摘要
地球物理反演在地震研究和预测中扮演着至关重要的角色.本文旨在概括传统反演方法的局限性,并专注介绍了一种以贝叶斯理论为基础的不确定性反演方法.贝叶斯反演通过不同类型的先验分布和似然函数计算后验分布,特别关注传统的马尔科夫链蒙特卡罗法(Markov Chain Monte Carlo,MCMC)和变分推断方法,以提高反演结果的可靠性.本文详细介绍了贝叶斯反演的关键技术,着重探讨正则化方法(如拉普拉斯正则化和冯卡门正则化),它们限制了地震反演的参数空间,并通过案例研究验证了其有效性.同时,对采样方法(如Metropolis-Hastings算法和Gibbs采样)进行了阐述,这些方法能够对参数空间进行抽样,并近似计算后验分布.尤其详述了Metropolis-Hastings算法在地震反演中的应用.在讨论中强调了模型参数选择的重要性,例如与断层几何形态选择相关的不确定性对反演结果的影响,并介绍了一种将断层几何形态的不确定性纳入反问题的方法.进一步探讨了在构建有限断层源模型时所面临的挑战,并提供了一个使用贝叶斯方法评估不同滑动模型集群可信度的案例研究.最后,文章总结了贝叶斯方法的局限性,并提出了未来研究的方向.在地球物理反演领域,贝叶斯方法的应用为解决传统方法的局限性提供了新的思路和可能性.
The role of geophysical inversion in seismic research and prediction is of paramount importance.This paper seeks to comprehensively outline the constraints associated with conventional inversion techniques,focusing on the introduction of a Bayesian-based uncertainty inversion method.Bayesian inversion involves computing posterior distributions utilizing diverse prior distributions and likelihood functions,with special emphasis on established techniques like the Markov Chain Monte Carlo(MCMC)and variational inference methods,thereby augmenting the reliability of inversion outcomes.The manuscript furnishes an elaborate exposition on pivotal techniques within Bayesian inversion,notably delving into regularization methods(such as Laplace and von Karman regularization)that confine the parameter space in seismic inversion,validated through rigorous case studies.Moreover,it expounds on sampling methodologies(including the Metropolis-Hastings algorithm and Gibbs sampling)that facilitate parameter space sampling and approximate posterior distributions.The application of the Metropolis-Hastings algorithm in seismic inversion is meticulously elucidated.The discussion accentuates the criticality of model parameter selection,notably the influence of uncertainty associated with fault geometric shape selection on inversion results.Additionally,it probes into the challenges encountered in constructing finite fault source models and presents a Bayesian-based case study evaluating the credibility of different slip model clusters.In conclusion,the paper summarizes the limitations inherent in the Bayesian approach and delineates potential avenues for future research directions.In the realm of geophysical inversion,the application of Bayesian methods presents novel prospects for overcoming the constraints of traditional methodologies.
作者
王者
刘云华
WANG Zhe;LIU YunHua(Institute of Geology,China Earthquake Administration,Beijing 100029,China)
出处
《地球物理学进展》
CSCD
北大核心
2024年第5期1771-1787,共17页
Progress in Geophysics
基金
国家自然科学基金(41874027)资助。
关键词
贝叶斯方法
地球物理反演
正则化方法
采样方法
模型参数
模型评价
Bayesian methods
Geophysical inversion
Regularization methods
Sampling methods
Model parameters
Model evaluation
