Stratified Autoregressive Generation Framework for Reservoir Characterization: Bridging Multiple-Point Geostatistics and Transformer
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摘要:
为了解决深度生成模型在硬数据约束下易发生模式崩溃和伪影的问题，本文提出一种分层自回归生成（Stratified Autoregressive Generation，SAG）框架.该框架利用离线训练的Transformer架构作为条件分布估计器，替代多点地质统计的在线搜索与计数过程；采用三级由粗到细的分层策略，先定义大尺度全局结构，再向细尺度传播约束，规避大网格上的二次计算复杂度.多组实验结果及多维尺度图与变差函数分析显示，本文方法生成的结果具备多样性，且准确再现了训练数据的全局统计特征与空间连续性；直方图交叉量化评估证实了无伪影的高局部模式保真度；不确定性评估显示不确定度由硬数据点向外逐渐增加，收敛模式符合地质规律.本文提出的方法在不同数量的硬数据约束下，其结果保持了空间连续性和样本多样性，实现了复杂储层结构及物性的准确表征.
Abstract:To address the mode collapse and artifacts encountered in deep generative models under hard data constraints, this study proposes a Stratified Autoregressive Generation (SAG) method, aiming to develop a robust reservoir characterization approach. The method utilizes an offline-trained Transformer architecture as a conditional distribution estimator to replace the computationally expensive online "search and count" process of MPS. A three-level, coarse-to-fine strategy is adopted to define global structures at large scales first and subsequently propagates constraints to finer scales, thereby avoiding the quadratic computational complexity on large grids. Multiple sets of experiments as well as multidimensional scaling and variogram analyses indicate that the generated realizations possess diversity and accurately reproduce the global statistics and spatial continuity of the training data. Quantitative assessment using histogram intersection further confirms high local pattern fidelity without artifacts. Uncertainty assessment reveals that uncertainty increases outward from hard data points, showing a convergence pattern consistent with geological laws. The results indicate that the proposed method maintains spatial continuity and realization diversity under varying amounts of hard data constraints, which achieves the accurate characterization of complex reservoir structures and properties.
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图 1 SAG中的多尺度自回归生成
左图展示了将高分辨率地质属性场分解为由粗到细的层级结构（L=2）；右图显示了所采用的Transformer模块的架构
Fig. 1. Multi-scale autoregressive generation in SAG
图 2 从训练集中随机选取的储层相样本
每个样本为64像素×64像素单元，坐标轴一致；黄色表示河道砂、蓝绿色表示天然堤砂、紫色表示泥岩
Fig. 2. Random chosen reservoir facies samples from the training set
图 3 真实训练样本（左）与SAG模型生成的图像（右）的并排比较
Fig. 3. Side-by-side comparison of real training samples (left) and images generated by the SAG model (right)
图 4 真实样本和生成样本分布的MDS可视化
N表示条件数据的数量
Fig. 4. MDS visualization of the distributions of real and generated samples
图 5 不同条件点数量（$ N $）下生成样本与参考集的相比例对比
分析涵盖了无条件情况（$ N=0 $）和$ N $从1增加到16的条件模拟，证明了所有三种岩相的生成比例与参考值紧密一致
Fig. 5. Facies proportions of generated samples versus the reference set across varying numbers of conditioning points (N)
图 6 生成的和参考的指示变差函数之间的IQR重叠百分比热图
Fig. 6. Heatmap of the IQR overlap percentage between generated and reference indicator variograms
图 7 生成数据和训练集的指示变差函数曲线比较
Fig. 7. Comparison of indicator variogram curves for generated and reference sets
图 8 三种相类别的模板模式频率分布比较：河道砂体（a）、堤岸砂体（b）与河道间泥岩（c）
不同条件点数量$ N $的模拟分布叠加在训练图像基线上.误差条代表95%置信区间
Fig. 8. Comparison of template pattern frequency distributions for the three facies classes: Channel sand (a), levee sand (b), and mudstone (c)
图 9 使用直方图交叉度量对每个相类别进行模式一致性定量评估
图中显示了不同条件点数量下模拟的平均直方图交叉值
Fig. 9. Quantitative evaluation of pattern consistency using the histogram intersection metric for each facies class
图 10 来自具有不同条件点数量$ N $的100个独立实现的熵网格图（a）和标准差（b）
Fig. 10. Entropy maps (a) and standard deviation maps (b) from 100 independent realizations with varying numbers of conditioning points (N)
表 1 三层级联架构参数方案
Table 1. Parameter settings of the three-level cascaded architecture
层级 模型 输入单元尺寸 分块
尺寸序列长度 嵌入维度 网络结构 k=0 $ {M}^{\left(0\right)} $ 64×64 4×4 256 1 024 32层, 16头 k=1 $ {M}^{\left(1\right)} $ 4×4 1×1 16 512 8层, 8头 k=2 $ {M}^{\left(2\right)} $ 单一特征向量 不适用 1 512 3层, 4头 
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