inversion only considers the fitting of data,and lacks constraints on the model.Thus,it cannot well describe the stratigraphic discontinuity.Considering the above problems,this paper studies the sparse regularization inversion method using Rayleigh wave multi-mode dispersion curves.Solving methodologies for inverse problems involve three aspects:forward simulation,inversion modeling,and numerical realization.For Rayleigh wave multi-mode dispersion curves inversion,the forward modeling of the dispersion curve is based on the classical generalized reflection-transmission coefficient method.A fast root-finding method for the numerical calculation of the Rayleigh wave phase velocity is employed.Compared with the commonly used bisection method in literature,it achieves the optimal solution in a short time.From the concept of continuum physics,the geophysical model is best described by a piecewise smooth set of discontinuous functions.This physical discontinuity of the shear wave velocity model can be described by the sparsity of model parameters.Therefore,the L1 norm regularization method is used to describe the sparseness of the model.This makes the inverted shear wave velocity model to be more realistic.In addition,the L1 norm regularization can improve the resolution and enhance robustness to non-Gaussian noise.In numerical realization,an implicit iterative regularization algorithm is proposed for solving the above sparse regularization problem.The iterative operator possesses the non-expansion characteristic and hence the algorithm converges to the optimal solution of the minimization.Numerical experimental results show that the new inversion scheme has the advantages of high computational efficiency,well sparsity characterization,and strong robustness to non-Gaussian noise. |
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| Keywords: | Rayleigh wave Multiple mode dispersion curve Sparse regularization inversion Velocity structure |
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