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Attenuation of dispersed waves

Knopoff, L. and Aki, K. and Archambeau, C. B. and Ben-Menahem, A. and Hudson, J. A. (1964) Attenuation of dispersed waves. Journal of Geophysical Research, 69 (8). pp. 1655-1657. ISSN 0148-0227. doi:10.1029/JZ069i008p01655.

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A measure of the absorption of elastic waves is the specific absorption coefficient 1/Q. In dispersive mediums, whether the dispersion is due to geometry, inhomogeneity, or both, measurements are often made outside the body and the measurements must be interpreted as to the distribution of values of 1/Q within the body. Two definitive experiments of this type are those performed using standing waves set up in a confined sample of the body and with waves that propagate through or on the surface of the body. Typical examples of these experiments involve the measurement of the damping coefficient of the free modes of vibration of the earth and the measurement of the attenuation factor of propagating surface waves on the earth. These two types of experiments can themselves be interpreted in terms of dimensionless attenuation factors. We call the dimensionless attenuation factors in the standing wave and propagating wave experiments 1/Q_T and 1/Q_x, defined as the logarithmic decrements π/QT and π/Q_x in each experiment. Then in a damped standing wave the amplitude will diminish with time t at a fixed point as exp (−πt/TQ_T), where T is the period. In a propagating monochromatic wave the amplitude will diminish with distance x as exp (−πx/cTQ_x), where c is the phase velocity.

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Additional Information:Copyright 1964 by the American Geophysical Union. (Received November 2, 1963.) Contribution 1217, Division of Geological Sciences, California Institute of Technology, Pasadena.
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Caltech Division of Geological Sciences1217
Issue or Number:8
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Official Citation:Knopoff, L., K. Aki, C. B. Archambeau, A. Ben-Menahem, and J. A. Hudson (1964), Attenuation of dispersed waves, J. Geophys. Res., 69(8), 1655–1657, doi:10.1029/JZ069i008p01655.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51501
Deposited By: George Porter
Deposited On:10 Nov 2014 19:05
Last Modified:10 Nov 2021 19:11

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