Stratigraphic modeling with quantified uncertainty is an open question in engineering geology. In this study, a novel stratigraphic stochastic simulation approach is developed by integrating a Markov random field (MRF) model and a discriminant adaptive nearest neighbor-based k-harmonic mean distance (DANN-KHMD) classifier into a Bayesian framework. The DANN-KHMD classifier is effective for extracting anisotropic patterns from sparse and heterogeneous spatial categorical data such as borehole logs. The MRF parameters can be initially estimated roughly or customized (if site-specific knowledge is available). Later these parameters can be updated and regularized in an unsupervised manner with constraints from site exploration results in a Bayesian manner. Throughout the learning process, both the soil profile and the MRF parameters are updated in a probabilistic manner. The advantages of the proposed approach can be summarized into four points: 1) inferring stratigraphic profile and associated uncertainty in an automatic and fully unsupervised manner; 2) reasonable initial stratigraphic configurations can be sampled and hence lower the computational cost; 3) both stratigraphic uncertainty and model uncertainty are taken into consideration throughout the inferential process; 4) relying on no training stratigraphy images. To illustrate the effectiveness of the developed approach, two synthetic cases and three real-world cases are studied and the advantages of the new approach over existing approaches are demonstrated.

具有量化不确定性的地层建模是工程地质学中的一个悬而未决的问题。在这项研究中，通过集成马尔可夫随机场 (MRF) 模型和基于判别式自适应最近邻的k，开发了一种新的地层随机模拟方法。-将谐波平均距离（DANN-KHMD）分类器转换为贝叶斯框架。DANN-KHMD 分类器可有效地从稀疏和异构的空间分类数据（例如钻孔测井）中提取各向异性模式。MRF 参数最初可以粗略估计或定制（如果有特定站点的知识）。稍后，这些参数可以以无监督的方式更新和规范化，并以贝叶斯方式受到现场探索结果的约束。在整个学习过程中，土壤剖面和 MRF 参数都以概率方式更新。所提出方法的优点可以总结为四点：1）以自动和完全无监督的方式推断地层剖面和相关的不确定性；2）可以对合理的初始地层配置进行采样，从而降低计算成本；3) 在整个推理过程中，地层不确定性和模式不确定性都被考虑在内；4）依靠没有训练的地层图像。为了说明所开发方法的有效性，研究了两个合成案例和三个真实案例，并展示了新方法相对于现有方法的优势。