Journal ArticleDOI
Long-Wave Elastic Anisotropy Produced by Horizontal Layering
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TLDR
In this article, a horizontally layered inhomogeneous medium is considered, whose properties are constant or nearly so when averaged over some vertical height l′, and conditions on the five elastic coefficients of a homogeneous transversely isotropic medium are derived which are necessary and sufficient for the medium to be "long-wave equivalent" to a horizontally-layered inhomogenous medium.Abstract:
A horizontally layered inhomogeneous medium, isotropic or transversely isotropic, is considered, whose properties are constant or nearly so when averaged over some vertical height l′. For waves longer than l′ the medium is shown to behave like a homogeneous, or nearly homogeneous, transversely isotropic medium whose density is the average density and whose elastic coefficients are algebraic combinations of averages of algebraic combinations of the elastic coefficients of the original medium. The nearly homogeneous medium is said to be ‘long-wave equivalent’ to the original medium. Conditions on the five elastic coefficients of a homogeneous transversely isotropic medium are derived which are necessary and sufficient for the medium to be ‘long-wave equivalent’ to a horizontally layered isotropic medium. Further conditions are also derived which are necessary and sufficient for the homogeneous medium to be ‘long-wave equivalent’ to a horizontally layered isotropic medium consisting of only two different homogeneous isotropic materials. Except in singular cases, if the latter two-layered medium exists at all, its proportions and elastic coefficients are uniquely determined by the elastic coefficients of the homogeneous transversely isotropic medium. The observed variations in crustal P-wave velocity with depth, obtained from well logs, are shown to be large enough to explain some of the observed crustal anisotropies as due to layering of isotropic material.read more
Citations
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Journal ArticleDOI
Dynamic elasticity of microbedded and fractured rocks
TL;DR: In this paper, an exact two-way method is used to propagate just a few plane waves, of frequency ƒ, a distance of several wavelengths from the source if an equivalent homogeneous medium exists at frequency ǫ, then the computed motions must also satisfy a one-way elastic wave equation for that equivalent medium.
Journal ArticleDOI
In Situ measurement of transverse isotropy in shallow‐water marine sediments
Patricia A. Berge,Subhashis Mallick,Gerard J. Fryer,Noël Barstow,Jerry A. Carter,George H. Sutton,John I. Ewing +6 more
TL;DR: In this article, the authors used an anisotropic reflectivity program to produce synthetic seismograms to estimate the five independent elastic stiffnesses necessary for describing the transverse isotropy.
Journal ArticleDOI
Sensitivity of the elastic anisotropy and seismic reflection amplitude of the Eagle Ford Shale to the presence of kerogen
TL;DR: In this paper, the authors show that the Eagle Ford Shale is anisotropic, with a correlation between anisotropy and total organic carbon, and that organic materials have a significant effect on the PP and PS reflection amplitudes from the Austin Chalk/Upper Eagle Ford interface.
Journal ArticleDOI
Is there seismic attenuation in the mantle
TL;DR: In this article, the Batchelor regime was used to explain the observed S and P attenuation of the Earth's mantle, and it was shown that the total contribution of 6-9% RMS density, velocity and anisotropic heterogeneities with similar 1/kspectra would explain the presence of small scale scattering by laminations.
Journal ArticleDOI
Validity of the acoustic approximation for elastic waves in heterogeneous media
Philippe Cance,Yann Capdeville +1 more
TL;DR: In this paper, the authors studied the effect of small size heterogeneities with respect to the minimum wavelength of the wavefield on the elastic and acoustic wave propagation and concluded that acoustic waves can only be a poor quality approximation of elastic waves.
References
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Book ChapterDOI
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TL;DR: In this paper, a matrix formalism developed by W. T. Thomson is used to obtain the phase velocity dispersion equations for elastic surface waves of Rayleigh and Love type on multilayered solid media.
Journal ArticleDOI
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Journal ArticleDOI
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