Constant Q and a fractal, stratifed Earth

Abstract

Frequency dependent measurements of the quality factor Q typically show a constant behaviour for low frequencies and a positive power law dependence for higher frequencies. In particular, the constant Q pattern is usually explained using intrinsic attenuation models due to anelasticity with either a single or multiple superposed relaxation mechanisms - each with a particular resonance peak. However, in this study, I show using wave localisation theory that a constant Q may also be due to apparent attenuation due to scattering losses. Namely, this phenomenon occurs if the Earth displays fractal characteristics. Moreover, if fractal characteristics exist over a limited range of scales only, even an absorption band can be created - in accordance with observations. This indicates that it may be very difficult to distinguish between intrinsic and scattering attenuation on the basis of frequency dependent measurements of the quality factor only.