基于贝叶斯理论的软夹层多模式瑞雷波频散曲线反演研究

Inversion of multimode Rayleigh-wave dispersion curves of soft interlayer based on Bayesian theory

获得较高精度的软夹层横波速度和厚度是瑞雷波频散曲线反演的难点之一,尤其对一些低敏感性的软夹层而言,单纯依靠传统的算法改进以及多模式反演,反演效果往往不是非常显著。首次尝试采用算法改进、多模式及非线性贝叶斯定理相结合反演低敏感性软夹层。算法改进体现在,将阻尼惯性权和混沌思想融入到粒子群算法中,但改进算法并未解决软夹层模型低敏感性的困扰;为从反演解的角度分析评价影响反演精度因素,采用无偏Metropolis-Hastings sampling(MHS)方法对后验概率进行数值积分,并通过参数旋转提高采用效率,积分得到的1D和混合边缘概率分布以及参数相关系数矩阵等参数反应了反演解的不确定性和参数间相关性等信息。为解决低敏感性反演精度低问题,尝试采用贝叶斯信息准则(BIC),判断出最佳参数化模型,而此准则得到的最佳模型与理论模型更为吻合。应用非线性贝叶斯方法和BIC准则反演实测防渗墙数据,得到的反演剖面也与已知防渗墙结构较好吻合。

Obtaining shear-wave velocity and thickness of soft interlayer with higher precision is always one of the difficulties in inversion of Rayleigh-wave dispersion curve, and it is not obviously improved when only depending on the improved algorithm and multimode inversion for low-sensitivity soft interlayer. The improved algorithm and combination of multimode and nonlinear Bayes' theorem are adopted to invert low-sensitivity soft interlayer. The damping inertia weight and chaos are added into the particle swarm optimization as improved algorithm. However, the improved algorithm does not solve the problem with low-sensitivity soft interlayer models. To analyze and evaluate the factors affecting the accuracy of inversion from the perspective of the inversion solution, the unbiased Metropolis-Hastings sampling(MHS) method is used for numerical integration posterior probability, and the rotation of parameters is used to improve the efficiency of sampling. The obtained integral 1D and mixed marginal probability distributions and correlation sufficiend matrix of parameters reflect the uncertainty and parameter inversion solution for correlation and other information. To solve the problem of low-curacy inversion of low-sensitivity soft interlayer, the Bayesian information criterion(BIC) is employed to determine the optimal parameters of the model. The optimal model agrees with thetheoretical one. Applying the nonlinear Bayesian inversion method and BIC to invert the measured data of seepage prevention wall, the obtained inversion profiles are also in good agreement with the structure of the known seepage prevention wall.