Bayesian Poroelastic Aquifer Characterization From InSAR Surface Deformation Data. Part I: Maximum A Posteriori Estimate
Bayesian Poroelastic Aquifer Characterization From InSAR Surface Deformation Data. Part I: Maximum A Posteriori Estimate
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DOI：
10.1029/2020wr027391
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发表时间：
2020-10-01
影响因子：
5.4
通讯作者：
Ghattas, Omar
中科院分区：
文献类型：
--
作者：
Alghamdi, Amal;Hesse, Marc A.;Ghattas, Omar
确定地下水含水层的特性对于预测含水层响应和管理地下水资源至关重要。在这项工作中，我们开发了一个高维的可扩展贝叶斯反演框架所管辖的三维准静态线性孔隙弹性模型来表征地下水含水层的横向渗透率变化。我们确定的最大后验（MAP）点的后渗透率分布从厘米级的表面变形测量干涉合成孔径雷达（干涉合成孔径雷达）。我们的方法的可扩展性，以高参数维数是通过使用伴随的衍生工具，不精确的牛顿方法来确定MAP点，和一个Matern类稀疏先验精度算子。总之，这些保证MAP点被发现的成本，测量的数量向前/伴随孔隙弹性解决方案，这是独立的参数尺寸。我们将我们的方法应用到测试案例中的一个市政井在Mesquite，内华达州，其中干涉合成孔径雷达和GPS地表变形数据。我们解决了多达320，824个状态变量自由度（DOF）和16，896个参数DOF的问题。采用一致的处理噪声水平，使含水层表征结果不依赖于表面变形数据的像素间距。我们的研究结果表明，使用干涉合成孔径雷达数据显着提高表征的横向含水层的异质性，和基于干涉合成孔径雷达的含水层表征恢复复杂的横向位移趋势观察独立的每日GPS测量。
Characterizing the properties of groundwater aquifers is essential for predicting aquifer response and managing groundwater resources. In this work, we develop a high-dimensional scalable Bayesian inversion framework governed by a three-dimensional quasi-static linear poroelastic model to characterize lateral permeability variations in groundwater aquifers. We determine the maximum a posteriori (MAP) point of the posterior permeability distribution from centimeter-level surface deformation measurements obtained from Interferometric Synthetic Aperture Radar (InSAR). The scalability of our method to high parameter dimension is achieved through the use of adjoint-based derivatives, inexact Newton methods to determine the MAP point, and a Matern class sparse prior precision operator. Together, these guarantee that the MAP point is found at a cost, measured in number of forward/adjoint poroelasticity solves, that is independent of the parameter dimension. We apply our methodology to a test case for a municipal well in Mesquite, Nevada, in which InSAR and GPS surface deformation data are available. We solve problems with up to 320,824 state variable degrees of freedom (DOFs) and 16,896 parameter DOFs. A consistent treatment of noise level is employed so that the aquifer characterization result does not depend on the pixel spacing of surface deformation data. Our results show that the use of InSAR data significantly improves characterization of lateral aquifer heterogeneity, and the InSAR-based aquifer characterization recovers complex lateral displacement trends observed by independent daily GPS measurements.