Field-scale properties of fractured rocks play a crucial role in many subsurface applications, yet methodologies for identification of the statistical parameters of a discrete fracture network (DFN) are scarce. We present an inversion technique to infer two such parameters, fracture density and fractal dimension, from cross-borehole thermal experiments data. It is based on a particle-based heat-transfer model, whose evaluation is accelerated with a deep neural network (DNN) surrogate that is integrated into a grid search. The DNN is trained on a small number of the heat-transfer model runs and predicts the cumulative density function of the thermal field. The latter is used to compute fine posterior distributions of the (to be estimated) parameters. Our synthetic experiments reveal that fracture density is well constrained by data, while fractal dimension is harder to determine. Adding nonuniform prior information related to the DFN connectivity improves the inference of this parameter.

中文翻译：

---

断裂岩石表征的热实验：理论分析和逆向建模

裂缝岩石的现场尺度特性在许多地下应用中起着至关重要的作用，但用于识别离散裂缝网络 (DFN) 统计参数的方法很少。我们提出了一种反演技术，可以从井间热实验数据中推断出两个这样的参数，即裂缝密度和分形维数。它基于基于粒子的传热模型，其评估通过集成到网格搜索中的深度神经网络 (DNN) 代理加速。DNN 在少量传热模型运行上进行训练，并预测热场的累积密度函数。后者用于计算（待估计）参数的精细后验分布。我们的综合实验表明裂缝密度受到数据的很好的约束，而分形维数更难确定。添加与 DFN 连接相关的非均匀先验信息可改进此参数的推断。