ABSTRACT
Q “Quality”; a measure of attenuation in an oscillating system. It is conventionally defined in terms of the energy in the oscillation:
Q = 2π E E
where E is the energy stored in the oscillation, and E is the energy dissipated over the period of one cycle. If there is no other process at work, then Q can be expressed in terms of the real and imaginary parts of the complex frequency:
Q = ωr 2ωi
where the amplitude of the oscillation is governed by
A = A0eiωt = A0ei(ωr+iωi )t = A0eiωr t e−ωi t . Q may also be written in terms of (or measured from) the width of the peak associated with the oscillation in a power spectrum (that might be obtained from data through a fourier transform):
Q = ω ω
ω in this case is real and is the frequency of the center of the peak, while ω is the width between the half power points on each side of the peak. Q may be a function of frequency. There are many different geophysical oscillations for whichQmay be defined, such as the free seismic oscillations of the Earth, torsional oscillations of the core, and gravity waves in the atmosphere.
