摘要
应用贝叶斯理论对一维(1D)大地电磁反演问题进行无偏差不确定度分析。在贝叶斯理论中,测量数据和先验信息包含在后验概率密度函数(PPD)中,它可以解释成模型的单点估计和不确定度等贝叶斯推断,这些信息的获取需要对反演问题进行优化求最优模型和在高维模型空间中对PPD进行采样积分。采样的完全、彻底和效率,对反演结果有着重要的影响。为了使采样更有效、更完全,数值积分采用主分量参数空间的Metropolis Hastings采样,并采用了不同的采样温度。在反演中,同时采用了欠参数化和超参数化方法,数据误差和正则化因子被当成随机变量。反演结果得到各参数的不确定度、参数间的相关关系和不同深度模型的不确定度分布。COPROD1数据的反演结果表明模型空间中存在双峰结构。非地电参数在反演中得到了约束,说明数据本身不仅包含地球物理模型信息(电导率等),还包含了这些非地电参数的信息。
This paper employs Bayesian inference theory to obtain unbiased parameter uncertainties,for the one-dimensional magnetotelluric(MT) inverse problem.In the Bayesian formulation,the data and the model parameters are considered random variables and the multi-dimensional posterior probability density(PPD),combining data and prior information,is interpreted in terms of parameter estimates,uncertainties,and inter-relationships,which requires optimizing and integrating the PPD.Integration applies Metropolis-Hastings sampling,rotated to a principal-component parameter space for efficient sampling of correlated parameters at different temperatures.In this paper,both under-parameterized and over-parameterized approaches are considered a 5-layer case and COPROD1 data.Nuisance parameters(e.g.data uncertainties and tradeoff parameter) are treated as unknown random quantities.The marginal distributions give complete insight in the parameter uncertainties,correlation and uncertainty distributions at different depth.For the COPROD1 MT data set,the inversion result represents multi-modal PPDs.The nuisance parameters are well constrained in the inversion as well,which indicates information content of Mt data is sufficient to determine the nuisance parameters in addition to geophysical parameters.
出处
《物探化探计算技术》
CAS
CSCD
2012年第4期371-379,365,共9页
Computing Techniques For Geophysical and Geochemical Exploration
基金
国家科技支撑计划项目(2011BAB04B08)
中国地质调查局科研项目(资[2011]03-01-64)
有色资源与地质灾害探查湖南省重点实验室项目(2010TP4012-6)
关键词
贝叶斯反演
采样
大地电磁法
bayesian inversion
sampling
magnetotelluric method
