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where
E
x
(
y
) is obtained from Helmholtz equations (10.11) with conditions at
infinity (10.12) and boundary conditions (10.13). According to (10.12) and (10.15),
,
z
,
W
zy
(
y
,
z
,
)
→
0
,
(10
.
16)
|
y
|→∞
i.e., the tipper vanishes as the distance from the anomalous zone tends to infinity.
3. MT inversion (TM-mode): the conductivity
(
y
,
z
) is found from the trans-
verse impedance
Z
⊥
. To determine the operator
Z
⊥
{
y
,
z
=
0
,
,
(
y
,
z
)
}
, we write
the transverse impedance as
z
=
0
H
x
(
y
,
z
,
)
,
=
,
z
E
y
(
y
z
0
)
1
Z
⊥
(
y
,
=
,
=−
)
=−
)
,
.
z
0
)
(10
17)
H
x
(
y
,
z
=
0
,
(
y
,
z
)
H
x
(
y
,
z
=
0
,
where
H
x
(
y
,
z
,
) is obtained from the equations
2
H
x
(
y
,
z
,
)
y
2
z
N
(
z
)
1
N
(
z
)
H
x
(
y
,
z
,
)
1
+
+
i
o
H
x
(
y
,
z
,
)
=
0
|
y
|
>
l
z
y
(
y
,
z
)
H
x
(
y
,
z
,
)
1
z
(
y
,
z
)
H
x
(
y
,
z
,
)
1
+
+
i
o
H
x
(
y
,
z
,
)
=
0
|
y
|≤
l
y
z
(10
.
18)
with the conditions at infinity
H
x
(
z
,
,
→
,
,
,
,
→
.
H
x
(
y
z
)
)
H
x
(
y
z
)
0
(10
19)
z
→∞
|
y
|→∞
and the boundary conditions
1
z
)
H
x
(
y
,
z
,
)
H
x
[
H
x
(
y
,
z
,
)]
S
=
0
,
S
=
0
H
x
(
y
,
z
=
0
,
)
=
(
)
,
(
y
n
(10
.
20)
where
H
x
(
z
) is the normal magnetic field.
According to (10.17) and (10.19), we have
,
E
y
(
z
,
)
Z
⊥
(
y
,
z
,
)
→
Z
N
(
z
,
)
=−
)
,
(10
.
21)
H
x
(
z
,
|
y
|→∞
,
) and
E
y
(
z
,
where
Z
N
(
z
) are the normal (one-dimensional) impedance and the
normal electric field.
