Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the parameters. Here we develop a Bayesian inversion framework that uses Interferometric Synthetic Aperture Radar (InSAR) surface deformation data to infer the laterally heterogeneous permeability of a transient linear poroelastic model of a confined GW aquifer. The Bayesian solution of this inverse problem takes the form of a posterior probability density of the permeability. Exploring this posterior using classical Markov chain Monte Carlo (MCMC) methods is computationally prohibitive due to the large dimension of the discretized permeability field and the expense of solving the poroelastic forward problem. However, in many partial differential equation (PDE)-based Bayesian inversion problems, the data are only informative in a few directions in parameter space. For the poroelasticity problem, we prove this property theoretically for a one-dimensional problem and demonstrate it numerically for a three-dimensional aquifer model. We design a generalized preconditioned Crank--Nicolson (gpCN) MCMC method that exploits this intrinsic low dimensionality by using a low-rank based Laplace approximation of the posterior as a proposal, which we build scalably. The feasibility of our approach is demonstrated through a real GW aquifer test in Nevada. The inherently two dimensional nature of InSAR surface deformation data informs a sufficient number of modes of the permeability field to allow detection of major structures within the aquifer, significantly reducing the uncertainty in the pressure and the displacement quantities of interest.
翻译:地下水(GW)含水层参数的不确定性量化对于高效管理和可持续提取GW资源至关重要。 这些不确定性是由数据、模型和关于参数的先前信息引入的。 我们在这里开发了贝叶斯的反向框架, 使用Interferrocism 合成孔径雷达( InSAR) 表面变形数据来推断封闭的GW含水层的瞬间线性孔径模型的横向多变性。 这个反向问题的贝叶斯式解决办法采取渗透性后概率密度的形式。 使用经典的Markov链Monte Carlo(MC) 的内向性方法来探索这一后表层。 由于分解的渗透性场的广度和解决孔径透性前问题的费用。 然而,在许多部分差异方(PDE)基的波纹性模型中,这些数据只在参数空间的几个方向上具有丰富性。 对于孔径问题,我们从理论上将这一属性用于一个一维度问题,并用数字来证明它对于三维含水层的内位性模型来说是令人难以接受的。 我们设计了一个通用的直径直径可变的基的含水层测地基模型, 。 正在用这个基的精度的精度的精度的精度的精度模型, 利用这个基的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度 。