Elastic Wave Velocities in Laminated Media

Abstract

The velocities of elastic waves in a laminated medium have been determined by calculating the effective elastic parameters and the effective density. The procedure is to assume the medium to be in static equilibrium and exposed to certain stresses. The stresses are of such a nature as to generate strains similar to those which would exist during the passage of an elastic wave through the medium. From the application of Hooke's law, an effective stiffness constant for the medium is obtained. The ratio of this effective stiffness to the effective density is the square of the velocity of the elastic wave. For a medium consisting of layers of two materials with the same density but with a velocity contrast of two (2), the velocity of compressional waves traveling parallel to the layering is 20 percent higher than the velocity of the same wave traveling perpendicular to the layers. The SH shear wave has a velocity which is 25 percent higher than the SV shear wave for the same laminated medium.

Gas hydrate saturations estimated from fractured reservoir at Site NGHP‐01‐10, Krishna‐Godavari Basin, India

“…For this study, gas hydrate saturations were estimated from both electrical resistivity logs and P and S wave velocities. In order to properly analyze the resistivity log, a theory developed by Kennedy and Herrick [2004] was used to account for the resistivity anisotropy of the fractured reservoir and to correctly estimate the saturation, whereas a transverse isotropic theory for laminated media [e.g., Backus , 1962; Postma , 1955; White and Angona , 1955] was used to describe the elastic velocities of the fractured reservoir.…”

On the Relationship between Engineering Properties and Delamination of Composite Materials

“…has stimulated many analytical studies of materials of this kind. The overall material parameters of a variety of composites have been studied by White and Angona [1], Hashin and Rosen [2], and others. For harmonic waves in elastic composites, both exact and approximate analyses have been performed ; see Achenbach et al [3], Nelson and Navi [4], and Nemat-Nasser [5] for examples of approximate calculations, and Brekhouskikh [6], Rytov [7], Sun et al.…”

Propagating modes of periodic solid layers in an ideal or viscous fluid by homogenization analysis

“…[1][2][3][4][5][6][7] These studies presented results on band structures as well as on averaged properties such as effective mass, elastic constants, and group velocities in the long-wavelength limit. In particular, Krokhin et al 8 used the pressure wave equation to derive the effective speed of sound for a periodic array of the liquid-gas mixture.…”