确定场地土层速度结构的改进半波长法

王继鑫, 荣棉水, 李小军, 喻烟

王继鑫, 荣棉水, 李小军, 喻烟. 2020: 确定场地土层速度结构的改进半波长法. 地震学报, 42(3): 362-376. DOI: 10.11939/jass.20190142
引用本文: 王继鑫, 荣棉水, 李小军, 喻烟. 2020: 确定场地土层速度结构的改进半波长法. 地震学报, 42(3): 362-376. DOI: 10.11939/jass.20190142
Wang Jixin, Rong Mianshui, Li Xiaojun, Yu Yan. 2020: Improved half-wavelength method for determining the velocity structure of site soil layer. Acta Seismologica Sinica, 42(3): 362-376. DOI: 10.11939/jass.20190142
Citation: Wang Jixin, Rong Mianshui, Li Xiaojun, Yu Yan. 2020: Improved half-wavelength method for determining the velocity structure of site soil layer. Acta Seismologica Sinica, 42(3): 362-376. DOI: 10.11939/jass.20190142

确定场地土层速度结构的改进半波长法

基金项目: 中国地震局地壳应力研究所基本科研业务费专项(ZDJ2018-10)、北京市自然科学基金项目(8182056)和国家自然科学基金重点国际合作项目(41720104006)共同资助
详细信息
    通讯作者:

    荣棉水: e-mail:waltrong@126.com

  • 中图分类号: P315.2

Improved half-wavelength method for determining the velocity structure of site soil layer

  • 摘要: 地球物理反演浅地表土层波速剖面通常基于初始速度结构模型,为避免对地勘资料产生较多依赖,充分利用地震和背景噪声等被动源观测记录,快速简便地构建出土层反演的初始模型,本文基于场地土层的频散曲线和水平与竖向谱比提出了一种改进半波长法。该方法首先通过水平与竖向谱比确定场地土层的卓越频率,获取场地覆盖层厚度,确定反演所需的频带范围;其次,利用瑞雷波相速度对剪切波速的偏导数随土层深度的变化规律反演出场地的初始速度结构,并结合工程场地勘探中的半波长法,对常见的三类典型土层模型和日本Kushiro场地实测模型进行了实例分析;最后,将反演得到的速度结构与理论或实测速度结构进行误差对比分析。结果表明:改进半波长法获得的初始速度结构相对于理论或实测速度结构的最大误差不超过35%,可为利用地球物理方法反演工程场地波速剖面构造一个较小的搜索模型空间,进而提高反演计算的速度和结果的可靠性。
    Abstract: The initial velocity structure model is generally necessary in the study of geophysical inversion for shallow surface soil wave velocity profile. In order to avoid excessive reliance on the surveying data instead, and to make full use of observation records of passive sources such as earthquakes and ambient noise to quickly and easily construct the initial model of soil inversion, this paper proposes an improved half-wavelength method based on the dispersion curve and the horizontal-to-vertical spectral ratio (HVSR) of the soil layer. Firstly, the method deter-mines the predominant frequency of the soil layer by HVSR, and then obtains the depth of overlying soil, and determines the frequency band range required for the inversion. Next, invert initial velocity structure of the site by using the variation of the partial derivative of the Rayleigh wave velocity to the shear wave velocity with the depth of the soil layer. Combined with the half-wavelength method in engineering site exploration, three types of soil layer models frequently encountered and the measured model of Kushiro site in Japan were analyzed, and the error analysis of the velocity structure was carried out and compared with the theoretical or measured velocity structures. The research shows that the initial velocity structure obtained by the improved half-wavelength method has a maximum error not more than 35%, which can be used to reconstruct a small searching model space in inversion for the wave velocity profile of engineering site by using the geophysical method, so as to improve the speed of inversion calculations and the reliability of result.
  • 图  1  

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    Figure  1.  

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    图  2   三类模型的理论频散曲线

    (a) 递增层模型;(b) 低速夹层模型;(c) 高速夹层模型

    Figure  2.   Theoretical dispersion curves of three types of models

    (a) The stratified media with S-wave velocity increasing from the top to the bottom;(b) The stratified media with the low-velocity layer in between;(c) The stratified media with the high-velocity layer in between

    图  3  

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    (a) 递增层模型;(b) 低速夹层模型;(c) 高速夹层模型

    Figure  3.  

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    $\partial {v_{\rm{R}}} / \partial {\lambda _{\rm{R}}}$

    (a) The stratified media with S-wave velocity increasing from the top to the bottom;(b) The stratified media with the low-velocity layer in between;(c) The stratified media with the high-velocity layer in between

    图  4   三类模型的理论水平与竖向谱比HVSR曲线

    (a) 递增层模型;(b) 低速夹层模型;(c) 高速夹层模型

    Figure  4.   Theoretical HVSR curves for three types of models

    (a) The stratified media with S-wave velocity increasing from the top to the bottom;(b) The stratified media with the low-velocity layer in between;(c) The stratified media with the high-velocity layer in between

    图  5   与反演厚度相关的三种模型的速度剖面(左)及传统、改进半波长法的相对百分比误差(右)

    (a) 递增层模型;(b) 低速夹层模型;(c) 高速夹层模型

    Figure  5.   The velocity profiles of the three models related to inversion thickness (left) and the relative percentage error variation by the traditional and improved half-wavelength methods with depth (right)

    (a) The stratified media with S-wave velocity increasing from the top to the bottom;(b) The stratified media with the low-velocity layer in between;(c) The stratified media with the high-velocity layer in between

    图  6   与实际厚度相关的三种模型的速度剖面(左)及传统、改进半波长法的相对百分比误差(右)

    (a) 递增层模型;(b) 低速夹层模型;(c) 高速夹层模型

    Figure  6.   The velocity profiles of the three models related to actual thickness (left) and the relative percentage error variation by the traditional and improved half-wavelength methods with depth (right)

    (a) The stratified media with S-wave velocity increasing from the top to the bottom;(b) The stratified media with the low-velocity layer in between;(c) The stratified media with the high-velocity layer in between

    图  7   日本钏路场地剪切波速度剖面、频散曲线与水平与竖向谱比(引自Arai,Tokimatsu,2005

    (a) 由钻孔法所得剪切波速度剖面;(b) 由观测数据采用fk法所得频散曲线;(c) 由三分量传感器观测所得HVSR曲线

    Figure  7.   Shear wave velocity profile,dispersion curve and horizontal-to-vertical spectral ratio HVSR of Kushiro site in Japan (after Arai,Tokimatsu,2005

    (a) Shear wave velocity profile obtained from drilling method;(b) The dispersion curve obtained by the fk method from the observed data;(c) Observed HVSR curve from three-component sensor

    图  8   与反演厚度相关的实测模型的速度剖面(a)及传统、改进半波长法的相对百分比误差(b)

    Figure  8.   The velocity profiles of the measured models related to inversion thickness (a) and the relative percentage error variation by the traditional and improved half-wavelength methods with depth (b)

    图  9   与实际厚度相关的实测模型的速度剖面(a)及传统、改进半波长法的相对百分比误差(b)

    Figure  9.   The velocity profiles of the measured models related to actual thickness (a) and the relative percentage error variation by the traditional and improved half-wavelength methods with depth (b)

    表  1   三类模型的具体属性参数

    Table  1   Specific attribute parameters of the three types of models

    模型层数层厚/mvP/(m·s−1vS/(m·s−1密度/(g·cm−3${Q}_{\rm P}$${Q}_{\rm S}$泊松比μ
    递增层 1 5 600 300 1.80 48 24
    2 10 700 350 1.90 56 28
    3 10 800 400 2.00 64 32
    4 10 1000 500 2.10 80 40
    无限半空间 1200 600 2.20 96 48
    低速夹层 1 5 600 300 1.80 48 24
    2 10 900 450 1.90 72 36
    3 10 700 350 2.00 56 28 0.33
    4 10 1000 500 2.10 80 40
    无限半空间 1200 600 2.20 96 48
    高速夹层 1 5 600 300 1.80 48 24
    2 10 700 350 1.90 56 28
    3 10 1100 550 2.00 88 44
    4 10 1000 500 2.10 80 40
    无限半空间 1200 600 2.20 96 48
    下载: 导出CSV

    表  2   三类模型的土层厚度

    Table  2   Soil thickness of three types of models

    模型名称卓越频率/Hz土层厚度/m
    递增层模型 3.6 32
    低速夹层模型 3.1 38
    高速夹层模型 5.6 21
    下载: 导出CSV

    表  3   理论模型与反演模型的平均波速及相对误差对比

    Table  3   Comparison of average wave velocity and relative error between theoretical model and inversion model

    反演方法递增层模型低速夹层模型高速夹层模型
    平均波速/(m·s−1相对误差平均波速/(m·s−1相对误差平均波速/(m·s−1相对误差
    理论模型 400.0 414.3 442.9
    传统半波长 429.4 −7.4% 437.1 −5.5% 464.6 −4.9%
    改进半波长 421.3 −5.3% 427.9 −3.3% 472.4 −6.7%
    下载: 导出CSV
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  • 收稿日期:  2019-08-15
  • 修回日期:  2019-09-27
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