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Computed Waves in a Nonlinear Solid

J. E. White
J. E. White
Marathon Oil Company Denver Research Center
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January 01, 2000


Analyses of seismic waves traveling in the earth and measurements on vibrating rock samples have established that earth materials lose energy in a characteristic fashion. Some of the experimental data are : When a sinusoidal stress cycle is applied to a small rock sample, the fractional energy lost per cycle is independent of the frequency; when a slender rod is driven near a resonant frequency, the factor Q (designating sharpness of resonance) is independent of frequency; for traveling waves, each frequency component suffers an exponential decrease with distance of travel, the exponent itself being proportional to frequency; and the same loss behavior is noted over a tremendous range of vibration amplitude. There is no reason to suppose that a single loss mechanism is dominant in all earth materials, and in fact experiments on some samples do not fit the above pattern. However, hundreds of observations on a wide range of rock types, covering a frequency range of nine decades, have led more than one author to conclude that seismic waves are subject to attenuation which varies as the first power of frequency, and therefore that a loss mechanism must be operative which yields this kind of exponential attenuation coefficient.

It has been suggested on a purely theoretical basis that the loss mechanism must be nonlinear. The intrinsically nonlinear phenomenon of sliding between solid surfaces in contact (Coulomb friction) is almost certainly involved in the distortion of granular materials. In any case, attention has been directed toward possible nonlinear stress-strain relations

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Society of Exploration Geophysicists Geophysics Reprint Series

Seismic Wave Propagation: Collected Works of J. E. White

J. E. White
J. E. White
Professor Emeritus, Colorado School of Mines
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Society of Exploration Geophysicists
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Publication date:
January 01, 2000




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