Delineation of subsurface stratigraphy is an essential task in site characterization. A three-dimensional (3D) subsurface geological model that precisely depicts stratigraphic relationships in a specific site can greatly benefit subsequent geotechnical analysis and designs. However, only a limited number of boreholes is usually available from a specific site in practice. It is therefore challenging to properly construct complex stratigraphic relationships in a 3D space based on sparse measurements from limited boreholes. To tackle this challenge, this study proposes a generative machine learning method called multi-scale generative adversarial networks (MS-GAN) for developing 3D subsurface geological models from limited boreholes and a 3D training image representing prior geological knowledge. The proposed method automatically learns multi-scale 3D stratigraphic patterns extracted from the 3D training image and generates 3D geological models conditioned on limited borehole data in an iterative manner. The proposed method is illustrated using 3D numerical and real data examples, and the results indicate that the proposed method can effectively learn the stratigraphic information from a 3D training image to generate multiple 3D realizations from sparse boreholes. Both accuracy and associated uncertainty of 3D realizations are quantified. Effect of borehole number on performance of the proposed method is also investigated.

中文翻译：

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多尺度生成对抗网络（GAN），用于根据有限的钻孔和先验地质知识生成三维地下地质模型

地下地层的描绘是场地描述中的一项重要任务。精确描述特定地点地层关系的三维 (3D) 地下地质模型可以极大地有利于后续的岩土分析和设计。然而，在实践中，特定地点通常只能获得有限数量的钻孔。因此，基于有限钻孔的稀疏测量在 3D 空间中正确构建复杂的地层关系具有挑战性。为了应对这一挑战，本研究提出了一种称为多尺度生成对抗网络 (MS-GAN) 的生成机器学习方法，用于从有限的钻孔和代表先前地质知识的 3D 训练图像开发 3D 地下地质模型。该方法自动学习从 3D 训练图像中提取的多尺度 3D 地层图案，并以迭代方式生成基于有限钻孔数据的 3D 地质模型。使用 3D 数值和实际数据示例说明了所提出的方法，结果表明所提出的方法可以有效地从 3D 训练图像中学习地层信息，从而从稀疏钻孔生成多个 3D 实现。 3D 实现的准确性和相关不确定性均得到量化。还研究了钻孔数量对所提出方法的性能的影响。