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f
are galvanic and induction parameters and
Z
N
,
Z
N
are normal
where
g
,
g
and
f
,
impedances in the left and right segments. By virtue of (7.21)
i
o
h
i
o
h
Z
N
=−
Z
N
=−
o
S
1
h
2
,
o
S
1
h
2
.
1
−
i
1
−
i
Z
N
and
Z
⊥
(
y
)
y
Z
N
.
Here
Z
⊥
(
y
)
y
→−∞
→
→
→∞
Solutions of these equations are
⎨
Z
N
Ae
g
y
/
f
+
y
≤
0
Z
⊥
(
y
)
=
(7
.
63)
⎩
Z
N
Be
−
g
y
/
f
+
y
≥
0
.
Note that behavior of
Z
⊥
within each segment is governed by local values of
galvanic and induction parameters,
g
and
f
.
The coefficients
A
and
B
are determined from the conditions that
S
1
Z
⊥
and
S
1
dZ
⊥
/
dy
are continuous at the boundary between the segments:
S
1
Z
⊥
y
=
0
=
S
1
Z
⊥
y
=
0
a
y
=
0
=
y
=
0
.
.
(7
64)
dZ
⊥
dy
dZ
⊥
dy
S
1
S
1
b
Condition (7.64
a
) provides the continuity of the horizontal component
j
y
of the
current density at the Earth's surface:
h
1
1
E
y
(
z
=
0)
h
1
H
x
S
1
Z
⊥
=−
=
j
y
(
z
=+
0)
,
H
x
while condition (7.64
b
) implies the continuity of the vertical component
j
z
of the
current density at the floor of the upper layer. By virtue of (7.17
c
)
S
1
dZ
⊥
1
H
x
dH
x
(
z
=
h
1
)
j
z
(
z
=
h
1
)
dy
=−
=−
.
dy
H
x
Substitution of (7.63) into (7.64) gives a system of linear equations for un-
knowns
A
and
B
:
S
1
Z
N
S
1
Z
N
S
1
A
S
1
B
−
=
−
g
f
g
f
(7
.
65)
S
1
S
1
A
+
B
=
0
,
