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On substituting (5.50) into (5.60), we write
∞
∞
y
)
H
o
y
(
x
o
,
y
)
H
o
x
(
x
o
,
Y
xx
(
x
,
y
o
)
−
Y
xy
(
x
,
y
o
)
i
o
2
H
o
x
(
x
,
y
)
+
(
x
dx
o
dy
o
=
F
x
(
x
,
y
)
π
−
x
o
)
2
+
(
y
−
y
o
)
2
−∞
−∞
∞
∞
y
)
H
o
y
(
x
o
y
)
H
o
x
(
x
o
Y
yx
(
x
,
,
y
o
)
−
Y
yy
(
x
,
,
y
o
)
i
o
H
o
y
(
x
,
y
)
+
(
x
dx
o
dy
o
=
F
y
(
x
,
y
)
,
2
π
−
x
o
)
2
+
(
y
−
y
o
)
2
−∞
−∞
(5
.
61)
where
H
o
x
+
y
)
E
o
x
+
y
)
E
o
y
F
x
(
x
,
y
)
=−
Y
xx
(
x
,
Y
xy
(
x
,
=
Y
xx
(
x
,
y
)
Z
N
H
o
y
−{
Y
xy
(
x
,
y
)
Z
N
+
1
}
H
o
x
,
H
o
y
+
y
)
E
o
x
+
y
)
E
o
y
F
y
(
x
,
y
)
=−
Y
yx
(
x
,
Y
yy
(
x
,
H
o
y
−
y
)
Z
N
H
o
x
={
Y
yx
(
x
,
y
)
Z
N
−
1
}
Y
yy
(
x
,
and
E
o
y
H
o
x
.
E
o
x
Z
N
=
H
o
y
=−
The integral equations (5.61) let us determine the horizontal components,
H
o
x
and
H
o
y
, of the anomalous magnetic field
H
o
at the Earth's surface from the mea-
sured admittance tensor [
Y
] and given normal impedance
Z
N
and normal magnetic
field
H
o
. It is advantageous to take
H
o
as a field linearly polarized in the direc-
tion, which ensures a maximum sensitivity of
H
o
to target structures. In regions
with elongated structures we merely direct the normal magnetic field against the
prevailing strike. Let the target structures be elongated along the
x
axis. Then, the
normal magnetic field reflecting the distribution of the longitudinal excess currents
is chosen as
H
o
−
H
o
y
1
y
. In that event
=
F
x
=
Y
xx
(
x
,
y
)
Z
N
H
o
y
,
(5
.
62)
H
o
y
,
F
y
={
Y
yx
(
x
,
y
)
Z
N
−
1
}
1as
x
2
where
Y
xx
(
x
,
y
)
Z
N
→
0 and
Y
yx
(
x
,
y
)
Z
N
→
+
y
2
→∞
.
Introduce normalized anomalous fields
H
o
y
(
x
,
y
)
H
o
x
(
x
,
y
)
H
o
x
(
x
H
o
y
(
x
,
y
)
=
,
,
y
)
=
.
(5
.
63)
H
o
y
H
o
y
On substituting (5.62) and (5.63) into (5.61), the system of the integral equations
for horizontal components of the anomalous magnetic field assumes the form
