In this work, we present a numerical method that provides accurate real-time detection for the widths of the fractures in a fractured porous medium based on observational data on porous medium fluid mass and velocity. To achieve this task, an inverse problem is formulated by first constructing a forward formulation based on the reduced fracture model of the diffusion equation. A parameter estimation problem is then performed online by utilizing a direct filter method. Numerical experiments are carried out to demonstrate the accuracy of our method in approximating the target parameters.

翻译：本文提出了一种数值方法，该方法能够根据多孔介质流体质量与速度的观测数据，对裂隙多孔介质中裂缝宽度进行精确的实时检测。为实现这一目标，我们首先基于扩散方程的简化裂缝模型构建正演公式，进而建立反问题。随后，通过采用直接滤波方法在线执行参数估计。数值实验验证了本方法在逼近目标参数方面的准确性。