In geosciences, generative adversarial networks have been successfully applied to generate multiple realizations of rock properties from geological priors described by training images, within probabilistic seismic inversion and history matching methods. Here, the use of generative adversarial networks is proposed not as a model generator but as a model reconstruction technique for subsurface models where we do have access to sparse measurements of the subsurface properties of interest. We use sets of geostatistical realizations as training datasets combined with observed experimental data. These networks are applied to reconstruct nonstationary sedimentary channels and continuous elastic properties, such as P-wave propagation velocity, in the presence and absence of conditioning data. The reconstruction examples shown herein can be considered a post-processing step applied after seismic inversion and performed at those locations where the convergence of the inversion is low, and therefore, the inverted models are associated with high uncertainty. The application examples show the suitability of generative adversarial networks in learning the spatial structure of the data from sets of geostatistical realizations. The generated models reproduce the first- and second-order statistical moments and the spatial covariance matrix of the training dataset.

中文翻译：

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生成对抗网络作为随机地下模型的重构

在地球科学中，生成对抗网络已成功地应用于概率地震反演和历史匹配方法中，通过训练图像描述的地质先验来生成岩石属性的多种实现。在这里，提出使用生成对抗网络不是作为模型生成器，而是作为地下模型的模型重建技术，在该模型中，我们确实可以访问感兴趣的地下属性的稀疏度量。我们使用地统计实现集作为训练数据集并结合观察到的实验数据。这些网络用于在存在和不存在条件数据的情况下重建非平稳的沉积通道和连续的弹性特性，例如P波传播速度。本文所示的重建示例可以被认为是地震反演后应用的后处理步骤，并且在反演收敛性较低的那些位置执行，因此，反演模型具有较高的不确定性。应用示例说明了生成对抗网络在从地统计实现集中学习数据的空间结构的适用性。生成的模型再现了训练数据集的一阶和二阶统计矩以及空间协方差矩阵。应用示例说明了生成对抗网络在从地统计实现集中学习数据的空间结构的适用性。生成的模型再现了训练数据集的一阶和二阶统计矩以及空间协方差矩阵。应用示例说明了生成对抗网络在从地统计实现集中学习数据的空间结构的适用性。生成的模型再现了训练数据集的一阶和二阶统计矩以及空间协方差矩阵。