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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Proceedings ArticleDOI
Scale-dependent Dynamic Wave Propagation In Heterogeneous Media: II. Theory
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Reservoir facies design and modeling using probabilistic rock-physics templates
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Characterization of batteries using ultrasound: applications for battery management and structural determination
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References
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Book ChapterDOI
The Dispersion of Surface Waves on Multilayered Media
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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Journal ArticleDOI
Wave propagation in a stratified medium
TL;DR: In this paper, the authors derived the wave equation from the stress-strain relations and the equation of motion, and showed that there are in general three characteristic velocities, all functions of the direction of the propagation.
Journal ArticleDOI
Elastic wave propagation in layered anisotropic media
TL;DR: In this article, the dispersion properties of transversely isotropic media were analyzed for a single solid layer in vacuo and a single layer in contact with a fluid halfspace, and the single layer solutions were generalized to n-layer media by the use of Haskell matrices.