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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Journal of the American Chemical Society 91 (1969), S. 6654-6662 
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Journal of the American Chemical Society 92 (1970), S. 1567-1568 
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 127 (1996), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: In this paper we study, theoretically and numerically, the influence of 2-D and 3-D random isotropic stationary inhomogeneities on the phase velocities of the transmitted compressional wavefield of an initially plane (or spherical) wave. Due to scattering by the inhomogeneities the wavefield becomes distorted as the wave propagates through the medium. The traveltimes fluctuate when considering different wavefield registrations acquired at the points of surfaces that are parallel to the wavefront of the initial wave. It is usually observed that the slowness obtained from the averaged traveltime differs from the averaged slowness of (he medium. In the geophysical lilerature this effect has been termed the ‘velocity shift’.Using the Rytov approximation we establish formulas for the frequency- and travel-distance-dependent phase velocity of the transmitted wavefield in 2-D and 3-D randomly inhomogeneous media. We also compare our analytical results with finite-difference simulations. Good agreement between numerical simulations and theory is observed. The low-frequency limit of our analytical results coincides with the known effective-medium limit of the phase velocity in statistically isotropic inhomogeneous fluids with constant densities. In the high-frequency limit our results coincide with the results previously obtained by the ray-perturbation theory. However, in contrast to the ray theory, our description is not restricted to media with differentiate correlation functions of fluctuations. Moreover, our results quantify the frequency dependence of the velocity shift in the intermediate-frequency range. This frequency dependence is of major importance for estimating this effect in realistic situations.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 114 (1993), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Estimates of seismic wave attenuation are strongly affected by scattering. Scattering is an important effect caused by interaction of seismic wavefields with inhomogeneities of hydrocarbon reservoirs, Earth's crust and mantle. In order to study the contribution of scattering to apparent attenuation we consider plane-wave propagation in acoustic 2-D and 3-D inhomogeneous media. Different attenuation estimates result depending on what wavefield function is being averaged during corresponding processing. By wave-theoretical analysis and high-order finite difference modelling in two dimensions we show that scattering attenuation estimates derived from the mean of amplitude spectra and from the mean logarithm of amplitude spectra depend on travel distance. For not too long travel distances, where the coherent part of the wavefield dominates, we give an analytical description of these estimates. In 2-D and 3-D the relations are established between the autocorrelation functions of velocity fluctuations of a random medium and the autocorrelation functions of amplitude and phase fluctuations on a receiver line perpendicular to the general propagation direction of an originally plane wave. For long distances, where the wavefield fluctuates strongly, we show that both mean logarithm of amplitude and logarithm of mean amplitude tend to constants. They differ approximately by a factor two in both scattering regimes. the scattering attenuation coefficient of the meanfield is not dependent on travel distance. We compared our theoretical results with numerical calculations and found excellent agreements. the concept presented clarifies the nature of seismic Q estimations in the presence of scattering and can help to yield statistical earth models from seismic data.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 110 (1992), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: I obtain the Born approximation for the scattered intensity I, the differential cross-sections σd, and the total scattering cross-sections σ of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and σd are valid for an arbitrary anisotropic random discrete or continuous inhomogeneity and they are in agreement with the well known results for discrete inclusions (Gubernatis, Domany & Krumhansl 1977b). For fractal inhomogeneities I show that: (1) for small angle scattering I∝ω4+ω(sin θ/2)n̈, where θ is a scattering angle and the constant n̈ depends linearly on the fractal dimension; (2) σ∝ω4+ω; (3) σ∝ω4+n̈ if n̈〉-2 and σ∝ω2 if n̈≤ -2; and (4) the Fourier transform of the correlation function of the wavefield Γ which is coherently radiated by white noise point sources distributed on fractal objects obeys [Γ] ∝ωσ. Applying the results for σd I show that the model of inhomogeneities with a fractal surface is in agreement with the fractal dimensions of some fault systems.
    Type of Medium: Electronic Resource
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  • 6
    facet.materialart.
    Unknown
    Minneapolis, Minn. : Periodicals Archive Online (PAO)
    Critique. 7:1 (1964:Spring) 87 
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