71
from the plane wave source. This implies that
E
0
represents the amplitude of a reflected
wave, and in a uniform earth where there are no reflectors, its amplitude must also be zero. So
or
.
The term with the imaginary exponent represents the wave component of the electric field and
the term with the real exponent defines the decay of the wave’s amplitude with depth. It is
convenient to specify distance in terms of the wavelength and, where EM waves penetrate
conductors, it is customary to use one radian as the standard distance. This distance is called a
skin depth. One wavelength is 2
radians so one skin depth is a bit less than one sixth of a
wavelength. Wavelength is given by
2
so one skin depth is given by
1
where the wave number
is
2
so
2
1
4
10
503
2
7
f
f
(meters)
At the earth's surface (z = 0) and from equation 6, Ex(0) =
. At the skin depth
, the
amplitude of the down-going wave has deceased to
E
E e
x
( )
0
1
which is 1/e or about 37 percent of its surface value. If a reflective layer existed at a depth
,
then the reflected, up-going wave would also be attenuated by 37 percent resulting in a total
attenuation of about 86 percent relative to the surface value of the down going wave.
E
E e
E e
E e
x
ikz
iz
i
z
i
0
0
0
1
2
(
)
E
E e
e
x
z
iz
0
2
2
E
0
