Joint Stochastic Non-Linear Inversion of Hydrogeophysical Data for Improved Vadose Zone Characterization and Monitoring

0439649 Rubin包气带是环境、农业和大气科学应用中极为重要的区域。随着包气带相关分析变得越来越复杂，提供更详细、高分辨率成像能力的压力越来越大。这方面的突破之一是采用地球物理调查作为水文特征描述的关键工具。然而，表征方法，可以处理的非线性和复杂性，包气带流动，包括滞后和优先流，和地球物理过程，仍然是一个挑战。最近已经提出了几种有前途的技术，需要进行更多的研究，以更好地了解它们的优势和局限性。拟议的研究的目标是开发一个随机反演程序，将允许解决这些挑战。我们将重点放在结合使用的跨孔雷达（GPR）和水文地质数据，如土壤水分和压力头，从钻孔，提供高分辨率的土壤水分动态成像，并随后进行反演建模。我们的假设是，一个反演框架的基础上，同时反演的地球物理和水文测量和非线性建模的流量过程和地球物理调查，提高了我们的能力，表征包气带。将使用流动和地球物理过程的非线性数学模型同时进行地球物理和水文地质数据的反演，以将目标参数（岩性、渗透率、相对电导率和保水性建模所需的其他土壤参数）与输入数据联系起来。这是出于以下意见。首先，目前的水文地质和地球物理数据集成方法是顺序或迭代的。顺序方法的问题是忽略了与地球物理反演相关的误差，而迭代方法的问题是不能保证收敛，除非满足难以评估的特殊条件。其次，最近已经探索了几个有前途的反演程序的基础上的线性化（低阶近似的可变性）的流量方程。我们完全非线性的方法将探索它们的优势和局限性。该过程在本质上是随机的，目标是通过目标参数的多元空间概率分布来表征目标参数。选择随机方法是因为它可以合理地对待由于空间变异性，数据稀缺性和测量误差的不确定性。将采用贝叶斯公式，因为它允许将先验信息与特定地点的测量相结合。基于熵的方法（MRE：最小相对熵）将用于以最小主观性从基于先验/无关信息的约束确定参数的先验概率分布。模糊神经网络将用于开发岩石物理模型。所提出的方法将进行测试，使用数字模拟为基础的合成模型，并在汉福德能源部网站进行了现场实验的数据。综合研究将测试我们确定远离威尔斯的土壤水力参数的能力，汉福德研究将评估我们提高预测能力的能力。其智力优势主要在于通过联合反演（非连续、非迭代）对地球物理和水文数据中的不确定性进行一致处理，以及对流量和地球物理过程使用非线性数学模型。虽然基于流动方程线性化的联合反演特设方法令人满意，但需要科学依据来确定其强度和局限性，并探索目前能力之外的问题（即，更大的可变性，不规则和瞬态边界条件，以及尖锐的前沿）。就该项目的更广泛影响而言，我们建议考虑两点。第一个是地球物理反演。在地球物理学界，忽略水文地质约束是很常见的。虽然地球物理调查正在向水文地质学进军，但反过来却并非如此。我们提出的解释方法可以在这方面产生积极的影响。我们认为重要的第二点是随机分析的整体方法，包括所有的误差来源，以及先验信息的合理处理。从狭义的角度来看，这种方法旨在消除地球物理数据处理的不一致性，避免先验的主观性，但从更广泛的角度来看，这些想法对于水文地质学内外的广泛一类反问题是有价值的，其中结合使用许多数据源，包括先验，仍然是一个挑战。

0439649RubinThe vadose zone is an extremely important region to consider for environmental, agricultural and atmospheric science applications. As analyses related to vadose zone become more sophisticated, there is a mounting pressure to provide more detailed, high-resolution imaging capabilities. One of the breakthroughs in that direction has been the introduction of geophysical surveys as a key tool for hydrologic characterization. Yet, a characterization approach that can handle the nonlinearities and complexities inherent in vadose zone flow, including hysteresis and preferential flow, and geophysical processes, is still a challenge. Several promising techniques have been proposed recently, and additional investigation is needed to better understand their strength and limitations. The objective of the proposed research is to develop a stochastic inversion procedure that will allow addressing these challenges. We shall focus on the combined use of crosshole radar (GPR) and hydrogeologic data such as soil moisture and pressure head, obtained from boreholes, to provide high-resolution imaging of soil moisture dynamics, and subsequently for inverse modeling. Our hypothesis is that an inversion framework that is based on simultaneous inversion of geophysical and hydrological measurements and on non-linear modeling of the flow processes and of the geophysical surveys, improves our ability to characterize the vadose zone. The inversion of the geophysical and hydrogeological data will be carried out simultaneously using non-linear mathematical models of the flow and geophysical processes to relate between target parameters (lithology, permeability, other soil's parameters needed for modeling of the relative conductivity and water retentivity), and input data. This is motivated by the following observations. First, current methods for integrating hydrogeological and geophysical data are either sequential or iterative. The problem with sequential methods is that the error associated with the geophysical inversion is ignored, and the problem with the iterative methods is that convergence is not guaranteed, unless special conditions are met, which are difficult to evaluate. Second, several promising inversion procedures have been explored recently based on linearization (low-order approximations in terms of variability) of the flow equation. Our fully non-linear approach will explore their strength and limitations. The procedure will be stochastic in nature, with the goal of characterizing the target parameters through their multivariate spatial probability distributions. A stochastic approach is chosen because it allows to treat rationally the uncertainty due to spatial variability, data scarcity and measurement error. A Bayesian formulation will be pursued, because it allows combining prior information with site-specific measurements. Entropy-based methods (MRE: minimum Relative entropy) will be employed for determining prior probability distributions of parameters from constraints based on prior/extraneous information, with minimum subjectivity. Fuzzy neural networks will be used to develop petrophysical models. The proposed approach will be tested using a digital analogue-based synthetic model, and data from a field experiment carried out at the DOE site at Hanford. The synthetic study will test our ability to identify the soil's hydraulic parameters away from wells, and the Hanford study will assess our capability to improve predictive capabilities. The intellectual merits are primarily in the consistent treatment of uncertainty in both the geophysical and hydrological data through joint inversion (non-sequential, non-iterative), and in the use of non-linear mathematical models for the flow and geophysical processes. While ad-hoc methods for joint inversion, based on linearization of the flow equation, were found satisfactory, a scientific basis is needed for establishing their strength and limitations, and for exploring problems which are outside of current capabilities (i.e., larger variability, irregular and transient boundary conditions, and sharp fronts). There are two points we propose to consider in terms of the broader impact of the project. The first concerns geophysical inversion. It is common in the geophysical community to ignore hydrogeological constraints. While geophysical surveys are making inroads into hydrogeology, this is not true the other way around. The interpretation approach we propose can create a positive impact in that direction. The second point we view as important is the holistic approach to stochastic analysis, including all sources of error, and a rational treatment of prior information. From a narrow perspective, this approach intends to remove inconsistency in the treatment of geophysical data and to avoid subjectivity in the prior, but from a broader perspective, these ideas are meritorious for a broad class of inverse problems in and outside hydrogeology, where combined use of many sources of data, including priors, is still a challenge.