Ensemble smoothers are among the most successful and efficient techniques currently available for history matching. However, because these methods rely on Gaussian assumptions, their performance is severely degraded when the prior geology is described in terms of complex facies distributions. Inspired by the impressive results obtained by deep generative networks in areas such as image and video generation, we started an investigation focused on the use of autoencoders to construct a continuous parameterization for facies models. In our previous publication, we combined a convolutional variational autoencoder (VAE) with the ensemble smoother with multiple data assimilation (ES-MDA) for history matching production data in models generated with multiple-point geostatistics. Despite the good results reported in our previous publication, a major limitation of the designed parameterization is the fact that it does not allow applying distance-based localization during the ensemble smoother update, which limits its application in large-scale problems. The present work is a continuation of this research project focusing on two aspects: firstly, we benchmark nine different formulations, including VAE, generative adversarial network (GAN), Wasserstein GAN (WGAN), WGAN with gradient penalty, WGAN with spectral normalization, variational auto-encoding GAN, principal component analysis (PCA) with cycle GAN, PCA with transfer style network, and VAE with style loss. These formulations are tested in a synthetic history matching problem with channelized facies. Secondly, we propose two strategies to allow the use of distance-based localization with the deep learning parameterizations.

合奏平滑器是当前可用于历史匹配的最成功，最有效的技术之一。但是，由于这些方法依赖于高斯假设，因此当根据复杂相分布描述现有地质时，它们的性能会严重下降。受到深层生成网络在图像和视频生成等领域获得的令人印象深刻的结果的启发，我们开始了一项针对使用自动编码器为相模型构建连续参数化的研究。在我们以前的出版物中，我们将卷积变分自编码器（VAE）与具有多个数据同化（ES-MDA）的整体平滑器相结合，用于在通过多点地统计生成的模型中历史匹配生产数据。尽管我们先前的出版物报告了良好的结果，设计的参数化的主要局限性在于它不允许在整体平滑更新过程中应用基于距离的定位，这限制了它在大规模问题中的应用。目前的工作是该研究项目在两个方面的延续：首先，我们对9种不同的公式进行了基准测试，包括VAE，生成对抗网络（GAN），Wasserstein GAN（WGAN），具有梯度罚分的WGAN，具有频谱归一化的WGAN，变分自动编码GAN，具有周期GAN的主成分分析（PCA），具有传输样式网络的PCA和具有样式丢失的VAE。这些配方在具有通道相的合成历史匹配问题中进行了测试。其次，我们提出两种策略，以允许在深度学习参数化中使用基于距离的本地化。