Dispersion effect of velocities on the evaluation of material elasticity

Journal of Mining Science (Impact Factor: 0.22). 07/2009; 45(4):347-354. DOI: 10.1007/s10913-009-0043-4

ABSTRACT The author employs the Kjartansson absorption model to prove that intrinsic dispersion of seismic wave velocities in absorbing
media is a basic factor responsible for the differences between elastic rock parameters measured dynamically and statically.
Dispersion of Young’s modulus predicted by this model for a frequency range from millihertz to tens of kilohertz matches well
the experimental data obtained for polyvinyl chloride plastic used as a test material in the study case.

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    ABSTRACT: LINEAR theories of attenuation of acoustic or seismic waves in media, such as rocks, which are characterised by constant or nearly constant Q factors (fractional energy loss per cycle equals 2π/Q) imply velocity dispersion and, therefore, frequency dependence of elasticity. The effect is small, corresponding to a change of order 1 % over the period range of seismological interest (1 s to 1 h), and is consequently difficult to observe. However, it leads to an internal inconsistency in the development of earth models by inversion of free oscillation data and to discrepancies between these models and body wave data1–3. It is a matter of considerable geophysical interest to resolve the problem. Validity of the linearity assumption has been questioned4 but we are now observing elliptical hysteresis loops in basalt and granite samples subjected to sinusoidal strains of order 10−6 and this is strong evidence that attenuation does become a linear phenomenon at low strain amplitudes. But whether or not perfect linearity applies, a direct demonstration of body wave dispersion is the most satisfying indication that earth model studies need revision.
    07/1977; 268(5617):220-222.
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    ABSTRACT: Thesis--Stanford University. Includes bibliographical references.
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    ABSTRACT: The elastic properties of several rocks, fused quartz, aluminum, and steel were calculated as a function of pressure to 10 kb from measured velocities of P and $ waves in three directions. Compressibility calculated from Vp and V, is within a few per cent (and therefore within the experimental error) of that measured directly by the use of strain gages, for pressures which range from 3 to 9 kb. Comparison is also good for fused quartz, steel, and aluminum, as well as for fine-grained limestone at atmospheric pressure. At atmospheric pres- sure a discrepancy of several hundred per cent between static and dynamic values is probably due to the different effects of cracks in the rocks on the two measurements. The good agree- ment of the two sets of compressibilities at pressures greater than 2 kb implies that other elastic properties calculated from velocities will be in good agreement with static values.
    Journal of Geophysical Research Atmospheres 11/1965; 70(22):5649-5656. · 3.44 Impact Factor