Q-factor, damping and the width of spectral lines

The quality of a resonance is expressed by the Q-factor (quality factor), defined as the ratio of the resonance frequency to the width of the spectral line:

Q = \frac{f}{\Delta f},

where \Delta f is the width of the line (typically at half the maximum power). A high Q means a sharp, weakly damped resonance; a low Q a broad, strongly damped line.

The Schumann resonance has a low Q-factor: for the first mode on the order of Q \approx 4-6, with a slightly increasing tendency for higher modes Surkov 2014. This is a direct consequence of the strong damping in the ionosphere — energy escaping into the lossy upper boundary dissipates rapidly, so the resonance lines are broad and slightly overlap one another. The low Q is therefore another face of the same phenomenon that shifts the frequencies (see #18): the finite conductivity of the ionosphere.

The Q-factor is also a practical parameter in data processing — it determines how sharply a mode can be separated from the background and how accurately its frequency and amplitude can be estimated in the spectral fit (see #25).