Thermoelastic attenuation of elastic waves by cracks

Zener's theory of thermoelastic attenuation by inhomogeneities has been applied to a medium containing cracks. The cracks have been approximated by elliptic cylinders, and energy losses per wave cycle have been calculated for both two-dimensional hydrostatic pressure and shear. Absorption spectrums vary less than an order of magnitude over a frequency range greater than 104 hz. The values of Q for both longitudinal waves (Qα) and transverse waves (Qβ) for a distribution of such cracks have been derived in terms of parameters measured in static testing. For granite the theoretical values (Qα = 200, Qβ = 350) are about twice the experimental values; however, the difference is not significant in view of the rather large uncertainties in some of the parameters. The theory also predicts that Qα/Qβ should be near ½ for most rocks; laboratory observations yield about the same value. Finally, the theory predicts a temperature dependence for Q which has not been observed.