Non-Stationary Random Field Simulation Method of Seabed Site Shear Wave Velocity Structures Considering Stratigraphy Variation and Nonlinear Trend
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摘要: 地层及其剪切波速（Vs）结构的空间变异性对场地地震反应有显著影响. 基于渤海湾海床钻孔资料，采用与耦合马尔可夫链相比对随机地层模拟范围更广、对地层界限模拟效果更光滑的嵌入式马尔可夫链模型模拟钻孔深度h以浅地层的变异性，模拟结果具有较高的精度.采用点估计法给出了以幂函数和线性函数描述海床Vs随h变化的趋势时相应Vs的均值和标准差随h的变化.基于实测钻孔的Vs剖面，采用非平稳条件随机场模拟随机Vs-结构的空间变异性. 发现考虑地层的变异性以及忽略Vs沿h变化的非线性趋势均显著增大随机Vs-结构模拟结果的标准差.采用隶属函数和模糊马尔可夫链模型，建立海域钻孔深度外延的未知地层和近岸陆地相应深度已知地层的相关性和转移概率，给出了钻孔深度以深的海床随机地层及其Vs-结构的可能空间分布. 为开展海洋工程场地地震反应分析提供了合理的随机地层和Vs-结构资料.Abstract: The spatial variabilities of stratigraphy and S-wave velocity (Vs) structures have significant influence on the results of seismic site response analyses. Based on the borehole data of the seabed of Bohai Bay, the embedded Markov chain model, which has a wider simulation range for random stratigraphy and smoother simulation effect for stratigraphic boundary than the coupled Markov chain, is used to simulate the variabilities of random stratigraphy with depth less than the borehole bottoms, and the simulation results have higher precision. The point estimation method is used to give the change of the means and standard deviations of Vs with h of the seabed when describing the variation trend of Vs with h by power function and linear function. Based on the measured Vs-profiles at the boreholes, the spatial variabilities of random Vs-structures are simulated by using the non-stationary conditional random field method. It is found that considering the spatial variabilities of the random stratigraphy and ignoring the nonlinear variation of Vs along h can significantly increase the standard deviations of the simulated random Vs- structures. The correlations and transfer probabilities between the unknown stratigraphy below the seabed borehole bottoms and the known stratigraphy at the same depth of near-shore land are established using the membership function and fuzzy Markov chain model, the possible spatial variabilities of random seabed stratigraphy and Vs-structures below the borehole bottoms are obtained. It provides reasonable random stratigraphy and Vs-structures for seismic response analysis of offshore engineering site.
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图 3 二维海床和剪切波速结构的随机模拟流程
Fig. 3. Random simulation flow of 2D seabed stratigraphy and S-wave velocity structures
图 4 耦合和嵌入式马尔可夫链模型模拟效果对比[基于（祁小辉等, 2017）的钻孔资料]
Fig. 4. Comparison of simulation effects of coupled and embedded Markov chain models (based on borehole data given by Qi et al., 2017)
图 5 各钻孔剖面中的土类和剪切波速值
Fig. 5. Soil profiles and the corresponding S-wave velocity values in each borehole
图 6 随机地层和随机Vs-结构的变异性和模拟次数关系
Fig. 6. Variabilities of random stratigraphy and random Vs -structures with simulation times
图 7 网格尺寸对随机地层模拟效果的影响
Fig. 7. Influences of grid sizes on the simulation effects of random stratigraphy
图 8 随机地层模拟精度的频数分布
Fig. 8. Frequency distribution of random stratigraphy simulation accuracy
图 10 随机地层空间变异性对随机Vs-结构空间变异性的影响
Fig. 10. Influence of random stratigraphy spatial variabilities on random Vs-structure spatial variabilities
图 11 以线性函数为趋势函数得到的随机Vs-结构模拟结果的标准差
Fig. 11. Standard deviation of random Vs-structure simulation results obtained with linear function as trend function
图 13 研究区和近岸陆地虚拟钻孔之间距离的计算
Fig. 13. Calculation of distance between virtual boreholes in the investigation region and the nearshore land
图 14 研究区内和近岸陆地虚拟钻孔之间隶属关系的确定
Fig. 14. Determination of affiliation between virtual boreholes in the investigation region and the nearshore land
图 15 模拟的研究区自海床表面到相对高程-270 m范围内随机地层(a)和随机Vs-结构(b)的一种可能分布
Fig. 15. A possible distribution for random stratigraphy (a) and random Vs-structure (b) from the seabed surface to the relative elevation of - 270 m in the investigation region
表 1 土体剪切波速拟合参数的统计特征
Table 1. Statistical characteristics of S-wave velocity fitting parameters of soils
土类 参数a 参数b 均值 标准差 均值 标准差 粉砂 25.13 3.48 0.65 0.06 粉土 23.02 4.24 0.58 0.05 粉质黏土 33.14 4.00 0.56 0.03 砂质粉土 73.35 7.78 0.40 0.04 细砂 111.59 12.47 0.33 0.02 
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