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to
. These induction effects appear at high frequencies and they attenuate with
lowering frequency.
The most simple situation we have in the two-dimensional model. Let the
x
-axis
run along the strike. Considering the TE-mode with components
E
x
,
H
y
,
H
z
and
the TM-mode with components
E
y
,
E
z
,
H
x
, we separate the galvanic and induction
anomalies.
The TE-mode is excited by the excess electric current of density
j
(
j
x
,
0
,
0) with
a single component
j
x
(
y
,
z
)
=
E
x
(
y
,
z
)
.
Here
=
j
x
=
j
x
1
y
−
j
x
di
v
j
x
=
0
,
curl
j
1
z
=
0
.
z
y
We see that the field
j
is solenoidal,
j
p
=
=
j
s
. The TE-mode is distorted
solely by the induction effects (currents flow along the strike and do not charge
the medium). Let us find the equivalent magnetic current,
j
s
0 and
j
, responsible for the
induction distortions. By virtue of (1.116) and (1.121)
M
∈
V
.
j
s
x
=
0
o
z
V
j
s
y
=
i
G
(
M
,
M
v
)
j
x
(
M
v
)
dV
(1
.
122)
o
y
V
j
s
z
=−
i
G
(
M
,
M
v
)
j
x
(
M
v
)
dV
The TM-mode is excited by the excess electric current of density
j
(0
,
j
y
,
j
z
)
where
j
y
(
y
,
z
)
=
E
y
(
y
,
z
) and
j
z
(
y
,
z
)
=
E
z
(
y
,
z
). Here
1
x
=
=
j
y
y
+
j
z
j
z
y
−
j
y
di
v
j
z
=
0
,
curl
j
=
0
.
(1
.
123)
z
In this case the electric excess current consists of potential and solenoidal parts.
Let us define the potential part,
j
p
, which causes the galvanic distortions. Accord-
ing to (1.115),
M
∈
V
.
j
p
x
(
M
)
=
0
M
v
)
dV
y
V
=−
j
y
(
M
v
)
+
j
z
(
M
v
)
j
p
y
(
M
)
G
(
M
,
y
z
(1
.
124)
M
v
)
dV
z
V
=−
j
y
(
M
v
)
+
j
z
(
M
v
)
j
p
z
(
M
)
G
(
M
,
y
z
Next we define the equivalent excess magnetic current,
j
s
, which may cause the
induction distortions. According to (1.116) and (1.121),
