Atmospheric Electricity - Ultra and Extremely Low Frequency Electromagnetic Fields - page 94

Fig. 3.27 Dynamic spectrogram ( upper panel ) and power spectral density of absolute value of the
magnetic field variations shown in Fig. 3.26 . Adapted from Surkov et al. ( 2010 )

spectrogram which corresponds to the magnetic variations shown in Fig. 3.26 .Every
so often the same tendency for oscillating spectra has been observed during the
2006/2007 winter campaign. A distinct resonance structure below 7 Hz is assumed
to be due to excitation of the so-called ionospheric Alfvén resonator (IAR) which
will be described in more detail in the text section. What is more important, the
power spectrum in Fig. 3.27 (lower panel) shows evidence of some vibrations with
maximum repetition period of about 15-20 Hz. These oscillations are much more
pronounced with the smooth envelope of the power spectrum shown in Fig. 3.27
with green line. To explain this peculiarity, one should note that the spectrum of net
magnetic field variations resulted from the causative lightning and the delayed sprite
is given by

B .!/ D B c . r c ;!/ C B s . r s ;!/ exp .i!T/; (3.27)

where T is the lag of time between the causative lightning and sprite occurrences,
and r c and r s are their position vectors, respectively. Since the power spectrum
is proportional to j B .!/ j

2 , it is evident that the amplitude modulation of the
power spectrum shown in Fig. 3.27 with green line can be due to the oscillatory
factor exp .i!T/ in Eq. ( 3.27 ). This implies that the sprite lag time is inversely
proportional to the “period” ! D 2=T of spectrum oscillations. In the next section