Travel times of nonlocal dispersion and their geoelectric approximation in Nevada's fractured welded tuffs

Purvance, David T.

doi:10.1029/2001wr000491

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…Both spectra are power‐law structured and of identical log‐log slope, indicating eh flow patterns of a common fractal dimension. Purvance [2001] observed that this fractal dimension is the same as the fractal dimension of fracture lengths measured in the same formation at Yucca Mountain, Nevada, located in Figure 1.…”

Section: Apparent Resistivity Spectral Analysissupporting

confidence: 76%

Roles apparent resistivity amplitude and phase play in an aquifer's electrical‐hydraulic conductivity correlation

Purvance

2003

Geophysical Research Letters

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This paper argues how the spectral characteristics of two borehole apparent resistivity traces further corroborate two statistically significant electrical‐hydraulic (eh) conductivity correlations previously reported in Nevada's fractured welded tuffs. Even though the eh conductivity correlation is positive in one borehole and negative in the other, as explained by low pore water electrical conductivity and the absence or presence of alteration minerals, both apparent resistivity amplitude spectra are identically power‐law structured. This is interpreted to mean that eh flow is occurring along rock fractures of a common regional fractal dimension. Furthermore, both apparent resistivity phase spectra are strikingly linear, as mandated by the condition of incompressible fluids. Linear phase implies a groundwater flow that is geostatistically nonstationary in the wide sense, a complication normally not considered by hydrogeologists.

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Section: Apparent Resistivity Spectral Analysissupporting

confidence: 76%

Roles apparent resistivity amplitude and phase play in an aquifer's electrical‐hydraulic conductivity correlation

Purvance

2003

Geophysical Research Letters

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“…Using standard methods of stochastic analysis, the truncated mode superposition approach allows one to investigate flow [ Di Federico and Neuman , 1998a] and transport [ Neuman , 1990, 1995; Di Federico and Neuman , 1998b; Purvance , 2001] in a hydraulic conductivity field with evolving scales of spatial variability. It allows one to upscale and downscale the random equivalent mean hydraulic conductivity of a domain embedded within such a field and assess its variance and spatial autocorrelation function, conditioned on a known mean value of support‐scale conductivity across the domain [ Di Federico et al , 1999; Hyun et al , 2002].…”

Section: Introductionmentioning

confidence: 99%

Relationship between juxtaposed, overlapping, and fractal representations of multimodal spatial variability

Neuman

2003

Water Resources Research

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[1] It has been shown by Neuman [1990], Di Federico and Neuman [1997], and Di Federico et al. [1999] that the power variogram of a statistically isotropic or anisotropic fractal field can be constructed as a weighted integral from zero to infinity of exponential or Gaussian variograms of overlapping, homogeneous random fields (modes) having mutually uncorrelated increments and variance proportional to a power 2H of the integral (spatial correlation) scale where H is the Hurst coefficient. Low-and high-frequency cutoffs are related to length scales of the sampling window (domain) and data support (sample volume), respectively. Intermediate cutoffs account for lacunarity due to gaps in the multiscale hierarchy, created by a hiatus of modes associated with discrete ranges of scales. Alternative mathematical representations of multimodal spatial variability were formulated by various authors in which space is filled by a discrete number of juxtaposed (mutually exclusive) materials or categories, each having its own architecture and attributes. The spatial distribution of categories is characterized by indicator random variables and their attributes by random fields. This paper focuses on expressions developed by Lu and Zhang [2002] in which the indicator variables and their attributes are mutually uncorrelated while each is autocorrelated and cross correlated within and between categories. Upon rewriting their expressions for statistically homogeneous and anisotropic media, it is demonstrated mathematically that in the limit as the categories stretch to occupy each point in space (overlap) in a way that preserves their local architecture, their attributes become mutually uncorrelated. Categories are said to overlap if they are found in fixed proportions within a representative sampling volume centered about any mathematical point throughout space; the idea is analogous to the well-known dual continuum concept in which two categories, most commonly fractures and porous blocks, are considered to overlap. In reality, the categories do not overlap but are considered to preserve their relative architectural arrangement throughout space. The variogram of an attribute, sampled jointly over overlapping statistically homogeneous and anisotropic categories, is the sum of the variograms of statistically homogeneous and anisotropic components of this attribute sampled over individual categories, weighted by their volumetric proportions. It is further demonstrated that when the overlapping categories represent an infinite or truncated hierarchy of modes whose attributes have exponential or Gaussian variograms, such that the product of category probability density function (pdf) and attribute variance is proportional to a power 2H + 1 of the attribute integral scale, they represent a fractal field characterized by a power or truncated power variogram as in the work of Di Federico and Neuman. Any category pdf that satisfies this condition, and any attribute pdf having a variance that satisfies the same condition, are admissible;...

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Travel times of nonlocal dispersion and their geoelectric approximation in Nevada's fractured welded tuffs

Cited by 2 publications

References 7 publications

Roles apparent resistivity amplitude and phase play in an aquifer's electrical‐hydraulic conductivity correlation

Roles apparent resistivity amplitude and phase play in an aquifer's electrical‐hydraulic conductivity correlation

Relationship between juxtaposed, overlapping, and fractal representations of multimodal spatial variability

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