Information Technology Reference
In-Depth Information
E
τ
1
e
−
i
E
a
E
1
+
a
E
1
1
a
E
+
ib
E
1
1
b
E
E
1
1
a
E
E
1
1
b
E
a
E
1
+
e
1
=
=
=
cos
+
i
sin
b
E
1
b
E
1
H
τ
1
e
−
i
H
a
H
1
+
a
H
1
1
a
H
+
ib
H
1
1
b
H
a
H
1
+
H
1
1
a
H
+
H
1
1
b
H
h
1
=
=
=
cos
i
sin
b
H
1
b
H
1
.
(2
64)
E
τ
2
e
−
i
E
a
E
2
+
a
E
2
1
a
E
+
ib
E
2
1
b
E
a
E
2
+
E
2
1
a
E
E
2
1
b
E
e
2
=
=
=
cos
+
i
sin
b
E
2
b
E
1
H
τ
2
e
−
i
H
a
H
2
+
a
H
2
1
a
H
+
ib
H
2
1
b
H
a
H
2
+
H
2
1
a
H
+
H
2
1
b
H
,
h
2
=
=
=
cos
i
sin
b
H
2
b
H
2
where
1
a
E
,
1
a
H
,
1
a
E
,
1
a
H
and
1
b
E
,
1
b
H
,
1
b
E
,
1
b
H
are unit vectors oriented along major
and minor semi-axes.
The components of normalized eigenfields
e
1
,
h
1
are
e
1
x
=
cos
E
1
cos
E
1
−
i
sin
E
1
sin
E
1
e
1
y
=
cos
E
1
sin
E
1
+
i
sin
E
1
cos
E
1
(2
.
65)
h
1
x
=
cos
H
1
cos
H
1
−
i
sin
H
1
sin
H
1
h
1
y
=
cos
H
1
sin
H
1
+
i
sin
H
1
cos
H
1
.
Taking into account (2.62) and (2.63), the components of normalized eigenfields
e
2
,
h
2
can be written as
e
2
x
=−
cos
E
1
sin
+
i
sin
E
1
cos
E
1
E
1
e
2
y
=
cos
E
1
cos
+
i
sin
E
1
sin
E
1
E
1
(2
.
66)
h
2
x
=−
+
cos
H
1
sin
i
sin
H
1
cos
H
1
H
1
h
2
y
=
cos
H
1
cos
+
i
sin
H
1
sin
.
H
1
H
1
-ambiguity
in phases of principal values of the impedance tensor. To remove this ambiguity,
we assume that the Earth is everywhere passive and the real part of the complex
Pointing vector calculated from
E
τ
1
and
H
τ
1
as well as from
e
1
and
h
1
cannot be
directed upwards:
Equations (2.65) and (2.66) have
-ambiguity in
H
1
, which leads to
h
1
)
z
≥
Re (
e
1
×
.
.
0
(2
67)
