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These boundary conditions differ from those given by Sheinman (1947) and Price
(1949) in the terms proportional to
h
. They account for the finite thickness of the
layer.
Using (7.16), we solve the problem for TM- and TE-modes. It will be remem-
bered that the
TM-mode
is associated with
H-polarized wave
(the field
H
is polarized
in the strike direction). This mode gives the transverse MT-curves (telluric current
flows across the structures). The
TE-mode
is associated with
E-polarized wave
(the
field
E
is polarized in the strike direction). This mode gives the longitudinal MT-
curves (telluric current flows along the structures). The main difference between
these modes is that in a two-dimensional medium the TM-mode charges the struc-
tures, and its anomalies are of the galvanic nature, while the TE-mode does not
charges the structures, and its anomalies are of the induction nature.
In the model under consideration the TM-mode is represented by the components
E
y
(
y
,
z
)
,
E
z
(
y
,
z
)
,
H
x
(
y
,
z
). On the Earth's surface
E
z
(
y
,
+
0)
=
0 and
H
x
(
y
,
0)
=
H
x
=
const
.
On the surface of the perfectly conductive basement
E
y
(
y
,
h
)
=
0
.
By virtue of (7.16)
o
h
1
H
x
,
=
,
+
E
y
(
y
0)
E
y
(
y
h
1
)
i
a
R
2
d
2
H
x
(
y
,
h
1
)
E
y
(
y
,
h
1
)
=
i
o
h
2
H
x
(
y
,
h
1
)
+
b
(7
.
17)
dy
2
H
x
H
x
(
y
,
h
1
)
=
+
S
1
(
y
)
E
y
(
y
,
0)
.
c
Eliminating
E
y
(
y
h
1
) from these relations, we get the equation for
the transverse impedance at the Earth's surface,
z
=0:
,
h
1
) and
H
x
(
y
,
d
2
dy
2
S
1
(
y
)
Z
⊥
(
y
)
o
S
1
(
y
)
h
2
]
Z
⊥
(
y
)
R
2
−
[1
−
i
=
i
o
h
,
(7
.
18)
where
Z
⊥
(
y
)
=−
,
/
H
x
=
h
1
+
h
2
.
E
y
(
y
0)
and
h
This differential equation can be
easily reduced to the integral equation
v
S
1
S
1
(
y
)
Z
N
+
1
S
1
(
y
)
Z
⊥
(
y
)
y
)
Z
⊥
(
y
)[
S
1
(
y
)
S
1
]
dy
,
=
G
(
y
−
−
(7
.
19)
−
v
where
Z
N
is the normal impedance defined in the approximation (1.44) as
i
o
h
Z
N
=−
1
−
i
o
S
1
h
2
y
) is the Green function of the equation (7.18):
and
G
(
y
−
fg
2
|
|
/
f
y
−
y
y
)
e
−
g
G
(
y
−
=
(7
.
20)
