基于贝叶斯理论面波频散曲线随机反演

doi:10.11720/wtyht.2021.1100

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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。

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	刘辉
	李静
	曾昭发
	王天琪

关键词 ：贝叶斯理论, 马尔科夫链随机反演, 瑞利波频散曲线, 约束反演

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.

Key words： Bayesian theory Monte Carlo Markov Chain (MCMC) stochastic inversion Rayleigh wave dispersion curve constraint inversion

收稿日期: 2020-03-09 修回日期: 2021-01-13 出版日期: 2021-08-20

ZTFLH:

P631.4

基金资助:国家自然科学基金项目(41874134);吉林省优秀青年基金(20190103142JH);吉林省自然科学基金(20200201216JC);中国科协第五届青年托举人才项目(2019QNRC001)

通讯作者: 李静

作者简介: 刘辉(1996-),男,硕士研究生,主要从事面波频散曲线反演方法研究工作。Email: 177344303@qq.com

引用本文:

刘辉, 李静, 曾昭发, 王天琪. 基于贝叶斯理论面波频散曲线随机反演[J]. 物探与化探, 2021, 45(4): 951-960.
LIU Hui, LI Jing, ZENG Zhao-Fa, WANG Tian-Qi. Stochastic inversion of surface wave dispersion curves based on Bayesian theory. Geophysical and Geochemical Exploration, 2021, 45(4): 951-960.

链接本文:

https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2021.1100 或 https://www.wutanyuhuatan.com/CN/Y2021/V45/I4/951

Fig.1 使用Voronoi核进行模型参数化
a—无先验信息的v_s均匀半空间模型;b—有先验信息的三层v_s空间模型

Fig.2 模型的4个扰动方式
a—改变核的v_s;b—改变核的深度;c—产出一个浮动核;d—移除一个浮动核

Fig.3 面波随机反演基本流程

Table 1 4层v_s递增模型参数

Fig.4 4层v_s递增模型基阶频散曲线反演
a—无约束反演结果;b—有先验约束反演结果;c—无约束反演的最佳模型与实际模型频散曲线;d—有先验约束反演的最佳模型与实际模型频散曲线;e—迭代误差曲线

Table 2 4层含低速夹层模型参数

Fig.5 4层含低速夹层模型基阶频散曲线反演
a—无约束反演结果;b—有先验约束反演结果;c—无约束反演的最佳模型与实际模型频散曲线;d—无约束反演频散曲线误差;e—有先验约束反演的最佳模型与实际模型频散曲线;f—带约束反演频散曲线误差;g—迭代误差曲线

Fig.6 探地雷达处理剖面(a)与基于卷积神经网络的GPR层界面识别结果(b)

Fig.7 实测数据反演
a—第13炮地震记录;b—由炮集记录提取的频散能量;c—无约束反演结果;d—GPR深度约束反演结果;e—迭代误差曲线

Fig.8 拟二维剖面反演结果对比
a—无约束反演结果组合成的拟2D剖面;b—GPR深度约束反演结果组合成的拟2D剖面

[1]	李庆春, 邵广周, 刘金兰, 等. 瑞雷面波勘探的过去、现在和未来[J]. 地球科学与环境学报, 2006,28(3):74-77.
[1]	Li Q C, Shao G Z, Liu J L, et al. Past,present and future of Rayleigh surface wave exploration[J]. Journal of Earth Sciences & Environment, 2006,28(3):74-77.
[2]	张立, 刘争平. 水平层状介质中基阶瑞利面波椭圆极化特征数值分析与研究[J]. 地球物理学报, 2013,56(5):1686-1695,doi: 10.6038/cjg20130526.
[2]	Zhang L, Liu Z P. A study of the elliptic polarization characteristics of fundamental mode Rayleigh wave based on numerical simulation[J]. Chinese Journal of Geophysics, 2013,56(5):1686-1695,doi: 10.6038/cjg20130526.
[3]	夏江海, 高玲利, 潘雨迪, 等. 高频面波方法的若干新进展[J]. 地球物理学报, 2015,58(8):2591-2605,doi: 10.6038/cjg20150801.
[3]	Xia J H, Gao L L, Pan Y D, et al. New findings in high frequency surface wave method[J]. Chinese Journal of Geophysics, 2015,58(8):2591-2605,doi: 10.6038/cjg20150801.
[4]	Li J, Hanafy S. Skeletonized inversion of surface wave:Active source versus controlled noise comparison[J]. Interpretation, 2016,4(3):11-19.
[5]	石耀霖, 金文. 面波频散反演地球内部构造的遗传算法[J]. 地球物理学报, 1995,38(2):189-198.
[5]	Shi Y L, Jin W. Genetic algorithms inversion of lithospheric structure from surface wave dispersion[J]. Chinese Journal of Geophysics, 1995,38(2):189-198.
[6]	Park C B, Miller R D, Xia J. Multichannel analysis of surface waves[J]. Geophysics, 1999,64(3):800-808.
[7]	Xia J H, Miller R D, Park C B. Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves[J]. Geophysics, 1999,64(3):691-700.
[8]	Song X H, Gu H M, Liu J P. Occam's inversion of high-frequency Rayleigh wave dispersion curves for shallow engineering applications[C]// Wuhan:Proceedings of the Second International Conference on Environmental and Engineering Geophysics (ICEEG), 2006: 124-130.
[9]	鲁来玉, 张碧星, 汪承灏. 基于瑞利波高阶模式反演的实验研究[J]. 地球物理学报, 2006,49(4):1082-1091.
[9]	Lu L Y, Zhang B X, Wang C H. Experiment and inversion studies on Rayleigh wave considering higher modes[J]. Chinese Journal of Geophysics, 2006,49(4):1082-1091.
[10]	罗银河, 夏江海, 刘江平, 等. 基阶与高阶瑞利波联合反演研究[J]. 地球物理学报, 2008,51(1):242-249.
[10]	Luo Y H, Xia J H, Liu J P, et al. Joint inversion of fundamental and higher mode Rayleigh waves[J]. Chinese Journal of Geophysics, 2008,51(1):242-249.
[11]	Beaty K S, Schmitt D R, Sacchi M. Simulated annealing inversion of multimode Rayleigh wave dispersion curves for geological structure[J]. Geophysical Journal International, 2002,151(2):622-631.
[12]	Song X, Gu H, Zhang X, et al. Pattern search algorithms for nonlinear inversion of high-frequency Rayleigh-wave dispersion curves[J]. Computers & Geosciences, 2008,34(6):611-624.
[13]	Song X, Tang L, Lyu X, et al. Application of particle swarm optimization to interpret Rayleigh wave dispersion curves[J]. Journal of Applied Geophysics, 2012,84(9):1-13,doi: 10.1016/j.jappgeo.2012.05.011.
[14]	蔡伟, 宋先海, 袁士川, 等. 基于萤火虫和蝙蝠群智能算法的瑞雷波频散曲线反演[J]. 地球物理学报, 2018,60(6):2409-2420,doi: 10.6038/cjg2018L0322.
[14]	Cai W, Song X H, Yuan S C, et al. Inversion of Rayleigh wave dispersion curves based on firefly and bat algorithms[J]. Chinese Journal of Geophysics, 2018,60(6):2409-2420,doi: 10.6038/cjg2018L0322.
[15]	于东凯, 宋先海, 江东威, 等. 改进蜂群算法及其在面波频散曲线反演中的应用[J]. 地球物理学报, 2018,61(4):1482-1495,doi: 10.6038/cjg2018L0424.
[15]	Yu D K, Song X H, Jiang D W, et al. Improvement of Artificial Bee Colony and its application in Rayleigh wave inversion[J]. Chinese Journal of Geophysics, 2018,61(4):1482-1495,doi: 10.6038/cjg2018L0424.
[16]	于东凯, 宋先海, 张学强, 等. 蚱蜢算法在瑞雷波频散曲线反演中的应用[J]. 石油地球物理勘探, 2019,54(2):288-301,doi: 10.13810/j.cnki.issn.1000-7210.2019.02.007.
[16]	Yu D K, Song X H, Zhang X Q, et al. Rayleigh wave dispersion inversion based on grasshopper optimization algorithm[J]. Oil Geophysical Prospecting, 2019,54(2):288-301,doi: 10.13810/j.cnki.issn.1000-7210.2019.02.007.
[17]	Aki K. Space and time spectra of stationary stochastic waves, with special reference to microtremors[J]. Bull. Earth. Res. Inst., 1957,35:415-456.
[18]	徐佩芬, 李世豪, 凌甦群, 等. 利用SPAC法估算地壳S波速度结构[J]. 地球物理学报, 2013,56(11):3846-3854.
[18]	Xu P F, Li S H, Ling S Q. Application of SPAC method to estimate the crustal S-wave velocity structure[J]. Chinese Journal of Geophysics, 2013,56(11):3846-3854.
[19]	张宝龙, 李志伟, 包丰, 等. 基于微动方法研究五大连池火山区尾山火山锥浅层剪切波速度结构[J]. 地球物理学报, 2016,59(10):3662-3673.
[19]	Zhang B L, Li Z W, Bao F. Shallow shear-wave velocity structures under the Weishan volcanic cone in Wudalianchi volcano field by microtremor survey[J]. Chinese Journal of Geophysics, 2016,59(10):3662-3673.
[20]	Dettmer J, Dosso S E, Holland C W. Trans-dimensional geoacoustic inversion[J]. The Journal of the Acoustical Society of America, 2010,128(6):3393-3405,doi: https:// doi.org/10.1121/ 1.3500674.
[21]	Maraschini M, Foti S. A Monte Carlo multimodal inversion of surface waves[J]. Geophysical Journal International, 2010,182(3):66,doi: https://doi.org/10.1111/j.1365-246X.2010.04703.x.1557-15
[22]	Denison D, Holmes C, Mallik B, et al. Bayesian methods for nonlinear classification and regression[M]. Chichester:John Wiley, 2002.
[23]	Qin T, Zhao Y, Hu S, et al. An interactive integrated interpretation of GPR and Rayleigh wave data based on the genetic algorithm[J]. Surveys in Geophysics, 2019: 1-26,doi: https://doi.org/10.1007/s10712-019-09543-x.
[24]	Li J, Chen Y Q, Schuster G. Separation of multi-mode surface waves by supervised machine learning methods[J]. Geophysical Prospecting, 2019,doi: 10.1111/1365-2478.12927.
[25]	Wang Y R. The geotechnical investigation report of Hongxueyaju in Huainan[R]. Anhui Hydrological Engineering Survey and Research Institute, 2013: 1-13,doi: https://wenku.baidu.com/view/dbf3624a3968011ca200913f.html.

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