• ISSN 2097-1893
  • CN 10-1855/P

地球物理反演问题中的贝叶斯方法研究

蒋星达 张伟 杨辉

引用本文: 蒋星达,张伟,杨辉. 2022. 地球物理反演问题中的贝叶斯方法研究. 地球与行星物理论评,53(2):159-171
Jiang X D, Zhang W, Yang H. 2022. The research on Bayesian inference for geophysical inversion. Reviews of Geophysics and Planetary Physics, 53(2): 159-171

地球物理反演问题中的贝叶斯方法研究

doi: 10.19975/j.dqyxx.2021-042
基金项目: 国家自然科学基金资助项目(U1901602);深圳市深远海油气勘探技术重点实验室资助项目(ZDSYS20190902093007855);深圳市科技计划资助项目(KQTD20170810111725321)
详细信息
    通讯作者:

    蒋星达(1989-),男,博士研究生,主要从事微地震监测、正反演方法的研究及应用. E-mail:11749289@mail.sustech.edu.cn

  • 中图分类号: P315

The research on Bayesian inference for geophysical inversion

Funds: Supported by the National Natural Science Foundation of China (Grant No. U1901602), the Shenzhen Key Laboratory of Deep Offshore Oil and Gas Exploration Technology (Grant No. ZDSYS20190902093007855) and the Shenzhen Science and Technology Program (Grant No. KQTD20170810111725321)
  • 摘要: 基于统计理论的贝叶斯反演方法在先验信息和观测数据的约束下,以后验概率分布的形式表征模型参数在不同区间的可能性大小. 相对于确定性反演理论,贝叶斯反演通过提取模型参数边缘概率分布、最大后验解、平均解、相关系数等定量评价反演结果的不确定性以及模型参数之间的相互关系,通过模型参数后验概率分布反映观测数据和先验信息对模型参数的约束能力. 本文基于贝叶斯方法在地球物理反演中的应用,总结了贝叶斯反演的基本流程,详细介绍了不同背景条件下的先验信息概率分布选择、似然函数建立、后验概率公式求解. 在优化参数方面,介绍了模型参数的固定维和变维反演概念,以及超参数的优化方法;在反演方法方面,着重介绍了固定维和变维反演马尔科夫链蒙特卡罗采样方法;在模型参数评价方面,介绍了不同情况下贝叶斯统计参数的求取. 然后讨论了贝叶斯反演方法采样效率提升的具体措施. 最后对贝叶斯方法在地球物理反演中的应用作出总结.

     

  • 图  1  贝叶斯反演一般流程

    Figure  1.  Flowchart of Bayesian inversion

    图  2  贝叶斯原理示意图

    Figure  2.  Schematic diagram of Bayesian principle

    图  3  模型参数化示意图.(a)一维模型Voronoi 参数化(修改自Sambridge et al., 2013);(b)二维模型Voronoi 网格参数化(修改自Bodin et al., 2012a). 方块表示网格节点,根据相邻网格节点垂直平分线确定网格边. m为模型参数,z为界面位置

    Figure  3.  The schematic diagram of model parameterization. (a) 1D Voronoi model parameterization (modified from Sambridge et al., 2013); (b) 2D Voronoi model parameterization (modified from Bodin et al., 2012a). The squares represent grid nodes, the grid boundaries are determined by the perpendicular bisector of adjacent grid nodes. m is model parameter. z is interface position

    图  4  根据后验概率分布确定S波速度结构(修改自Bodin et al., 2012c

    Figure  4.  S-wave velocity structure determined by posterior probability density distribution (modified from Bodin et al., 2012c)

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出版历程
  • 收稿日期:  2021-08-04
  • 录用日期:  2021-08-27
  • 网络出版日期:  2021-09-06
  • 刊出日期:  2022-03-01

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