时间域航空电磁数据的自适应变维贝叶斯反演研究

Adaptive trans-dimensional Bayesian inversion of airborne time-domain electromagnetic data

求解地球物理反演问题的目的,不仅是要获得"最佳的"解,还需要提供反演参数的不确定性信息,从而对反演结果的可靠性进行有效地评价.因此,变维贝叶斯反演方法被引入到时间域航空电磁数据的反演解释中.然而,变维贝叶斯反演过程中,Markov链的初始状态和模型采样的步长对反演的效率和结果精度都有较大的影响.为解决Markov链初始状态和模型采样步长的选择问题,本文提出一种时间域航空电磁数据的自适应变维贝叶斯反演方法.该方法采用电导率-深度成像的结果构建Markov链的初始状态,以提高Markov链的收敛性,并缩短"预热"期的时间;同时,在采样过程中通过每次采样模型的数据拟合误差变化情况来自动调整采样步长,以避免采样步长设置不合理带来的影响,并提高模型采样的接受率.最后,通过对正演模拟数据进行反演测试,并与正则化反演结果进行对比,验证了该方法的有效性.反演结果表明,该反演方法不仅可提高反演的效率,还能改善反演结果的精度.

The purpose of solving geophysical inversion problem is not only to obtain the"best"solution,but also to provide the uncertainty information of inversion parameters,so as to effectively evaluate the reliability of inversion results.Therefore,the trans-dimensional Bayesian inversion method is introduced into the inversion of airborne time-domain electromagnetic data.However,in trans-dimensional Bayesian inversion,the initial state of Markov chain and the step size of model sampling have a great influence on the efficiency and precision of inversion.To solve the selection problem of initial state and sampling step size,in this paper we propose an adaptive trans-dimensional Bayesian inversion method for airborne time-domain electromagnetic data.In this method,the initial state of Markov chain is constructed with the results of conductivity-depth imaging which can improve the convergence of Markov chain and shorten the time of"burn-in"period.At the same time,it automatically adjusts the sampling step length in the sampling process through the data fitting error of each sampling model,so as to avoid the influence of unreasonable sampling step size and improve the acceptance rate of model sampling.Finally,the validity of the proposed method is verified by inversion test on the forward modelling data and comparison with the regularized inversion results.The inversion results show that the adaptive trans-dimensional Bayesian inversion method can not only improve the efficiency of inversion,but also improve the accuracy of inversion results.