Error Correction in Geological Model Based on Stratigraphic Interdependency
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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.Abstract: In geological exploration, the bottom interface of deep stratum is not sampled in most boreholes, and incorrect sample information limits the accuracy of geological models. In order to improve the accuracy of geological model, we proposes a method to correct geological model based on stratigraphic interdependency. Due to the formation mechanism of the strata, the morphology of the adjacent strata is similar. Based on this character, the Copula function is used to model the dependence structure of adjacent strata, and the joint distribution model of adjacent strata and the likelihood function of the stratum to be corrected are constructed. In the Bayesian framework, the established interface model is taken as the prior model, and the likelihood function is used to update the prior model to obtain the posterior distribution. In the end, the condition expectation of the interface is calculated as the posterior model. The proposed approach is illustrated through a case study of the geological interface model of the coastal zone near Beihai. The results show that the error of the geological interface model is reduced after model correction.
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Key words:
- geologic models /
- error correction /
- stratigraphic interdependency /
- Bayes /
- Copula
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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 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 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 … … … … … … 
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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
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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
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