跨维贝叶斯反演在地球物理中的研究进展

Research Progress of Trans-dimensional Bayesian Inversion in Geophysics

贝叶斯反演不仅能够得到最佳的模型参数估计,还可以提取丰富的模型参数统计信息,从不同的角度分析数据所包含的模型参数信息。跨维贝叶斯反演将模型参数维数以未知数包含在反演中,根据数据信息和先验信息确定其维数大小,并将模型参数维数的不确定度信息包含在模型参数误差估计中,该方法已经广泛应用于地球物理反演。为了理清该方法在地球物理中的应用情况和全面认识现阶段该方法理论发展水平,通过最新的文献综述,从跨维贝叶斯反演基本理论、起始模型选取、采样方法、数据噪声处理等方面介绍跨维贝叶斯反演,阐述了一维跨维贝叶斯反演的基本原理、发展历程以及研究现状,高维地球物理跨维贝叶斯反演的研究现状,最后探讨了跨维贝叶斯反演的发展趋势。

Bayesian inversion can not only obtain the best estimation of model parameters,but also extract abundant statistical information of model parameters,and analyze the model parameter information from different angles.In trans-dimensional Bayesian inversion,the dimension of the model space is included in the inversion as an unknown number,and it is determined by the data information and the prior information.The uncertainty of themodel parameterization is included in the estimation of model parameter error.It has been widely used in geophysical inversion.To provide an overview on its application and technique development,this paper reviews the trans-dimensional Bayesian inversion in geophysics in terms of the theory development,the method to obtain the original model,the sampling algorithm,the noise treatment to describe the basic principle,development course and research status of one-dimensional cross-Bayesian inversion and to discuss the research status of high-dimensional geophysical cross-Bayesian inversion.At the end,it gives some perspective sights in its future application.