地球物理反演问题中的贝叶斯方法研究

蒋星达; 张伟; 杨辉

doi:10.19975/j.dqyxx.2021-042

地球物理反演问题中的贝叶斯方法研究

doi: 10.19975/j.dqyxx.2021-042

蒋星达^{1, 3, ,},
张伟^{2, 3},
杨辉^{2, 3}

1.
哈尔滨工业大学航天工程与力学系，哈尔滨 150006
2.
南方科技大学深圳市深远海油气勘探技术重点实验室，深圳 518055
3.
南方科技大学地球与空间科学系，深圳 518055

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
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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

The research on Bayesian inference for geophysical inversion

Jiang Xingda^{1, 3
, ,},
Zhang Wei^{2, 3},
Yang Hui^{2, 3}

1.
Department of Mechanics and Aerospace Engineering, Harbin Institute of Technology, Harbin 150006, China
2.
Shenzhen Key Laboratory of Deep Offshore Oil and Gas Exploration Technology, Southern University of Science and Technology, Shenzhen 518055, China
3.
Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen 518055, China

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

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.
- 贝叶斯方法 /
- 地球物理反演 /
- 马尔科夫链蒙特卡罗方法 /
- 后验概率分布 /
- 计算效率 /
- 模型评价
Abstract: Based on statistical theory, the Bayesian inversion method adopts the posterior probability distribution to evaluate the model parameters under the constraints of prior information and observation data. Compared to deterministic inversion theory, Bayesian inference is beneficial to quantitative evaluation of inversion uncertainty by the model parameter marginal probability distribution, maximum a posterior estimation (MAP), mean model estimation and correlation coefficient, which accurately reflects the constraint ability of observation data and prior information on model parameters. We systematically summarized the application of the Bayesian inference in geophysical inversion and proposed the basic flowchart to realize Bayesian model evaluation. Firstly, the Bayesian theory is simply introduced. The prior information probability distribution, the likelihood function formula, and the construction of the posterior probability equation are explained in detail. Secondly, the implementation process of Bayesian inversion is discussed in detail. As for model parameter updates, the concepts of fixed and trans-dimensional inversion with the hyperparameter optimization are discussed. In terms of inversion methods, the Markov Chain Monte Carlo (MCMC) sampling methods of fixed and trans-dimensional inversion are highlighted. In consideration of model parameter evaluation, the calculation of Bayesian statistical parameters under different conditions is introduced. Then the specific measures to improve the sampling efficiency of Bayesian inversion are discussed. Finally, the application of Bayesian inference in geophysical inversion is summarized.
- Bayesian inference /
- geophysical inversion /
- Markov Chain Monte Carlo method /
- posterior probability distribution /
- sampling efficiency /
- model evaluation

HTML全文

图 1 贝叶斯反演一般流程

Figure 1. Flowchart of Bayesian inversion

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图 2 贝叶斯原理示意图

Figure 2. Schematic diagram of Bayesian principle

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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

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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)

下载: 全尺寸图片幻灯片

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