一种有效的Richards方程三维反演数值方法
A numerical method for efficient 3D inversions using Richards equation
摘要：
渗流区中的流体流动由Richards方程控制;它由水力传导系数参数化，水力传导系数是压头的非线性函数。在包气带的调查通常需要表征分布的水力特性。饱和度或压头数据可以包括从钻孔进行的直接测量。水文地球物理学的代用测量越来越多地被用来提供在空间和时间上更密集的数据集。从这样的数据集推断水力参数需要能够有效地求解和确定性地优化非线性时域Richards方程。这是特别重要的，因为在包气带反演中要估计的参数的数量持续增长。在本文中，我们描述了一种有效的技术来反演分布式水力特性在1D，2D和3D。我们的算法不存储雅可比矩阵，而是计算与向量的乘积，这使得反演问题的大小比有限差分或自动微分等方法大得多;这些方法分别受到计算和内存的限制。我们展示了我们的算法在实践中的饱和渗透率的三维反演饱和数据通过时间。运行我们的示例的代码是开源的，并且所提出的算法允许这个反演过程在适度的计算资源上运行。
英文摘要：
Fluid flow in the vadose zone is governed by Richards equation; it is parameterized by hydraulic conductivity, which is a nonlinear function of pressure head. Investigations in the vadose zone typically require characterizing distributed hydraulic properties. Saturation or pressure head data may include direct measurements made from boreholes. Increasingly, proxy measurements from hydrogeophysics are being used to supply more spatially and temporally dense data sets. Inferring hydraulic parameters from such datasets requires the ability to efficiently solve and deterministically optimize the nonlinear time domain Richards equation. This is particularly important as the number of parameters to be estimated in a vadose zone inversion continues to grow. In this paper, we describe an efficient technique to invert for distributed hydraulic properties in 1D, 2D, and 3D. Our algorithm does not store the Jacobian, but rather computes the product with a vector, which allows the size of the inversion problem to become much larger than methods such as finite difference or automatic differentiation; which are constrained by computation and memory, respectively. We show our algorithm in practice for a 3D inversion of saturated hydraulic conductivity using saturation data through time. The code to run our examples is open source and the algorithm presented allows this inversion process to run on modest computational resources.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
