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    一种基于地层相关结构约束的地质模型修正方法

    梁栋 花卫华 赵亚博 刘志鹏 刘修国

    梁栋, 花卫华, 赵亚博, 刘志鹏, 刘修国, 2023. 一种基于地层相关结构约束的地质模型修正方法. 地球科学, 48(8): 3179-3192. doi: 10.3799/dqkx.2021.139
    引用本文: 梁栋, 花卫华, 赵亚博, 刘志鹏, 刘修国, 2023. 一种基于地层相关结构约束的地质模型修正方法. 地球科学, 48(8): 3179-3192. doi: 10.3799/dqkx.2021.139
    Liang Dong, Hua Weihua, Zhao Yabo, Liu Zhipeng, Liu Xiuguo, 2023. Error Correction in Geological Model Based on Stratigraphic Interdependency. Earth Science, 48(8): 3179-3192. doi: 10.3799/dqkx.2021.139
    Citation: Liang Dong, Hua Weihua, Zhao Yabo, Liu Zhipeng, Liu Xiuguo, 2023. Error Correction in Geological Model Based on Stratigraphic Interdependency. Earth Science, 48(8): 3179-3192. doi: 10.3799/dqkx.2021.139

    一种基于地层相关结构约束的地质模型修正方法

    doi: 10.3799/dqkx.2021.139
    基金项目: 

    国家重点研发计划课题“城市地下全要素信息集成与智能建模技术” 2019YFC0605102

    详细信息
      作者简介:

      梁栋(1988-), 博士, 主要从事地统计学、不确定性分析等方面研究.ORCID: 0000-0002-3761-4490.E-mail: bomer2000@sina.com

      通讯作者:

      刘修国, ORCID: 0000-0002-0045-9642.E-mail: liuxg318@163.com

    • 中图分类号: P628

    Error Correction in Geological Model Based on Stratigraphic Interdependency

    • 摘要: 在地质勘探中,多数钻孔存在深部地层底板未采样的情况,不完整的采样信息限制了地质模型的准确性.为了提高模型准确性,提出了一种基于地层相关结构约束的地层面模型修正方法.由于地层的形成机制及后期构造运动,相邻地层的形态具有相似性.基于此,利用Copula函数对相邻地层面的相关结构进行建模,构建相邻地层面的联合分布模型和待更新地层面的似然函数.在贝叶斯框架中,利用似然函数对待修正的模型进行贝叶斯更新,得到地层面的后验分布,计算地层面的条件期望作为模型修正值.利用该方法,对北海海岸带地区的钻孔数据和地层面模型进行了实验.实验结果表明,模型修正后,地层面模型的误差降低,所提方法可以提高地质模型准确性.

       

    • 图  1  钻孔存在深部地层底板未采样的情况

      Fig.  1.  The lacking samples of deep strata in boreholes.

      图  2  沉积地层面的自相关与互相关

      Fig.  2.  Correlation in the sedimentary strata

      图  3  待修正地层面数据的两种情况

      Fig.  3.  Two different cases of interface B recorded in No. 2 borehole.

      图  4  不等式约束下的截尾分布

      Fig.  4.  Truncated distribution under inequality constraints.

      图  5  基于双地层Copula的模型修正流程图

      Fig.  5.  Model correction flowchart based on Copula of two adjacent strata

      图  6  北海市三维地质建模效果图

      Fig.  6.  3D geological model of Beihai city.

      图  7  ⑤-2和⑥-1地层面高程值的分布图

      Fig.  7.  Scatter diagrams of the elevation of interface ⑤-2 and ⑥-1

      图  8  ⑤-2和⑥-1地层面高程统计直方图和边际概率分布

      Fig.  8.  Histogram and marginal probability distribution of elevation of interface ⑤-2 and ⑥-1

      图  9  ⑤-2和⑥-1地层面高程Copula密度图

      Fig.  9.  Copula densities of interface ⑤-2 (u1) and interface ⑥-1 (u2) in 3D and contour map

      图  10  #8钻孔位置上的⑥-1地层面贝叶斯更新

      Fig.  10.  Bayesian updating of probability distributions of interface ⑥-1 at borehole #8

      图  11  #8钻孔位置上的⑥-1地层面高程似然函数$ f\left({z}_{1}={V}_{1}|{z}_{2}\right) $

      Fig.  11.  Likelihood function $ f\left({z}_{1}={V}_{1}|{z}_{2}\right) $ of interface ⑥-1 at borehole #8

      表  1  验证位置上修正前后的模型值与样本值的比较(m)

      Table  1.   Model values (unit: m) before and after correction comparing with observed values in validation boreholes

      钻孔位置 样本值 不准确样本值 IDW模型值 未截尾修正值 截尾修正值
      #V1 -51.50 -40.15 -24.85 -36.05 -42.61
      #V2 -68.60 -64.60 -21.18 -40.78 -65.59
      #V3 -27.56 -19.91 -17.97 -28.35 -30.21
      #V4 -19.82 -13.23 -20.74 -19.79 -19.81
      #V5 -26.99 -17.76 -19.24 -19.95 -24.92
      #V6 -21.48 -15.73 -16.82 -21.98 -24.64
      #V7 -50.20 -48.65 -23.93 -38.64 -52.34
      #V8 -34.60 -29.60 -15.08 -22.61 -31.41
      #V9 -69.40 -66.80 -23.34 -38.48 -69.00
      #V10 -18.50 -12.45 -20.76 -12.53 -19.62
      #V11 -13.72 -10.12 -25.91 -20.88 -21.54
      #V12 -5.60 -3.15 -6.81 -5.92 -6.08
      #V13 -6.50 -4.10 -6.17 -5.09 -6.09
      #V14 -5.60 -3.45 -9.15 -8.43 -8.44
      #V15 -12.50 -10.6 -5.78 -5.96 -11.35
      #V16 -10.80 -8.05 -13.68 -12.61 -12.97
      #V17 -13.10 -11.10 -12.00 -12.87 -14.08
      #V18 -13.50 -11.90 -13.92 -16.24 -17.32
      #V19 -13.00 -9.85 -15.42 -15.31 -15.31
      #V20 -26.50 -15.85 -20.22 -19.72 -19.73
      下载: 导出CSV

      表  2  修正前后模型误差统计(m)

      Table  2.   Cross-validation errors (unit: m)

      地层面模型 MAE ME RMSE
      IDW 8.18 2.25 12.60
      未截尾修正值 6.77 0.74 9.59
      截尾修正值 4.77 -2.34 6.59
      下载: 导出CSV

      表  3  未钻透位置上不准确测量值与修正后模型值的比较(m)

      Table  3.   Model values before and after correction comparing with biased observed values in inaccurate boreholes(m)

      钻孔位置 不准确样本值 IDW模型值 截尾修正值
      #U1 -20.00 -18.24 -20.63
      #U2 -20.00 -19.92 -21.25
      #U3 -5.60 -20.77 -20.35
      #U4 -15.00 -21.08 -20.55
      #U5 -20.00 -20.95 -21.41
      #U6 -50.50 -26.83 -54.81
      #U7 -50.20 -41.62 -53.20
      下载: 导出CSV
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