CMG Collaborative Research: Subsurface Imaging and Uncertainty Quantification.

这是一个为期三年的多学科合作项目，旨在解决确定(或“成像”)地下地质材料的位置及其控制地下水和污染物运动的物理性质的空间分布这一根本问题。这些空间变化以复杂的模式和各种规模的尺度发生。需要对这些变化进行准确成像的地下工程应用包括可靠的环境监测、预测性建模和有效的地下水修复。该项目将开发下一代地下成像工具，以显著改进对地层和属性分布的估计，并改进相应预测不确定性的量化，以便为管理或政策决策提供可靠的基础。斯坦福大学、赖斯大学、犹他州大学和博伊西州立大学已经组建了一支在数学、统计学、建模和水文地质学方面拥有重叠专业知识的科学家和工程师团队。理论和模拟的发展将与现场规模的测试设施(博伊西水文地球物理研究场地，或BHRS)的受控实验相结合，该设施具有三个已知的沉积结构和性质变化尺度，包括具有高对比度和渐变边界的层和透镜。特别是，研究小组将：(I)在关于测量完整性的现实假设下，为反问题(或成像)的分析奠定坚实的数学基础，包括改进的表示复杂系统的方法；(Ii)利用计算方面的最新进展和趋势，利用新的统计工具；(Iii)为具有实际可变性的随机(或统计上不确定的)系统开发新的分析方法；(Iv)将这些发展与实验研究相结合，并根据BHRS提供的档案数据集对模型性能进行独立评估；以及(V)提出一种新兴的实地方法(水力层析成像)，以获取用于模拟含水层三维水力传导性分布的数据集。学生和一名博士后科学家将与资深研究人员合作，并将参与该项目的所有方面，以获得跨学科的知识和经验。除了通过同行评议的文献和专业会议进行传播外，该小组还将利用该项目的数据和模型开发基于网络的教程和培训集，以及关于该项目的实地和建模方法的短期课程。该项目对社会以及科学和工程基础设施具有广泛的影响。大多数可用的淡水都储存在地下。地下水是超过50%的美国人的主要水源，在农村地区约有95%的人是地下水。在世界上，许多最重要的含水层正在逐渐枯竭。在世界人口增长最快的沿海地区，随着地下水位下降和/或海平面上升，海水侵入含水层。这项研究将通过基于逆建模、随机微分方程、多尺度模拟和新的现场方法(如水力层析成像)的数学进步来开发下一代地下成像能力，从而为管理这一重要资源带来更好的方法。

This is a collaborative multi-disciplinary three-year project that addresses the fundamental problem of determining (or "imaging") the location of subsurface geologic materials and the spatial distributions of their physical properties that control movement of groundwater and contamination. These spatial variations occur in complex patterns and at all size scales. Subsurface engineering applications that require accurate imaging of these variations include reliable environmental monitoring, predictive modeling, and efficient groundwater remediation. The project will develop the next generation of subsurface imaging tools to significantly improve estimates of formation and property distributions, and to improve quantification of the corresponding predictive uncertainty to provide a sound basis for management or policy decisions. A team of scientists and engineers with overlapping expertise in mathematics, statistics, modeling, and hydrogeology has been assembled from Stanford, Rice, Utah, and Boise State universities. Theoretical and modeling developments will be combined with controlled experiments at a field-scale test facility (Boise Hydrogeophysical Research Site, or BHRS) with three known scales of sedimentary structure and property variation, including layers and lenses with both high-contrast and gradational boundaries. In particular, the research team will: (i) develop a firm mathematical foundation for the analysis of inverse problems (or imaging) under realistic assumptions about the completeness of measurements, including improved methods for representing complex systems; (ii) employ novel statistical tools that exploit recent advances and trends in computation; (iii) develop new analytical approaches for stochastic (or statistically uncertain) systems with realistic variability; (iv) combine these developments with experimental studies and independent evaluation of model performance against archive data sets available from BHRS; and (v) advance an emerging field method (hydraulic tomography) to acquire data sets for modeling 3D hydraulic conductivity distributions in aquifers. Students and a post-doctoral scientist will work with senior researchers and will participate in all aspects of this project to gain cross-disciplinary knowledge and experience. In addition to dissemination through peer-reviewed literature and professional meetings, the team will develop web-based tutorials and training sets with data and models from the project, and a short course on field and modeling methods from the project. This project has broad impacts for society and for scientific and engineering infrastructure. Most available freshwater is stored in the subsurface. Groundwater is the primary source of water for over 50 percent of Americans, and for roughly 95 percent in rural areas. In the world, many of the most important aquifers are being gradually depleted. In coastal areas, where world population is growing the fastest, seawater intrudes into aquifers as groundwater levels drop and/or sea levels rise. This research will lead to better methods for management of this important resource by developing the next generation of subsurface imaging capabilities based on advancements in the mathematics of inverse modeling, stochastic differential equations, multi-scale simulations, and new field methods such as hydraulic tomography.