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Substitution of (8.13) into (8.12) gives
∞
1
∞
1
l
2
h
1
(
h
2
−
b
n
n
2
cos
nly
h
o
cos
ly
)
+
l
{
(
h
1
+
h
2
)
−
h
o
cos
ly
}
b
n
n
cos
nly
∞
1
H
y
cos
ly
Z H
y
−
h
2
)
H
y
.
+
b
n
cos
nly
−
i
o
h
o
=−
i
o
(
h
1
+
(8
.
14)
Fourier coefficients
b
n
are found by minimizing the misfit of (8.14). Restricting
ourselves to series with 6 terms, we determine the low-frequency longitudinal
impedance as
1
6
Z
H
y
+
b
n
cos
nly
E
x
(
y
)
H
y
(
y
)
=
Z
(
y
)
=
b
n
n
cos
nly
.
(8
.
15)
1
6
H
y
+
l
i
o
In
the
case
that
h
o
≤
0
.
3
h
2
and
L
≥
4
h
o
,
the
low-frequency
longitudinal
impedance is approximated by formula
Z
(
y
)
≈
o
h
(
y
)
,
(8
.
16)
where
h
2
−
h
o
cos
2
L
h
(
y
)
=
h
1
+
y
.
:
Here
is a distortion factor dependent on the
inductive ratio
L
h
1
+
e
−
0
.
7
/
(
)
1
.
2
=
=
,
.
(8
.
17)
h
min
2
⊥
<
1 and
<
1
Returning to (8.10) and (8.16), we see that the magne-
totelluric sounding smoothes out the asthenosphere topography. Instead of the true
amplitude
h
o
, we get a reduced amplitude
h
o
Note that
.
a
⊥
h
o
due to the galvanic screening
effect in the TM-mode and a reduced amplitude
h
o
=
=
a
h
o
due to the induction-
flattening effect in the TE-mode. According to (8.11), departure of
⊥
from 1 does
from
not exceed 0.1 provided that
L
>
12
d
min
. According to (8.17), departure of
h
mi
2
).
The TM- and TE-mechanisms of the electromagnetic distortions caused by the
asthenosphere relief is shown in Fig. 8.21. We see here the conductive redistribution
of the transverse currents (TM-mode) and the mutual induction of the longitudinal
currents (TE-mode).
What is relation between these two effects? Consider some typical examples. Let
1
=
1 does not exceed 0.1 provided that
L
>
5(
h
1
+
·
,
h
1
=
,
2
=
·
,
h
min
2
=
,
d
min
=
.
10 Ohm
m
1km
10000 Ohm
m
50 km
227 km
The