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应用地球物理  2016, Vol. 13 Issue (1): 103-115    DOI: 10.1007/s11770-016-0527-3
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基于双约束项的广义线性多波联合反演
方圆1,张丰麒2,王彦春1
1. 地下信息探测技术与仪器教育部重点实验室,中国地质大学(北京),北京 100083
2. 中国石化石油勘探开发研究院,北京 100083
Generalized linear joint PP–PS inversion based on two constraints
Fang Yuan1, Zhang Feng-Qi2, and Wang Yan-Chun1
1. Key laboratory of Geodetection (China University of Geosciences (Beijing)), Ministry of Education, Beijing 100083, China).
2. Petroleum Exploration and Production Research Institute, Beijing 100083, China.
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摘要 常规多波联合反演采用Zoeppritz方程的近似式构建正演方程,反演过程中需要假定背景纵横波速度比为常数,其反演精度不高,稳定性不好。本文提出了一种基于精确Zoeppritz方程的多波联合反演方法,结合贝叶斯方法进行广义线性反演。本方法基于精确Zoeppritz方程构建正演方程,避免了近似式反演在大角度时引起的误差;利用贝叶斯方法引入模型参数的先验分布信息,作为反演的正则化项,降低了反演的不适定性;反演目标函数中引入低频软约束,稳定了反演低频结果,提高了反演的鲁棒性;在求解反演目标函数时,利用快速算法,降低了反演的运算量。经过模型试算,证明了该方法的优越性和抗噪性;并在实际资料的应用中证明了该方法的实用性和有效性。
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方圆
张丰麒
王彦春
关键词: 多波联合反演   精确Zoeppritz方程   广义线性反演   贝叶斯反演   低频软约束     
Abstract: Conventional joint PP–PS inversion is based on approximations of the Zoeppritz equations and assumes constant VP/VS; therefore, the inversion precision and stability cannot satisfy current exploration requirements. We propose a joint PP–PS inversion method based on the exact Zoeppritz equations that combines Bayesian statistics and generalized linear inversion. A forward model based on the exact Zoeppritz equations is built to minimize the error of the approximations in the large-angle data, the prior distribution of the model parameters is added as a regularization item to decrease the ill-posed nature of the inversion, low-frequency constraints are introduced to stabilize the low-frequency data and improve robustness, and a fast algorithm is used to solve the objective function while minimizing the computational load. The proposed method has superior antinoising properties and well reproduces real data.
Key words: joint PP–PS inversion   Zoeppritz equations   generalized linear inversion   Bayesian statistics   low-frequency constraints   
收稿日期: 2015-09-11;
基金资助:

本研究由国家高技术研究发展计划(863计划)(编号:2013AA064201)资助。

引用本文:   
方圆,张丰麒,王彦春. 基于双约束项的广义线性多波联合反演[J]. 应用地球物理, 2016, 13(1): 103-115.
Fang Yuan,Zhang Feng-Qi,Wang Yan-Chun. Generalized linear joint PP–PS inversion based on two constraints[J]. APPLIED GEOPHYSICS, 2016, 13(1): 103-115.
 
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