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and
P
Z
N
H
r
=−
π
i
o
r
3
P
r
Z
N
H
A
=−
(7
.
114)
2
π
i
o
r
3
3
P
Z
N
H
z
=
o
r
4
,
2
π
2
where
Z
N
is the normal Tikhonov-Cagniard impedance on the Earth's surface.
Now evaluate the ratio between vertical component of the anomalous magnetic
field and two-dimensional divergence of its horizontal components. By virtue of
(7.114)
H
z
di
H
z
−
o
=−
o
=
,
i
i
Z
N
r
rH
r
+
H
A
H
A
τ
1
r
v
whence
H
z
H
z
H
z
di
H
z
+
−
i
o
=−
i
o
=−
i
0
=
Z
N
,
(7
.
115)
di
v
H
τ
di
v
H
N
τ
+
di
v
H
A
τ
v
H
A
τ
where
H
z
H
N
λ
0
defines a zone, in which
we can estimate
Z
N
, using the magnetovariational ratio (1.3).
Next evaluate the ratio between orthogonal components of the anomalous electric
and magnetic fields. By virtue of (7.113) and (7.114)
=
0 and
di
v
τ
=
0
.
So, the condition
r
>>
Z
N
1
/λ
L
e
−
r
/λ
L
E
A
(
r
)
r
2
2
S
1
Z
N
h
eff
λ
π
2
r
(
r
)
=
+
H
r
L
Z
N
1
1
e
−
r
/λ
L
(7
.
116)
E
r
(
r
)
r
3
S
1
Z
N
h
eff
λ
π
2
r
1
(
r
)
=−
+
+
.
H
A
/λ
/λ
L
2
r
L
L
Assume that along with condition
r
>>
λ
o
the condition
r
>>
λ
L
is observed. Dis-
regarding the second term in the braces, we get
E
A
(
r
)
H
r
(
r
)
=−
E
r
(
r
)
H
A
(
r
)
=
Z
N
,
(7
.
117)
whence
