Elastic wave velocities

Phonon transport is the main conduction mechanism below 300°C. Compositional effects are significant because the mean free phonon path is limited by the random glass stmcture. Estimates of the mean free phonon path in vitreous siUca, made using elastic wave velocity, heat capacity, and thermal conductivity data, generate a value of 520 pm, which is on the order of the dimensions of the SiO tetrahedron (151). Radiative conduction mechanisms can be significant at higher temperatures. 

Figure 4.23. Elastic wave velocities as a function of pressure along the Hugoniot of iron. The solid curve is the calculated bulk sound velocity. (From Brown and McQueen (1982).)...

Molar elastic wave velocity u V-u1/3 Sound wave velocity U... 

The mechanical properties of polymers are controlled by the elastic parameters the three moduli and the Poisson ratio these four parameters are theoretically interrelated. If two of them are known, the other two can be calculated. The moduli are also related to the different sound velocities. Since the latter are again correlated with additive molar functions (the molar elastic wave velocity functions, to be treated in Chap. 14), the elastic part of the mechanical properties can be estimated or predicted by means of the additive group contribution technique. 

Walhs (1969) also derived an equation for the elastic wave velocity ... 

Verloop and Heertjes (1970) used Eq. (36) for the voidage propagation velocity. The elastic wave velocity was calculated on the basis that the fluidized bed was considered to be an elastic substance ... 

Ed and Foo are the values of drag force on a particle in a fluidized bed and on a particle in an infinite medium, respectively. is the dimensionless distance (x/dp) between the particles. The following equations were derived for the elastic wave velocity ... 

While estimating dFIde, the value of the superficial velocity was assumed constant. Substitution of Eqs. (48) and (49) in (47) results in the following equation for the elastic wave velocity ... 

Measurements of elastic wave velocities in olivine and wadsleyite at high pressures and... 

Mumaghan FD (1937) Finite deformations of an elastic solid. Am J Math 49 235-260 Niesler H, Jackson I (1989) Pressure derivatives of elastic wave velocities from ultrasonic interferometric measurements on jacketed poly crystals. J Acoust Soc America 86 1573-1585 Nomura M, Nishizaka T, Hirata Y, Nakagiri N, Fujiwara H (1982) Measurement of the resistance of Manganin under liquid pressure to 100 kbar and its application to the measurement of the transition pressures of Bi and Sn. Jap J Appl Phys 21 936-939 Nye JF (1957) Physical Properties of Crystals. Oxford University Press, Oxford... 

Chen GL, Cooke JA, Gwanmesia GD, Liebermann RC (1999) Elastic wave velocities of Mg3Al2Si30j2-pyrope garnet to 10 GPa. Am Mineral 84 384-388... 

Li, B. and Zhang, J., 2005. Pressure and temperature dependence of elastic wave velocity of MgSi03 perovskite and the composition of the lower mantle. Phys. Earth Planet. Interior, 151, 143-54. 

Material Constants, Elastic wave velocities have been obtained for oil shale by ultrasonic methods for various modes of propagation. Elastic constants can be inferred from these data if the oil shale is assumed to be a transversely isotropic solid (9). This is a reasonable approximation considering the bedded nature of the rock. Many of the properties of oil shale depend on the grade (kerogen content), which in turn is correlated with the density ( 10). The high pressure behavior of oil shale under shock loading has been studied in gas-gun impact experiments (11). 

Gebrande H., 1982. Elastic wave velocities and constants of elasticity at normal conditions. In Hellwege K.H. (ed) Landolt-Bornstein. Numerical Data and Functional Relationships in Science and Technology. Group V Geophysics and Space Research 1, Physical Properties of Rocks, Subvolume b. Springer Verlag, Berlin, pp 8-35... 

Wyllie M.R., Gregory A.R., Gardner L.W., 1956. Elastic wave velocities in heterogeneous and porous media. 

In the formulas, e t), e(t), a t) is respectively strain rate, strain and stress. C is the elastic wave velocity in pressure bar, 5060 m/s. is the elastic modulus of bar material, 200 Gpa. A, L is respectively cross-sectional area and length of specimen. The impact velocity of experiment was controlled within 2-6 m/s. Because the impact velocity of bullet is provided by high pressure gas, the impact speed of coal and limestone samples will vary slightly. 

The transverse elastic wave velocity through a covalently bonded ceramic is higher than that through an ionically bonded ceramic. True or False ... 

Imai T, Yoshimura Y (1970) Elastic wave velocity and soil properties in soft soil. Tsuchito-Kiso 18(l) 17-22. As cited in Hasancebi N, Ulusay R (2007) Empirical correlation between shear wave velocity and penetration resistance for ground shaking assessment. Bull Eng Geol Environ 66 203-213... 

The elastic-wave velocity in a polycrystalline material is given by the following equations. For the longitudinal... 

Bryant, S. and S. Raikes, Prediction of elastic wave velocities in sandstones using structural models, Geophysics 60, 437-446 (1995). 

In siliciclastic rocks, many physical properties (elastic wave velocity, electrical resistivity, permeability) show a strong correlation to porosity. In carbonate rocks, correlations superimposed by the heterogeneous pore distribution, pore type, pore connectivity, and grain size (Westphal et al., 2005). Table 1.3 compares some prominent properties of the two main groups of reservoir rocks. 

Porosity is a fundamental volumetric rock property it describes the potential storage volume of fluids (water, gas, and oil) and influences most physical rock properties (for example elastic wave velocity, electrical resistivity,... 

On the other hand, if elastic wave velocities and bulk density are known from measurements, the elastic parameters can be calculated ... 

The various pore fluids (water, oil, gas, and mixtures of them) influence elastic wave velocities as a result of effects that are different for compressional and shear waves ... 

Fractures, cracks, and other defects of the solid mineralic substance change the elastic properties (and other physical properties like electrical, hydrauhc, thermal) dramatically. Elastic wave velocities decrease and a strong dependence on pressure results. As demonstrated by experiments and the foregoing sections, the porosity as the ratio of the volume of the defects (cracks, etc.) to the total volume alone cannot express these effects—microcracks with mily a small porosity can significantly reduce the velocity (see, for example. Fig. 6.8). Other parameters such as aspect ratio and crack density are necessary to describe the physical effects of these defects. 

Obviously, the elastic wave velocities are affected by these processes and stages. The designed plots can be used to interpret measured velocity data... 

Despite the fundamental difference in the mechanism, empirical correlations have been used successfully to predict static moduli from elastic wave velocities or dynamic moduli. These correlations are valid for the type of rock used to establish the correlation. Some further examples are presented in the following ... 

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