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Considering 2-D ergodic log-normal random fields of fluid conductivity, we demonstrate, in absence of surface conductivity, that observing the components of the <i>M</i>-tensor allows univocally determining the variance and anisotropy of the field. Further, time-series of the <i>M</i>-tensor under diffusion-limited mixing allows distinguishing between different characteristic temporal scales of diffusion, which are directly related to the initial integral scales of the salinity field. Under advective-diffusive transport and for a pulse injection, the time-series of <i>M</i> have a strong dependence on the Péclet number. Since <i>M</i> is defined in the absence of surface conductivity, we investigate how to correct measurements for surface conductivity effects. The parameter <i>M</i> provides conceptual understanding about the impact of saline heterogeneity on electrical measurements. 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引用次数: 0
摘要
使用电学或电磁地球物理方法对水文状态变量进行定量估算时,会因方法解析的空间尺度以下的被忽略的异质性而产生系统性偏差。我们在连续(如达西)尺度上对多孔介质中电导的高盐度渐近极限进行了概括,引入了一个新的岩石物理参数--混合因子 M,该因子考虑了流体电导率异质性对等效电导率张量的影响;它用平均去除的流体电导率与电场乘积的体积平均值表示。我们研究了 M 在静态和不断变化的流体电导情况下的行为。考虑到流体电导率的二维对数正态随机场,我们证明,在没有表面电导率的情况下,观察 M 张量的分量可以统一确定场的方差和各向异性。此外,在扩散受限的混合条件下,M 张量的时间序列可以区分扩散的不同特征时间尺度,这些尺度与盐度场的初始积分尺度直接相关。在平流扩散输运和脉冲注入条件下,M 的时间序列与佩克莱特数有很大关系。由于 M 是在没有表面传导性的情况下定义的,因此我们研究了如何校正测量结果的表面传导性效应。参数 M 使我们从概念上理解了盐水异质性对电学测量的影响。下一步工作将研究如何将其纳入水文地质物理反演公式和解释框架。
An Electrical Parameter Characterizing Solute Heterogeneity: The Mixing Factor M
Quantitative estimates of hydrological state variables using electrical or electromagnetic geophysical methods are systematically biased by overlooked heterogeneity below the spatial scale resolved by the method. We generalize the high-salinity asymptotic limit of electrical conduction in porous media at the continuous (e.g., Darcy) scale, by introducing a new petrophysical parameter, the mixing factor M, which accounts for the effect of fluid conductivity heterogeneity on the equivalent electrical conductivity tensor; it is expressed in terms of the volume-average of the product of mean-removed fluid conductivity and electric fields. We investigate the behavior of M for static and evolving fluid conductivity scenarios. Considering 2-D ergodic log-normal random fields of fluid conductivity, we demonstrate, in absence of surface conductivity, that observing the components of the M-tensor allows univocally determining the variance and anisotropy of the field. Further, time-series of the M-tensor under diffusion-limited mixing allows distinguishing between different characteristic temporal scales of diffusion, which are directly related to the initial integral scales of the salinity field. Under advective-diffusive transport and for a pulse injection, the time-series of M have a strong dependence on the Péclet number. Since M is defined in the absence of surface conductivity, we investigate how to correct measurements for surface conductivity effects. The parameter M provides conceptual understanding about the impact of saline heterogeneity on electrical measurements. Further work will investigate how it can be incorporated into hydrogeophysical inverse formulations and interpretative frameworks.
期刊介绍:
Water Resources Research (WRR) is an interdisciplinary journal that focuses on hydrology and water resources. It publishes original research in the natural and social sciences of water. It emphasizes the role of water in the Earth system, including physical, chemical, biological, and ecological processes in water resources research and management, including social, policy, and public health implications. It encompasses observational, experimental, theoretical, analytical, numerical, and data-driven approaches that advance the science of water and its management. Submissions are evaluated for their novelty, accuracy, significance, and broader implications of the findings.