基于贝叶斯方法的二维大地电磁尖锐边界反演研究

针对常规大地电磁（Magnetotelluric，MT）反演方法对电阻率异常体边界不太敏感的问题，本文尝试基于贝叶斯理论开展二维大地电磁电阻率尖锐边界反演研究.在反演中，模型参数由边界位置及内部电阻率组成，通过贝叶斯理论将模型参数与数据相联系，采用Markov Chain Monte Carlo（MCMC）的Metropolis-Hastings（MH）方法对后验概率密度函数（Posteriori Probability Density，PDD）进行采样.采样过程中无罚值函数约束，完全以数据自身所包含的信息对模型进行约束，同时与有限约束进行比较，并考虑不同起始采样点对结果的影响.以接受率为参考，用模型算例说明MH方法中建议分布函数选择的重要性.当模型参数间相关性较弱时，使用边缘概率分布对采样结果进行分析.该方法能给出模型参数的分布范围，并给出该模型参数范围对应的数据范围.通过与已知模型的对比及数据拟合情况分析检验了该反演方法的有效性.该方法有助于提高大地电磁尖锐边界反演的分辨能力.

Two-dimensional sharp boundary magnetotelluric inversion using Bayesian theory

As the conventional magnetotelluric (MT) inversion is not sensitive to anomalous body sharp boundary, we try to develop a two-dimensional MT inversion method based on Bayesian theory, aiming at better inversion of resistivity sharp boundary. To invert for the boundary of anomalous body, we deal with the boundary position and internal resistivity as model variable, and adopt Bayesian theory to link model variables with data. Then we sample the posteriori probability density (PDD) using the Metropolis-Hastings (MH) method of Markov Chain Monte Carlo method. In the sampling process, there is no penalty function constraint, i.e., the model is completely constrained by all the information of the data. We compare the results with those from the finite-constraint and investigate the influence of different initial sampling points on the results. Taking the acceptance rate as a reference, the importance of the selection of proposal distribution function in the MH method is illustrated by model examples. When cross-correlation of model variables is weak, marginal probability distribution is available to analyze sampling result. This method can give the distribution of the model parameters. The corresponding data distribution can be obtained from the distribution of the model parameters. The inversion method is validated by comparing with the known models and the evaluation of data fitting. This method is helpful to improve the resolution of sharp boundary MT inversion.