Multi-modal, shape-based Inverse Methods for the Characterization of DNAPL Source Zone Architecture

DNAPL源区结构表征的多模态和基于形状的反演方法地下水被致密非水相液体（DNAPLs）污染是美国和世界范围内的一个主要社会问题。昂贵的原位修复方法，从地下完全去除污染物的质量，未能提供一个全面的解决方案，从而导致最近，增加的兴趣，旨在减少下游污染物的质量流量的修复方法。发展DNAPL污染的空间分布在源区的定量了解是至关重要的通量为基础的补救和管理策略。事实上，已经表明，这种源区结构与羽流的下游行为密切相关。不幸的是，源区结构的估计是一个非常具有挑战性的逆problem.We提出了一种方法，源区表征的基础上联合，基于物理的水文（梯度通量和浓度）和地球物理（电阻抗断层成像）数据的反演。我们的处理方法通过采用一种新的表示源区解决了这个反问题的不适定性。而不是使用有限的数据来恢复DNAPL的空间分布的精细尺度，像素化的表示，我们参数化分离池，神经节和非污染区域的边界。正在开发算法，以估计这种几何结构沿着与空间变化的DNAPL饱和度在污染区。在图像处理和计算机视觉领域的最新工作的基础上，我们采用了一种新形式的参数活动轮廓模型来描述池和神经节区域的边界。这些模型结合了联合收割机传统水平集思想的拓扑灵活性和与蛇相关的低阶参数表示。我们的方法的性能进行评估，使用一套广泛的数值模拟，以及一组实验室规模的实验。模拟和实验将探讨（一）的准确性和实用性的阿尔奇型混合规则映射的地球物理水文变量，和（B）的鲁棒性的方法，以未建模的体积不均匀性在两个电气和水文properties的subsecond.Intellectual优点：从这项研究中获得的知识将提高几何为基础的方法，通过将这些概念扩展到水文反演。除了推进水文领域，我们的研究将通过开发新的基于形状的多模态逆问题方法来扩展数学成像。这项研究还试图量化的限制与使用电阻抗和水文数据来表征准静态DNAPL源区architecture.Broader影响：该项目有可能影响基础科学，工程和教育培训领域。适当确定源区结构将为设计和选择适当的补救战略提供指导。在这个项目中开发的方法有潜力的应用领域，如地球科学，医学成像和无损评价，从高度异构的数据源中提取几何信息的问题是广泛遇到在所有这些领域。

Project AbstractMulti-Modal and Shape-Based Inverse Methods for the Characterization of DNAPL Source Zone ArchitectureGroundwater contamination by dense, non-aqueous phase liquids (DNAPLs) represents a major societal problem both within the United States and worldwide. Costly in situ remediation methods directed at the complete removal of contaminant mass from the subsurface have failed to provide a comprehensive solution to this problem thereby leading to recent, increased interest in an approach to remediation aimed at the reduction of downstream contaminant mass flux. Developing a quantitative understanding of the spatial distribution of DNAPL contamination in the source zone is critical to flux-based remediation and management strategies. Indeed, it has been shown that this source zone architecture is closely linked to downstream behavior of the plume. Unfortunately, the estimation of the source zone architecture is a very challenging inverse problem.We propose an approach to source zone characterization based on the joint, physics-based inversion of hydrological (down-gradient flux and concentration) and geophysical (electrical impedance tomography) data. Our processing approach addresses the ill-posed nature of this inverse problem by employing a novel representation of the source zone. Rather than using the limited data to recover a fine scale, pixilated representation of the spatial distribution of DNAPL, we parameterize the boundaries separating pools, ganglia, and non-contaminated regions. Algorithms are being developed to estimate this geometry along with the space-varying DNAPL saturation in the contaminated zones. Building on recent work in the image processing and computer vision fields, we employ a new form of parametric active contour models to describe the boundaries of the pool and ganglia regions. These models combine the topological flexibility of traditional level set ideas with the low order parametric representation associated with snakes. The performance of our approach is evaluated using an extensive suite of numerical simulations, as well as a set of laboratory-scale experiments. Simulations and experiments will explore (a) the accuracy and utility of Archie-type mixing rules for mapping geophysical to hydrological variables, and (b) the robustness of the method to un-modeled volumetric heterogeneities in both the electrical and hydrological properties of the subsurface.Intellectual Merit: Knowledge gained from this research will improve geometry-based methods for inversion by extending these concepts into hydrology. In addition to advancing the field of hydrology, our research will expand mathematical imaging through the development of new, shape-based methods for multi-modal inverse problems. This research also seeks to quantify the limits associated with using electrical impedance and hydrological data to characterize quasi-static DNAPL source-zone architecture.Broader impact: This project has potential to impact areas of basic science, engineering, and educational training. Proper identification of source zone architecture will provide guidance in designing and choosing appropriate remediation strategies. The methods developed in this project have the potential for application in fields such as earth sciences, medical imaging, and nondestructive evaluation, as the problem of extracting geometric information from highly heterogeneous data sources is widely encountered in all these areas.