多模式面波非线性反演

doi:10.13278/j.cnki.jjuese.20180288

摘要/Abstract

摘要： 利用高频面波反演横波速度一直是浅地表地震工程研究的热点。为深入认识利用高频面波（瑞雷波和勒夫波）评价横波速度的能力，本文首先采取高阶交错网格有限差分法实现两层模型的瑞雷波和勒夫波数值模拟，并应用τ-p变换形成频散能量图。相比瑞雷波，不同模式的勒夫波频散能量很接近，这说明易于实现多模式勒夫波反演。然后利用线性映射实现广义模式识别这种非线性反演方法对含软弱夹层的四层模型的基模式、多模式瑞雷波和勒夫波的变厚度反演。若初始模型很拙劣，相比勒夫波，瑞雷波基模式反演不能重建地层中含有软弱夹层这一特征，瑞雷波多模式反演则可以重建这一特征；勒夫波基模式和多模式反演都可以重建这一特征。即使在地层的泊松比与估计值相差很大时，瑞雷波多模式反演仍能重建地层结构，但其频散曲线总是存在"模式接吻"现象，容易模式误判；而勒夫波反演则不用估计地层泊松比，也不存在"模式接吻"现象。一系列算例表明：高模式瑞雷波的加入会显著提高横波速度评价结果的精度；而高模式勒夫波的加入会令反演系统对半空间以上异常层的参数过于敏感，造成参数过度估计，但也会显著提升对半空间横波速度的评价能力。最后，应用本文方法实现了对实测勒夫波数据的分析。

关键词: 高频面波, 模式识别, 线性映射, 多模式反演, 横波速度

Abstract: Utilization of high frequency surface waves to invert S-wave velocity has been a hotspot in shallow seismic engineering research. To deeply understand the ability of high-frequency surface waves (Rayleigh waves and Love waves) to invert S-wave velocity, in this study, the high-order staggered-grid finite-difference method is used to simulate the Rayleigh and Love waves of a two-layer model. The t-p transformation is adopted to generate the dispersion energy image. Compared with Rayleigh waves, the Love waves dispersion energy of different modes is extremely consistent, which shows that multi-mode inversion is easier to achieve. The generalized pattern search is then realized by linear mapping to achieve the variable-thickness inversion of base mode and multi-mode Rayleigh waves and Love waves of a four-layer model with a weak interlayer. If the initial model is extremely poor, compared to Love waves,the base mode inversion of Rayleigh waves cannot reconstruct the feature of strata with a weak interlayer, which can be attained by multi-mode inversion of Rayleigh waves. Base mode and multi-mode inversion of Love waves can reconstruct this feature. Even when the Poisson's ratio of the stratum is much different from the estimated value, the multi-mode inversion of Rayleigh waves can still reconstruct the stratum structure. However, the multi-mode dispersion curve of Rayleigh waves always has the phenomenon of mode kissing, leading to misjudge. The Love-wave inversion does not require an estimated value of Poisson's ratio, and there is no mode kissing. A series of examples show that an addition of high-mode Rayleigh waves can significantly improve the accuracy of the shear wave velocity evaluation results;although an addition of high-mode Love waves would make the inversion system too sensitive to the parameters of anomalous strata above the half space, making the parameters excessive, it can improve the ability significantly to evaluate the shear wave velocity of the half space. Finally, the analysis of field Love-wave data is realized by using this method.

Key words: high frequency surface waves, pattern search, linear mapping, multi-mode inversion, S-wave velocity

中图分类号:

P631.4

闫英伟, 王者江, 韩飞, 刘聪, 曾凡杰. 多模式面波非线性反演[J]. 吉林大学学报(地球科学版), 2019, 49(6): 1768-1779.

Yan Yingwei, Wang Zhejiang, Han Fei, Liu Cong, Zeng Fanjie. Nonlinear Inversion of Multi-Mode Surface Waves[J]. Journal of Jilin University(Earth Science Edition), 2019, 49(6): 1768-1779.

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