基于深度学习的数据同化裂隙网络分布模拟

徐朝晖; 康学远; 于军; 龚绪龙; 韩正; 吴吉春; 施小清

doi:10.16030/j.heg.202412011

摘要:

目的准确表征裂隙网络的空间分布是描述裂隙介质中地下水流动和污染物运移的关键前提。由于裂隙介质中裂隙和基质参数的强非高斯性，当观测数据有限时，常用的随机反演方法（如地质统计学方法）因高斯假设先验，导致推估得到裂隙网络高渗区域容易过于平滑。

方法本研究提出一种基于深度学习的反演框架来表征裂隙网络，利用卷积变分自编码器（convolutional variational autoencoder，CVAE）识别图像的优势，通过学习裂隙先验信息提取其空间模式。为了增强该反演框架在野外实际的适用性，在训练样本构建中将裂隙数量设置为特定数量区间的随机分布。将训练后的CVAE与基于集合的数据同化方法（ensemble smoother multiple data assimilation，ESMDA）集成，通过水力层析成像技术（hydraulic tomography，HT）获取的水头数据估计裂隙场。基于二维裂隙网络数值算例验证该框架的反演性能。

结果训练后的CVAE成功再现了裂隙网络的非高斯特性。相比于标准的ESMDA方法，所构建框架CVAE-ESMDA刻画的裂隙网络精度从65.5%提升至83.3%，溶质运移预测平均误差降低31.7%。进一步探讨观测数据量对于CVAE-ESMDA性能的影响，研究发现相比1512个水头观测数据，反演框架在504个水头观测数据情况下仍能刻画出裂隙网络的大体分布与连通情况，但具体裂隙的刻画精度有所下降，从而影响了溶质运移趋势预测的准确性，整体溶质运移预测的平均误差增加17.1%。

结论提出的CVAE-ESMDA反演框架能有效克服裂隙含水层参数非高斯特性并高效学习裂隙网络的结构特征，在不同观测数据量下均能一定程度刻画出裂隙网络分布特征。

Abstract:

Objective Accurate characterization of the spatial distribution of fracture networks is crucial for understanding groundwater flow and contaminant transport in fractured media. However, due to the strongly non-Gaussian characteristics between hydraulic parameters of fracture and matrix in fractured media, traditional stochastic inversion approaches (such as geostatistical methods) based on Gaussian assumptions tend to produce overly smoothed estimates of high-permeability regions in fracture networks when observation data are limited.

Method This study proposed a deep learning-based inversion framework to characterize fracture networks. Leveraging the advantages of convolutional variational autoencoders (CVAE) in image recognition, the framework first extracts spatial patterns by learning prior information of fractures. To enhance the applicability of the inversion framework under field conditions, the number of fractures in the construction of training samples was modeled as a random distribution within a predefined range. Then the trained CVAE was integrated with an ensemble-based data assimilation method (i.e., ensemble smoother multiple data assimilation, ESMDA) to estimate the fracture field by conditioning on hydraulic head data from hydraulic tomography (HT). Numerical experiments on 2D fracture networks validate the inversion performance of the framework.

Results The trained CVAE successfully preserves the non-Gaussian characteristics of fracture networks. Compared to the standard ESMDA method, the proposed CVAE-ESMDA framework improves the accuracy of fracture network characterization from 65.5% to 83.3% and reduces the average solute transport prediction error by 31.7%. Further analysis of the impact of observation data quantity on the performance of CVAE-ESMDA reveals that, compared to 1512 hydraulic head observations, the framework can still capture the overall distribution and connectivity of the fracture network with 504 hydraulic head observations. However, the accuracy of depicting specific fractures decreases, leading to reduced precision in predicting solute transport trends. Consequently, the average error in solute transport prediction increases by 17.1%.

Conclusion The proposed CVAE-ESMDA inversion framework can effectively address the non-Gaussian characteristics of fractured aquifer parameters and efficiently learn the structural features of fracture networks, and can characterize the distribution characteristics of fracture networks under different amounts of observation data.

基于深度学习的数据同化裂隙网络分布模拟

Characterization of fracture networks using deep learning-based data assimilation