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An observational hint towards the lightning effect on the ionosphere was provided
by Burke et al. ( 1992 ) using DE-2 satellite measurements over the hurricane Debbie.
The burst of electric field with amplitude about 40 mV/m and the bursts of electron
flux intensity with energies 854 eV and 35 keV have been detected by DE-2 space-
borne sensors. At the same time, the variation of quasi-static electric field is not
found to exceed 0.5 mV/m while the electron number density varies within 10 %.
One may speculate that an Alfvén pulse generated by the mesospheric discharge
can be a cause of the observed effects. Additionally, the bursts of 35 keV electron
flux intensity following 1-2 s agreed satisfactorily with the Trimpi-effect, caused
by the interaction of electrons trapped in the overlying radiation belt with whistlers
radiated by the lightning that in turn result in the scattering and precipitation of
electrons (e.g., Rodger 1999 ).
Final remarks we wish to emphasize are as follows. All the ULF/ELF electro-
magnetic effects treated here seem to be weak at the background level of natural and
man-made electromagnetic noises. A majority of the theories predict that the EQs,
volcano eruption, tsunami, and other disasters can provide a small but detectable
value of the electromagnetic effects only at short distance from the sources. One
of the challenges of experimental study is how to increase the signal-to-noise ratio
in order to distinguish the effect of our interest from other noises and how to find
the location of the ULF/ELF source. At the moment we have a few competitive
theories, which can explain, in principle, the ULF phenomena associated with
natural catastrophes. The problem is that the most theories describing the tectonic
and electromagnetic processes at higher depth are based on such parameters, whose
real values cannot be extracted with confidence from the ground-based data. Further
experiments are required to sort out this interesting problem in seismically active
regions in order to elaborate the theoretical conceptions studied in this section.
Despite the recent studies have shown that at the moment the short-term prediction
of impending EQs is impossible, we must extend our knowledge on electromagnetic
phenomena associated with natural disasters. The understanding of the origin of the
ULF signals can be extremely useful for the interpretation of experimental data
possibly related to impending EQs.
Appendix H: Averaging over the Crack Orientation
In order to study the displacements due to the formation and evolution of the crack
ensemble we first consider the dynamic displacement field due to single crack
growth (Surkov and Hayakawa 2006 ). Acoustic waves generated by the growing
cracks in a uniform elastic medium are defined by the wave equation (Aki and
Richards 2002 )
@ t u D . C 2/ r . r u / r . r u /:
(10.57)
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