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

鲁宾包气带对于环境、农业和大气科学的应用来说是一个极其重要的区域。随着与包气带相关的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。在这方面取得的突破之一是采用地球物理调查作为确定水文特征的关键工具。然而，能够处理包气带流动固有的非线性和复杂性，包括滞后和优先流动，以及地球物理过程的表征方法，仍然是一个挑战。最近提出了几种很有前途的技术，还需要进一步的研究来更好地了解它们的优点和局限性。拟议研究的目标是开发一种能够应对这些挑战的随机反演程序。我们将重点结合使用井间雷达(GPR)和从钻孔获得的土壤水分和压力水头等水文地质数据，以提供土壤水分动态的高分辨率成像，并随后进行反向建模。我们的假设是，基于地球物理和水文测量的同时反演以及流动过程和地球物理调查的非线性建模的反演框架，提高了我们描述包气带特征的能力。将利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，以建立目标参数(岩性、渗透率、相对电导率和持水率建模所需的其他土壤参数)与输入数据之间的关系。这是由以下观察到的结果推动的。首先，目前综合水文地质和地球物理数据的方法要么是连续的，要么是迭代的。序贯方法的问题是忽略了与地球物理反演有关的误差，而迭代方法的问题是除非满足难以评估的特殊条件，否则不能保证收敛。其次，基于流动方程的线性化(变异性方面的低阶近似)，最近已经探索了几种有前途的反演方法。我们的完全非线性方法将探讨它们的优点和局限性。这一过程本质上是随机的，目的是通过目标参数的多变量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处理由空间变异性、数据稀缺性和测量误差引起的不确定性。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)将被用来从基于先验/无关信息的约束中确定参数的先验概率分布，主观性最小。模糊神经网络将被用于建立岩石物理模型。建议的方法将使用基于数字模拟的合成模型和在能源部汉福德现场进行的现场实验数据进行测试。这项综合研究将测试我们识别远离油井的土壤水力参数的能力，而汉福德的研究将评估我们提高预测能力的能力。智能的优点主要是通过联合反演(非顺序、非迭代)一致地处理地球物理和水文数据中的不确定性，以及使用流动和地球物理过程的非线性数学模型。虽然基于流动方程线性化的联合反演特别方法是令人满意的，但需要一个科学基础来确定其强度和局限性，并探索当前能力之外的问题(即，较大的可变性、不规则和瞬变的边界条件以及陡峭的锋面)。就该项目的更广泛影响而言，我们建议考虑两点。第一个问题是地球物理反演。在地球物理学界，忽视水文地质约束是很常见的。虽然地球物理勘测正在进入水文地质学领域，但反过来却并非如此。我们提出的解释方法可以在这个方向上产生积极影响。我们认为重要的第二点是随机分析的整体方法，包括所有误差来源，以及对先验信息的合理处理。从狭隘的角度来看，这种方法意在消除在处理地球物理数据方面的不一致，并避免先前的主观性，但从更广泛的角度来看，这些想法对于水文地质学内外的一大类反问题是有价值的，在这些问题中，综合使用许多数据来源，包括以前的数据来源，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.