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Equating the coefficients of this Fourier decomposition to zero, we obtain a sys-
tem of the linear algebraic equations in a o ,
a 1 ...
a n + 1 :
b o =
a o +
i
o h
=
0
1
2 l 2 S o R 2 ( a o +
l 2 S 1 R 2 ) a 1 +
b 1 =
(1
+
a 2 )
=
0
(7
.
39)
n 2
2
n 2 l 2 S 1 R 2 ) a n +
l 2 S o R 2 ( a n 1 +
b n =
(1
+
a n + 1 )
=
0
.
It is not difficult to show that a n is proportional to S o . Thus, at the sufficiently
small amplitude S o << S 1 we can restrict ourselves to the first and second terms of
the impedance decomposition (7.36). By virtue of (7.39)
l 2 S o R 2
a o =−
i
o ha 1 =
i
o h
,
(7
.
40)
1
+
l 2 S 1 R 2
whence
o h 1
cos ly
l 2 S o R 2
Z ( y )
=
a o +
a 1 cos ly
=−
i
.
(7
.
41)
1
+
l 2 S 1 R 2
Here the transverse impedance Z ( y ) is subjected to the S -effect. It reflects the
variations in the conductance S 1 ( y ) of the upper layer and delivers the oscillating
apparent depth h A ( y ) to the conductive bottom:
h 1
cos ly
l 2 S o R 2
h A ( y )
=
=
h
h o cos ly
,
(7
.
42)
1
+
l 2 S 1 R 2
where
l 2 S o R 2
h o =
h
l 2 S 1 R 2 .
1
+
To estimate the intensity of the S
effect, we correlate the relative amplitudes
l 2 S o R 2
h o
h =
S o
S 1 .
h
=
l 2 S 1 R 2 ,
S
=
(7
.
43)
1
+
The measure of the S
effect intensity can be introduced in the form
h
1
1
Q
=
=
l 2 S 1 R 2 =
2 d 2 ,
(7
.
44)
1
+
1
/
1
+
L 2
/
4
π
S
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