EVIDENCE FOR A LINEAR ATTENUATION MECHANISM

Abstract

Comparison of the attenuation of the Fourier components of an elastic pulse with the attenuation of sinusoidal waves of the same frequencies constitutes a test whether the attenuation mechanism is linear. As an example of this linearity test, attenuation by the nonlinear, variable‐friction mechanism proposed by Knopoff and MacDonald has been examined. The Q spectrums obtained from the Fourier components of several pulses calculated from the equations governing that attenuation mechanism differ radically from the flat spectrum expected for sinusoidal waves. Thus the mechanism could readily be identified as nonlinear by the linearity test. The test was applied to experimental observations of attenuation in metals, and it is found that the attenuation mechanism is linear. The same result is suggested by existing observations of the attenuation in Pierre shale and Westerly granite, as well as other independent evidence. Thus mechanisms involving nonlinear processes, including all those mechanisms which depend on ordinary friction, are not likely to be important sources of loss.