Attenuation des ondes sismiques dans les solides
Journal name: Geophysical Prospecting
Issue: Vol 9, No 3, September 1961 pp. 370 - 381
Info: Article, PDF ( 575.71Kb )
For the propagation of acoustic waves in formations, laboratory experiments yield an expression of the form:
A is the amplitude (strain or stress)
A0 some constant coefficient
x the coordinate according to which propagation takes place
α the attenuation coefficient
ω the angular frequency of sinusoidal oscillation.
No analogy between this law and that of electromagnetic waves can be made, since:
The present paper shows how results are compatible if losses of energy are accounted for by a hysteresis phenomenon that is analyzed (see Figure). Stress T is in abscissae, and strain δu/δx, multiplied by a coefficient E′ characteristic of the elastic properties of the solid, is in ordinates. The horizontal part of the curve is θ. It is supposed that the absorption properties of the ground are given by some dimensionless coefficient
Then one gets
If λ≪ 1, we get the propagation law
An attenuation takes place without phase shift, and consequently without dispersion.
The author reverts to the inapplicability of the superposition principle, and foresees theoretically, for instance, that a strain T′ cos ω′t, where T′ > T and ω′ > ω, can completely cancel coefficient α.