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  • 1
    Electronic Resource
    Electronic Resource
    The fractal geometry of flow paths in natural fractures in rock and the approach to percolation (1989)
    Springer
    Pure and applied geophysics 131 (1989), S. 111-138 
    Details
    ISSN: 1420-9136
    Keywords: Fractals ; fractures ; fluid flow ; percolation ; rock mechanics ; geohydrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The distributions of contact areas in single, natural fractures in quartz monzonite (Stripa granite) are found to have fractal dimensions which decrease fromD=2.00 to values nearD=1.96 as stress normal to the fractures is increased from 3 MPa up to 85 MPa. The effect of stress on fluid flow is studied in the same samples. Fluid transport through a fracture depends on two properties of the fracture void space geometry. the void aperture; and the tortuosity of the flow paths, determined through the distribution of contact area. Each of these quantities change under stress and contribute to changes observed in the flow rate. A general flow law is presented which separates these different effects. The effects of tortuosity on flow are largely governed by the proximity of the flow path distribution to a percolation threshold. A fractal model of correlated continuum percolation is presented which quantitatively reproduces the flow path geometries. The fractal dimension in this model is fit to the measured fractal dimensions of the flow systems to determine how far the flow systems are above the percolation threshold.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00874483
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  • 2
    Electronic Resource
    Electronic Resource
    Fractures: Finite-size scaling and multifractals (1992)
    Springer
    Pure and applied geophysics 138 (1992), S. 679-706 
    Details
    ISSN: 1420-9136
    Keywords: Fractures ; fractals ; multifractals ; scaling ; percolation ; geohydrology ; rock mechanics ; permeability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The distributions of contact area and void space in single fractures in granite rock have been determined experimentally by making metal casts of the void spaces between the fracture surfaces under normal loads. The resulting metal casts on 52 cm diameter core samples show a complex geometry for the flow paths through the fracture. This geometry is analyzed using finite-size scaling. The spanning probabilities and percolation probabilities of the metal casts are calculted as functions of observation scale. Under the highest stresses of 33 MPa and 85 MPa there is a significant size-dependence of the geometric flow properties for observation scales smaller than 2 mm. Based on this data, the macroscopic percolation properties of the extended fracture can be well represented by relatively small core samples, even under normal stresses larger than 33 MPa. The metal casts also have rich multifractal structure that changes with changing stress.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00876344
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  • 3
    Electronic Resource
    Electronic Resource
    Laser-based ultrasound detection using photorefractive quantum wells (1998)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 73 (1998), S. 1041-1043 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We demonstrate a laser-based adaptive ultrasonic homodyne receiver using dynamic holography in AlGaAs/GaAs photorefractive multiple quantum wells. The dynamic hologram acts as an adaptive beamsplitter that compensates wavefront distortions in the presence of speckle and requires no path-length stabilization. The photorefractive quantum wells have the unique ability to achieve maximum linear homodyne detection regardless of the value of the photorefractive phase shift by tuning the excitonic spectral phase. We achieve a root mean square noise-equivalent surface displacement of 6.7×10−7 Å(W/Hz)1/2. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.122078
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  • 4
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    Laser-based ultrasound detection using photorefractive quantum wells (1998)
    American Institute of Physics
    Details
    Publication Date: 1998-08-24
    Print ISSN: 0003-6951
    Electronic ISSN: 1077-3118
    Topics: Physics
    Published by American Institute of Physics
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  • 5
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    A discontinuous Galerkin method with a modified penalty flux for the propagation and scattering of acousto-elastic waves (2016)
    Oxford University Press
    Details
    Publication Date: 2016-04-07
    Description: We develop an approach for simulating acousto-elastic wave phenomena, including scattering from fluid–solid boundaries, where the solid is allowed to be anisotropic, with the discontinuous Galerkin method. We use a coupled first-order elastic strain-velocity, acoustic velocity–pressure formulation, and append penalty terms based on interior boundary continuity conditions to the numerical (central) flux so that the consistency condition holds for the discretized discontinuous Galerkin weak formulation. We incorporate the fluid–solid boundaries through these penalty terms and obtain a stable algorithm. Our approach avoids the diagonalization into polarized wave constituents such as in the approach based on solving elementwise Riemann problems.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 6
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    Wave guiding in fractured layered media (2014)
    Geological Society (of London)
    Details
    Publication Date: 2014-06-04
    Description: Many carbonate rocks are composed of layers and contain fracture sets that cause the hydraulic, mechanical and seismic properties to be anisotropic. Co-located fractures and layers in carbonate rock lead to competing wave-scattering mechanisms: both layers and parallel fractures generate compressional-wave (P-wave) guided modes. The guided modes generated by the fractures may obscure the presence of the layers. In this study, we examine compressional-wave guided modes for two cases: wave guiding by fractures in a layered medium with sub-wavelength layer thickness; and wave guiding in media with competing scattering mechanisms, namely layering (where the thickness is greater than a wavelength) and parallel sets of fractures. In both cases, the fracture spacing is greater than a wavelength. When the layer thickness is smaller than a wavelength, P-wave guiding is controlled by the spacing of the fractures, fracture specific stiffness, the frequency of the signal and the orientation of the layering relative to the fracture set. The orientation of the layering determines the directionally dependent P-wave velocity in the anisotropic matrix. When the layer thickness is greater than a wavelength and an explosive point source of a signal is located in the layer containing a fracture, the fracture either enhanced or suppressed compressional-mode wave guiding caused by the layering in the matrix.
    Print ISSN: 0305-8719
    Electronic ISSN: 2041-4927
    Topics: Geosciences
    Published by Geological Society (of London)
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  • 7
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    Interface waves along fractures in anisotropic media (2013)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2013-07-13
    Description: The detection of fractures in an anisotropic medium is complicated by discrete modes that are guided or confined by fractures such as fracture interface waves. Fracture interface waves are generalized coupled Rayleigh waves whose existence and velocity in isotropic media depend on the stiffness of the fracture, frequency of the source, and shear-wave polarization. We derived the analytic solution for fracture interface waves in an orthorhombic medium and found that the existence and velocity of interface waves in anisotropic media are also affected by the orientation of a fracture relative to the layering. Laboratory measurements of fracture interface waves using ultrasonic transducers (central frequency $$\sim 1\hbox{ \hspace{0.17em} }\hbox{ \hspace{0.17em} }$$ MHz) on garolite specimens confirmed that the presence of fracture interface waves can mask the textural shear-wave anisotropy of waves propagating parallel to the layering. At low stresses, a layered medium appears almost isotropic when a fracture is oriented perpendicular to the layering, and conversely, a layered medium exhibits stronger anisotropy than the matrix for a fracture oriented parallel to the layering. The matrix shear-wave anisotropy is recovered when sufficient stress is applied to close a fracture. The theory and experimental results demonstrated that the interpretation of the presence of fractures in anisotropic material can be unambiguously interpreted if measurements are made as a function of stress, which eliminates many fractured-generated discrete modes such as fracture interface waves.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 8
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    Intersection Waves (2017)
    Wiley
    Details
    Publication Date: 2017-08-29
    Description: Intersections in a fracture network control the connectivity of the flow paths through rock. The long near-linear geometric nature of fractures makes them difficult to identify and characterized. We present a new type of elastic wave, an intersection wave, which travels along an intersection and is sensitive to the coupling between two orthogonal fractures that define the intersection. Group theory for C 2 v and C 4 v point groups predict sets of propagating elastic waves confined to the fracture intersection. Along with the use of the wave equation and displacement discontinuity boundary conditions, the dispersion relationships for intersection waves were predicted. Experimental ultrasonic measurements on a non-welded linear intersection between two orthogonal, synthetic fractures in aluminum confirm the existence of multiple modes that travel between the speed of wedge waves (sub-Rayleigh waves) when the intersection is completely open or decoupled, and bulk shear waves, when the intersection is closed, as predicted by theory. In between these two limits, the intersection behaves as a non-welded contact and yields these new intersection waves that are dispersive and sensitive to the coupling along the intersection. Intersection waves provide the foundation for new geophysical approaches for characterizing the hydraulic connectivity of fracture networks.
    Print ISSN: 0148-0227
    Topics: Geosciences , Physics
    Published by Wiley on behalf of American Geophysical Union (AGU).
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  • 9
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    Stratified continuum percolation: Scaling geometry of hierarchical cascades (1991)
    American Physical Society
    Details
    Publication Date: 1991-11-01
    Print ISSN: 1050-2947
    Electronic ISSN: 1094-1622
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Published by American Physical Society
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  • 10
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    Coexisting two-phase flow in correlated two-dimensional percolation (1997)
    American Physical Society
    Details
    Publication Date: 1997-11-01
    Print ISSN: 1063-651X
    Electronic ISSN: 1095-3787
    Topics: Physics
    Published by American Physical Society
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