Electromagnetic Effects Resulted from Natural Disasters - Ultra and Extremely Low Frequency Electromagnetic Fields - page 374

of about 0.1-1 km at higher depth around the EQ focus. An enhancement of
the crack formation activity inside this zone may give rise to both acoustic and
electromagnetic noises, which can be detected on the ground surface. For example,
the intense acoustic emission in the frequency band of 0.03-1 kHz along with
noticeable ULF magnetic noise has been detected by Gorbatikov et al. ( 2002 )at
Matsushiro Observatory, Japan before and after seismic events occurred within
distance range of about 150 km.
As the cracked zone is situated at higher depth, the rock conductivity will result
in strong damping of the electromagnetic noise. Considering the ULF band, the
cracked zone is supposed to be located at the depth which is smaller than the
corresponding skin-depth, that is, no more than several kilometers from the ground
surface. The rock fracture inside the cracked zone brings about the crack growth
and formation of the fresh crack followed by radiation of acoustic waves. The
sequence of acoustic impulses due to the crack growth is supposed to be a stationary
random process which can be described by Poisson distribution given by Eq. ( 4.64 ).
Magnitude of acoustic impulses radiated by a single crack depends not only on
distance to the sensor but also on both the crack size and orientation of the crack
plane with respect to the sensor.
The electric currents in the conducting ground and GMPs resulted from the
acoustic emission of the crack ensemble form a random process as well. Thus, the
net GMP, ı B t . r ;t/, is the sum of random impulses. Additionally, we assume that
the distance from the cracked zone to the ground-recording station is much greater
than the typical cracked zone size. We obtain the following,
ı B t . r ;t/ D X
k

ı B k . r ;t t k ; n k ;l k /; (10.8)

where the subscript k is the impulse number occurred during the interval .0;t/,
and the unit vector n k normal to the crack plane defines a random orientation of
the crack. Likewise, the moment of radiation onset, t k , and the crack size l k are
random values. Suppose that all these random values, t k , n k and l k , are statistically
independent of each other and their probability distributions are independent of the
impulse number.
The mean value and other characteristics of Poisson random process are studied
in more detail in Appendix B. In particular, if all the cracks are identical in size
and orientation, the mean value of magnetic field is given by an equation similar to
Eq. ( 4.71 ), that is

Z

h ı B t . r ;t/ iD N ı B 1 . r ;t 0 /dt 0 ;

(10.9)

1

where N is the number of cracks generated in unit time and ı B 1 denotes the
magnetic field excited by a single crack. Notice that h ı B t . r ;t/ i is not a function
of time since the Poisson process is a stationary random process.