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应用地球物理  2015, Vol. 12 Issue (3): 378-388    DOI: 10.1007/s11770-015-0510-4
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起伏地形条件下二维声波频率域全波形反演
张钱江1,戴世坤1,陈龙伟1,李昆1,赵东东1,黄兴兴2
1. 中南大学 地球科学与信息物理学院,长沙 410083
2. 中国石油大学(北京) 地球物理与信息工程学院,北京 102249
Two-dimensional frequency-domain acoustic full-waveform inversion with rugged topography
Zhang Qian-Jiang1, Dai Shi-Kun1, Chen Long-Wei1, Li Kun1, Zhao Dong-Dong1, and Huang Xing-Xing2
1. School of Info-physics and Geomatics Engineering, Central South University, Changsha 410083, China.
2. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China.
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摘要 本文以有限单元法为基础,对起伏地形条件下二维声波频率域全波形反演进行了研究。在正演算法中,针对截断边界问题,并考虑多频率联合反演中计算区域采用同一套剖分网格的需求,提出了一种适用于起伏地形的衰减边界条件算法。该算法的核心思想是在控制方程波数项中引入衰减因子,通过一定方式调节衰减因子使得声波在衰减层中充分衰减,达到压制截断边界影响的目的。根据指数衰减规律,文中推导出了一种新的衰减因子计算公式,并给出了不同频率条件下衰减层厚度计算公式;在反演算法中,采用共轭梯度法求解高斯牛顿反演迭代方程组,避免直接求解雅克比矩阵和Hessian矩阵带来的巨额计算量,并采用相同的反演模型,对比分析了不同初始模型和频率组合对全波形反演结果的影响。起伏地形模型数值模拟和全波形反演数值试验表明,本文提出的指数衰减边界条件算法和基于该算法的全波形反演算法具有很好的应用效果。
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张钱江
戴世坤
陈龙伟
李昆
赵东东
黄兴兴
关键词全波形反演   起伏地形   衰减边界条件   有限单元法     
Abstract: We studied finite-element-method-based two-dimensional frequency-domain acoustic FWI under rugged topography conditions. The exponential attenuation boundary condition suitable for rugged topography is proposed to solve the cutoff boundary problem as well as to consider the requirement of using the same subdivision grid in joint multifrequency inversion. The proposed method introduces the attenuation factor, and by adjusting it, acoustic waves are sufficiently attenuated in the attenuation layer to minimize the cutoff boundary effect. Based on the law of exponential attenuation, expressions for computing the attenuation factor and the thickness of attenuation layers are derived for different frequencies. In multifrequency-domain FWI, the conjugate gradient method is used to solve equations in the Gauss–Newton algorithm and thus minimize the computation cost in calculating the Hessian matrix. In addition, the effect of initial model selection and frequency combination on FWI is analyzed. Examples using numerical simulations and FWI calculations are used to verify the efficiency of the proposed method.
Key wordsFull-waveform inversion   rugged topography   attenuation boundary condition   finite element method   
收稿日期: 2014-08-25;
基金资助:

本研究由国家高技术研究发展计划(编号:2012AA09A20105)和国家自然科学(编号:41574127)联合资助。

引用本文:   
张钱江,戴世坤,陈龙伟等. 起伏地形条件下二维声波频率域全波形反演[J]. 应用地球物理, 2015, 12(3): 378-388.
Zhang Qian-Jiang,Dai Shi-Kun,Chen Long-Wei et al. Two-dimensional frequency-domain acoustic full-waveform inversion with rugged topography[J]. APPLIED GEOPHYSICS, 2015, 12(3): 378-388.
 
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