Estimating spatially distributed properties such as hydraulic conductivity (K) from available sparse measurements is a great challenge in subsurface characterization. However, the use of inverse modeling is limited for ill-posed, high-dimensional applications due to computational costs and poor prediction accuracy with sparse datasets. In this paper, we combine Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP), a deep generative model that can accurately capture complex subsurface structure, and Ensemble Smoother with Multiple Data Assimilation (ES-MDA), an ensemble-based inversion method, for accurate and accelerated subsurface characterization. WGAN-GP is trained to generate high-dimensional K fields from a low-dimensional latent space and ES-MDA then updates the latent variables by assimilating available measurements. Several subsurface examples are used to evaluate the accuracy and efficiency of the proposed method and the main features of the unknown K fields are characterized accurately with reliable uncertainty quantification

翻译：从有限的稀疏测量数据中估计水力传导系数（K）等空间分布属性是地下表征中的一项巨大挑战。然而，由于计算成本高且稀疏数据集预测精度差，反演建模在不适定、高维应用中的使用受到限制。本文结合了带梯度惩罚的Wasserstein生成对抗网络（WGAN-GP）——一种能精确捕捉复杂地下结构的深度生成模型，与多重数据同化集成平滑器（ES-MDA）——一种基于集成的反演方法，以实现精确且加速的地下表征。WGAN-GP通过训练从低维潜在空间生成高维K场，随后ES-MDA通过同化可用测量数据来更新潜在变量。利用多个地下实例评估了所提方法的准确性与效率，并通过可靠的 Uncertainty量化精确刻画了未知K场的主要特征。