Stochastic inversion of surface wave dispersion curves based on Bayesian theory
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摘要: 面波频散曲线反演是获得地下横波速度结构的重要地球物理方法。常规基于迭代最小二乘等线性反演方法依赖于初始模型,且存在多极值、容易陷入局部最小、反演精度低等问题。基于贝叶斯理论的随机反演方法是一种可以融合先验信息的非线性反演方法,该方法无需人为给定初始模型,仅利用先验信息对模型进行随机采样,根据概率分布筛选接受合适的后验概率密度估计结果,可达到对细节信息的准确估计。本文针对瑞利面波频散曲线,提出了基于GPR数据先验资料约束的贝叶斯马尔科夫蒙特卡洛(MCMC)随机反演方法,通过随机改变模型参数并计算其频散曲线与实际频散曲线的似然函数来选择是否接受新的模型参数,不断重复此过程,最终得到与实际频散曲线拟合效果最佳的最优解以及横波速度解的后验概率密度分布。通过理论模型以及实际数据反演测试,验证了该方法与常规无约束的随机反演相比,可以有效地提高反演速度和反演精度。Abstract: Surface wave dispersion curve inversion is an important geophysical method for obtaining the velocity and thickness distribution of underground shear wave.Conventional linear inversion methods,such as iterative least squares,relying on the initial model and multiple solution,are easy to fall into local minimum and low inversion accuracy.The stochastic inversion method based on Bayesian theory is a nonlinear inversion method which can integrate prior information.This method does not need initial model,only uses prior information to sample the model randomly,and selects and accepts the appropriate inversion model according to the probability distribution.It achieves the accurate estimation of the detail information.In this paper,the authors present a Bayesian Markov Monte Carlo (MCMC) stochastic inversion method based on GPR data constraints to invert the Rayleigh-waves dispersion curve.In the inversion process,by randomly changing the model parameters and calculating the likelihood function of the dispersion curve and the actual dispersion curve,researchers can choose whether to accept the new model parameters,repeat this process continuously,and finally get the best fitting result with the actual dispersion curve and the posterior probability density distribution of the VS solution.The typical numerical model test and field seismic data demonstrate that,compared with the conventional unconstrained stochastic inversion,the proposed method can effectively reduce the multiple solution and improve the efficiency and accuracy.
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