Bayesian-MCMC (Markov Chain Monte Carlo) Based Three-Dimensional Geological Model Optimization by Data and Knowledge Fusion
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摘要: 为了充分利用已有地质知识来降低三维地质模型的不确定性，采用了一种基于贝叶斯-马尔科夫链蒙特卡洛（Bayesian-MCMC，Bayesian-Markov chain Monte Carlo）方法的三维地质模型概率性推断框架，在协同克里金（Cokriging）插值的三维地质隐式建模过程中，显式地考虑先验参数（即建模数据集）的不确定性，并将已有地质知识（如地层厚度、地层产状、断层产状等）或地球物理勘探数据以似然函数的方式嵌入到推断框架中，来充分保证三维地质模型符合已有的地质知识. 首先，基于Bayesian概率理论，建立不同建模数据集的先验分布以及已有地质知识似然函数约束；其次，使用MCMC随机采样的方法对先验参数的后验概率空间进行采样，获得大量既满足建模数据先验分布、又符合已有地质知识似然约束的建模数据样本；再次，由重新计算的建模数据样本集采用Cokriging插值算法获得一系列模型实现，获得符合已有地质知识的三维地质模型；最后，相比确定性三维地质建模方法，Bayesian-MCMC概率性建模框架可得到一系列模型实现，同时采用信息熵对模型的不确定性进行评价. 以桂西南地区凌念-那茶地区为例，采用本文构建的Bayesian-MCMC概率性推断框架，考虑地层、断层采样点及产状数据的不确定性，由已知的地层厚度、地层倾角和断层倾角等地质知识对三维地质模型进行优化，结果表明该方法既能重建地质体的三维空间形态，又可降低三维地质模型的不确定性，为地质学家通过已有地质知识来降低三维地质模型的不确定性提供了有效的途径.Abstract: To fully utilize known knowledge to reduce uncertainty of three-dimensional (3D) geological model, a Bayesian-Markov chain Monte Carlo (Bayesian-MCMC) based 3D geological model inference framework is proposed to consider the uncertainty of modeling data (prior parameter) and integrate known knowledge or geophysical exploration data as likelihood function into the process of 3D geological implicit modeling by Cokriging interpolant, which well satisfies the known knowledge. Firstly, different prior distributions of modeling data and likelihood functions of known knowledge are built based on Bayesian probabilistic theory. Secondly, the posterior space of prior parameter (modeling data) can be explored by Markov chain Monte Carlo (MCMC) sampling method to obtain a large number of samples which simultaneously satisfy the prior distributions of modeling data and likelihood constraints of know knowledge. Thirdly, a series of 3D geological model realizations satisfying known knowledge can be constructed by Cokriging interpolant using above newly obtained samples of modeling data. Finally, compared with the deterministic 3D geological modeling methods, the Bayesian-MCMC probabilistic inference framework can obtain a series of model realizations to allowably apply information entropy to evaluate model uncertainty. Taking the Lingnian-Nacha area in the southwestern Guangxi Zhuang Autonomous Region (GZAR) of China as am example, the proposed Bayesian-MCMC probabilistic inference framework was used to optimize 3D geological model simultaneously considering location and attitude uncertainties of strata and fault and known knowledge of stratum thickness and attitudes of strata and fault. The results of case study show that the proposed method can not only reconstruct 3D spatial geometry of geological body but also reduce uncertainty of 3D geological model, which provides geologist with an effective way to integrate modeling data and known knowledge to reconstruct 3D geological model and reduce its uncertainty.
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Key words:
- implicit modeling /
- Bayes /
- MCMC /
- uncertainty /
- cokriging interpolant
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图 3 基于Bayesian-MCMC的三维地质模型推断框架
Fig. 3. Bayesian-MCMC based 3D geological model inference framework
图 4 由平面地质图和剖面地质图来提取建模数据
Fig. 4. Extracted modeling data from geological map and cross-section
图 5 数据与知识融合的三维地质建模贝叶斯网络
Fig. 5. Bayesian network for 3D geological modeling fusing data and knowledge
图 6 模型参数迭代轨迹(a)和后验分布图(b)
Fig. 6. (a)Iterative trajectories and (b) posterior distributions of model parameter
图 8 三维地质模型的沿Y轴剖面
a. 无约束建模；b. 约束建模
Fig. 8. Cross-sections along Y axis of 3D geological models
图 10 信息熵模型剖面对比
a. 无约束建模；b. 约束建模
Fig. 10. Comparison of information entropy cross-sections
图 11 统计建模结果信息熵直方图对比
Fig. 11. Comparison of information entropy histograms of stochastic modeling results
表 1 地层厚度似然表达
Table 1. Likelihood expression of formation thickness
地层厚度似然表达 均值（m） 标准差（m） 百逢组 717 45 马脚岭组 778 30 茅口阶 170 50 栖霞组 219 30 石炭系上统 223 15 石炭系中统 311 10 
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表 2 倾角似然表达
Table 2. Inclination Likelihood Expression
倾角似然表达 均值（°） 标准差（°） 百逢组下段 29.61 6 马脚岭组 26.10 6 茅口阶 25.55 6 栖霞组 25.31 5 石炭系上统 26.07 5 石炭系中统 26.39 5 石炭系下统 26.16 5 断层 72.00 3
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