Attenuation of elastic waves

The attenuation of elastic waves is quantitatively represented by Q value. When the wave with energy level E is attenuated by AE over one-wavelength propagation, Q is defined as. 

Table 11.1 shows a comparison of some parameters of small and large seismic events. The size of the source determines the duration of the primary pulse (the slip velocity is independent of the source size) and thus the upper limit of frequency spectra which corresponds to the reciprocal of pulse duration. On the other side with increasing frequency, i.e. with smaller source dimensions, the mean attenuation of elastic waves increases and, therefore, the distance between sensors has to be reduced to smaller values. 

Measurements of the velocity and attenuation of elastic waves at ultrasonic frequencies are important, especially for oriented polymers and composites. Compact solid specimens with dimensions of the order of 10 mm are required. 

Attenuation of Elastic Wave Energy in Rocks—Overview... 

Attenuation of elastic wave energy in rocks is a complex process of different mechanisms. The mechanisms are frequently connected with processes that occur at defects of the solid rock components (grain-grain contacts, fractures, etc.), at inhomogeneities (pores, fractures), scattering, and with fluid motion in pores and fractures. 

Hudson, J.A., 1981. Wave speeds and attenuation of elastic waves in material containing cracks. Geophys. J. R. Astron. Soc. 64, 133-150. 

Knopoff, L., 1965. Attenuation of elastic waves in the earth. In Mason, W.S. (Ed.), Physical AcousticsIIIB, Academic Press, New York, pp. 287-324. 

Rao, A.A., 1967. Some studies on attenuation of elastic waves in rocks. Bull. NGRJ, New Delhi 5 (4), 183-194. 

W. Herrmann, D.L. Hicks, and E.G. Young, Attenuation of Elastic-Plastic Stress Waves, in Shock Waves and the Mechanical Properties of Solids (edited by J.J. Burke and V. Weiss), Syracuse University Press, Syracuse, 1971, pp. 23-63. 

Y.M. Gupta, Stress Dependence of Elastic-Wave Attenuation in LiF, J. Appl. Phys. 46, 3395-3401 (1975). 

Anyone who has successfully used a microscope to image properties to which it is sensitive will sooner or later find himself wanting to be able to measure those properties with the spatial resolution which that microscope affords. Since an acoustic microscope images the elastic properties of a specimen, it must be possible to use it to measure elastic properties both as a measurement technique in its own right and also in order to interpret quantitatively the contrast in images. It emerged from contrast theory that the form of V(z) could be calculated from the reflectance function of a specimen, and also that the periodicity and decay of oscillations in V(z) can be directly related to the velocity and attenuation of Rayleigh waves. Both of these observations can be inverted in order to deduce elastic properties from measured V(z). 

Applications of ultrasonic techniques to solid-gas systems rely on the fact that velocity and attenuation of US-waves in porous materials is closely related to pore size, porosity, tortuosity, permeability and flux resistivity. Thus, the flux resistivity of acoustic absorbents oan be related to US attenuation [118,119], while the velocity of slow longitudinal US is related to pore tortuosity and diffusion, and transport properties, of other porous materials [120]. Ultrasound attenuation is very sensitive to the presence of an external agent suoh as moisture in the pore space [121] and has been used to monitor wetting and drying prooesses [122] on the other hand, US velocity has been used to measure the elastic coefficients of different types of paper and correlate them with properties such as tensile breaking strength, compressive strength, etc. [123]. 

Because the energy state of a Jahn-Teller complex depends on the local lattice distortions, the macroscopic long-distant strain that produces an ultrasonic wave should influence it as well. The cross effect is initiated by the Jahn-Teller complexes (1) the dispersion (i.e., frequency-dependent variation of phase velocity) and (2) attenuation of the wave. In terms of the elastic moduli it sounds as appearance (or account) of the Jahn-Teller contribution to the real and imaginary parts of the elastic moduli. For a small-amplitude wave it is a summand Ac. Obviously, interaction between the Jahn-Teller system and the ultrasonic wave takes place only if the wave, while its propagation in a crystal, produces the lattice distortions corresponding to one of the vibronic modes. 

In the self-consistent approach of McRae (54, 55, 58, 59,177) and others (43, 68) the complete multiple diffraction problem, with attenuation of the wave by elastic backscattering alone, has been solved in self-consistent fashion for certain idealized cases. Inelastic losses were not included in the theory at all. However, in the recent work of Duke and Tucker (179) and of Jones and Strozier (66) inelastic absorption is treated as the dominant effect, and this is nearer reality when considering the LEED problem at all but the lowest energies. 

The fourth and last solution is a pressure-porosity wave in which fluid flow at the incompressible limit of fluid motions is coupled to elastic deformations of the matrix. The attenuation of this wave is highly frequency dependent, but it is quite conservative at low frequencies. Unlike the previous three solutions which each exist as an independent process, this solution is always coupled to porosity diffusion. It can leave behind an increase in pressure as it propagates, converting some of the inertial energy associated with the... 

Hamilton, E.L. 1971. Elastic properties of marine sediments. Journal of Geophysical Research, 76 579-604. Hamilton, E.L. 1972. Compressional waves attenuation in marine sediments. Geophysics, 37 620-646. Hamilton, E.L. 1974. Prediction of deep-sea sediment properties State of the art. In Deep-Sea Sediments Physical and Mechanical Properties, Inderbitzen, A.L., ed.. Plenum Press, New York, pp. 1-43. Hamilton, E.L. 1976. Attenuation of shear waves in marine sediments. Journal of the Acoustical Society of America, 60 334-338. 

The propagation of elastic waves in a civil engineering structure depends on its geometry and shape as well as on the occurring construction elements. Each material has different properties of wave propagation (velocity, attenuation). Elements like reinforcement bars or prestressing tendons may lead to anisotropy and guided waves. 

The study of elastic wave attenuation particularly in sedimentary rocks carries information about rock properties and is important for the design of seismic investigations. The mechanisms and relationships to extract information from attenuation parameters are not yet fuUy understood and still a problem. 

Introduction of the surface-nucleation mechanism in numerical computation of elastic-plastic wave evolution leads to enhanced precursor attenuation in thin specimens, but not in thicker ones. Inclusion of dislocation nucleation at subgrain boundaries indicates that a relatively low concentration of subgrain boundaries ( 2/mm) and nucleation density (10"-10 m ) is sufficient to obtain predicted precursor decay rates which are comparable to those obtained from the experiments. These experiments are only slightly above the threshold necessary to produce enhanced elastic-precursor decay. 

Figure 8.9. The effect of attenuation of the pullback wave signal in an elastic-plastic material. Amplitude of the pullback signal at the recording interface will be diminished due to wave attenuation and will not provide an accurate measure of the material spall strength.

By measuring V z), which includes examining the reflectance function of solid material, measuring the phase velocity and attenuation of leaky surface acoustic waves at the liquid-specimen boundary, the SAM can be used indetermining the elastic constants of the material. 

Dransfeld, K. and Salzmann, E. (1970). Excitation, detection and attenuation of high-frequency elastic surface waves. In Physical acoustics VII (ed. W. P. Mason and R. N. Thurston), pp. 260-83. Academic Press, New York. [117]... 

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