Vibration of flexible and rigid plates on transversely isotropic layered media

2012 ◽  
Author(s):  
Josué Labaki Silva
Keyword(s):  
Transversely Isotropic ◽  
Layered Media

Traveltime approximation in vertical transversely isotropic layered media

2017 ◽  
Vol 65 (6) ◽  
pp. 1559-1581 ◽  
Author(s):  
Igor Ravve ◽  
Zvi Koren
Keyword(s):  
Transversely Isotropic ◽  
Layered Media

Long‐wave elastic anisotropy in transversely isotropic media

Geophysics ◽  
1979 ◽  
Vol 44 (5) ◽  
pp. 896-917 ◽  
Author(s):  
James G. Berryman
Keyword(s):  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Layered Media ◽  
Seismic Signal ◽  
Perturbation Scheme ◽  
Low Velocity ◽  
Compressional Waves ◽  
Long Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Compressional waves in horizontally layered media exhibit very weak long‐wave anisotropy for short offset seismic data within the physically relevant range of parameters. Shear waves have much stronger anisotropic behavior. Our results generalize the analogous results of Krey and Helbig (1956) in several respects: (1) The inequality [Formula: see text] derived by Postma (1955) for periodic isotropic, two‐layered media is shown to be valid for any homogeneous, transversely isotropic medium; (2) a general perturbation scheme for analyzing the angular dependence of the phase velocity is formulated and readily yields Krey and Helbig’s results in limiting cases; and (3) the effects of relaxing the assumption of constant Poisson’s ratio σ are considered. The phase and group velocities for all three modes of elastic wave propagation are illustrated for typical layered media with (1) one‐quarter limestone and three‐quarters sandstone, (2) half‐limestone and half‐sandstone, and (3) three‐quarters limestone and one‐quarter sandstone. It is concluded that anisotropic effects are greatest in areas where the layering is quite thin (10–50 ft), so that the wavelengths of the seismic signal are greater than the layer thickness and the layers are of alternately high‐ and low‐velocity materials.

On: “Long‐wave elastic anisotropy in transversely isotropic media” by J. G. Berryman, and “Seismic velocities in transversely isotropic media” by F. K. Levin (GEOPHYSICS, v. 44, May 1979, p. 896–917 and p. 918–936, respectively).

Geophysics ◽  
1981 ◽  
Vol 46 (3) ◽  
pp. 336-338 ◽  
Author(s):  
Felix M. Lyakhovitskiy
Keyword(s):  
Poisson’S Ratio ◽  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Layered Media ◽  
Thin Layers ◽  
Poisson's Ratio ◽  
Seismic Velocities ◽  
Long Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Berryman and Levin made an assumption about constancy or limited variations of Poisson’s ratio in the thin layers, in their analyses of elastic anisotropy in thin‐layered media. Berryman states (p. 913): “Rare cases can occur with large variations in Poisson’s ratio.” However, on p. 911 Berryman does point out (with reference to Benzing) that range of variations of the parameter γ = VS/VP from 0.45 to 0.65 is typical of rocks. That corresponds to a range of variations of Poisson’s ratio of 0.373 to 0.134 (i.e., almost three times as much).

Anisotropy and dispersion in periodically layered media

Geophysics ◽  
1984 ◽  
Vol 49 (4) ◽  
pp. 364-373 ◽  
Author(s):  
K. Helbig
Keyword(s):  
Dispersion Equation ◽  
Isotropic Medium ◽  
Layered Medium ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Layered Media ◽  
Spatial Period ◽  
Transversely Isotropic Medium ◽  
Low Frequencies ◽  
Vertical Dispersion

Elastic waves propagating in a periodically layered medium exhibit transverse isotropy, provided the wavelength is long compared to the spatial period of the layer sequence. The elastic constants of the long‐wave equivalent transversely isotropic medium can be calculated in several ways, all of which are based on the low‐frequency limit: one either determines from the outset the macroscopic (in average homogeneous) strain response of a representative block of the periodically layered medium to (in average homogeneous) stresses, or one determines the dispersion equation for such media and evaluates this equation for low frequencies. Both approaches yield the same replacement medium. The replacement of a layered medium by a homogeneous transversely isotropic medium is justified if all wavelengths are sufficiently long. High‐resolution techniques, the increasing use of shear waves, and attention to stratigraphic detail require a quantitative evaluation of what is sufficiently long, as well as a study of what happens for wavelengths between that limit and the limit of resolution. Such information can be obtained through a numerical evaluation of the general dispersion equation: one obtains the frequency as a function of the spatial wave vector k. The phase velocity is the v=ωk/(k⋅k) and the group velocity [Formula: see text]. In general, both dispersion and anisotropy are to be expected. This method has been applied to SH-waves in periodically layered media in general, and the dispersion equation has been evaluated numerically for two representative media. The most significant result is that the long‐wavelengths approach, i.e., a nondispersive transversely isotropic replacement medium, is strictly valid for wavelengths larger than three times the spatial period of layering. For small angles against the vertical, dispersion for shorter wavelength is significant. However, for directions making an angle of more than about 30 degrees with the vertical, dispersion sets in at much shorter wavelengths and is in general much more gentle.

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