Abstract Accurately modeling and constructing a geologically realistic subsurface model remains an outstanding problem as the morphology controls the flow behaviors. Particularly, one of the pattern-based methods, namely cross-correlation based simulation, has been proved to be an effective way to reconstruct a realistic model, at both small and large scales. However, conditioning to point data in the large-scale problems is still a crucial issue in these algorithms, since there is always a trade-off between the quality of the realizations and the degree of point data reproduction. Specifically, it is not practical to build a training image (TI) which includes all the possibilities and variabilities. Therefore, finding a pattern that can represent the point data and, at the same time, preserving the connectivities is difficult. This leads to producing highly-connected realizations with a significant mismatch or poor models with a reasonable degree of point data reproduction. To accurately reproduce the densely distributed hard data, pixel-based methods can also produce some unrealistic artifacts around the hard data. In this paper, to overcome this challenge, however, we use pattern-based methods as they often produce more disconnected geobodies when dealing with dense hard data, and proposed a hybrid algorithm using the pattern-based methods and convolutional neural network (CNN). The trained CNN model is utilized to improve the quality of conditioning to point data for the original realizations generated by the pattern-based algorithm. As such, the mismatch locations are identified, and the same regions are used in the training of CNN to mimic the procedure through which a missing region can be filled. To evaluate the performance of the proposed hybrid algorithm, it is tested on cases with different dimensions and different numbers of facies. Then, the newly improved realizations are compared with the initial realizations generated by the pattern-based algorithm. The comparison is also conducted by the flow simulation test. And it indicates that the proposed hybrid algorithm can better reproduce the point data, while the connectivities are better preserved.

中文翻译：

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混合地质建模：结合机器学习和多点统计

摘要 由于形态控制流动行为，准确建模和构建地质真实的地下模型仍然是一个突出的问题。特别是，基于模式的方法之一，即基于互相关的模拟，已被证明是在小尺度和大尺度上重建现实模型的有效方法。然而，在大规模问题中调整点数据仍然是这些算法中的一个关键问题，因为在实现质量和点数据再现程度之间总是存在权衡。具体来说，构建包含所有可能性和可变性的训练图像 (TI) 是不切实际的。因此，找到一种可以表示点数据并同时保留连接性的模式是很困难的。这导致产生具有显着不匹配的高度连接的实现或具有合理程度的点数据再现的不良模型。为了准确地再现密集分布的硬数据，基于像素的方法也会在硬数据周围产生一些不切实际的伪影。然而，在本文中，为了克服这一挑战，我们使用基于模式的方法，因为它们在处理密集硬数据时通常会产生更多断开的地质体，并提出了一种使用基于模式的方法和卷积神经网络 (CNN) 的混合算法。训练后的 CNN 模型用于提高由基于模式的算法生成的原始实现的点数据的调节质量。因此，识别出不匹配的位置，并且在 CNN 的训练中使用相同的区域来模拟可以填充缺失区域的过程。为了评估所提出的混合算法的性能，它在具有不同维度和不同相数的情况下进行了测试。然后，将新改进的实现与基于模式的算法生成的初始实现进行比较。比较也是通过流动模拟试验进行的。这表明所提出的混合算法可以更好地再现点数据，同时更好地保留了连通性。将新改进的实现与基于模式的算法生成的初始实现进行比较。比较也是通过流动模拟试验进行的。这表明所提出的混合算法可以更好地再现点数据，同时更好地保留了连通性。将新改进的实现与基于模式的算法生成的初始实现进行比较。比较也是通过流动模拟试验进行的。这表明所提出的混合算法可以更好地再现点数据，同时更好地保留了连通性。