Information Technology Reference
In-Depth Information
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