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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
 
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