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Fig. 8.19
One-dimensional
apparent-resistivity curves
over the asthenospheric
conductive layer at a depth of
90 km. The sediments
conductance 150 S; curve
parameter - asthenosphere
conductance in 1000 S;
h-lines for 100, 200, and
400 km are shown. From
(Vanyan and Shilovsky, 1983)
in Fig. 8.20. Here the layers
2
simulate the conductive sediments and resis-
tive lithosphere, while the highly conductive basement,
1
and
0, is identified with
asthenosphere. The asthenosphere surface has the cosine relief with the period
L
and amplitude
h
o
counted off from the mean depth
h
1
+
3
=
h
2
. The local depth to the
asthenosphere is defined as
h
(
y
)
=
h
1
+
h
2
(
y
)
=
h
1
+
h
2
−
h
o
cos
ly
,
(8
.
6)
where
l
L
.
First we consider the TM-mode. It is clear that the transverse impedance
Z
⊥
(
y
)
is an even periodic function with the period
L
that can be represented by a Fourier
decomposition
=
2
π/
∞
E
y
(
y
)
H
x
(
y
)
=
Z
Z
⊥
(
y
)
=−
+
a
n
cos
nly
,
(8
.
7)
1
where
Z
is a normal impedance obtained at
h
o
=
0. Substituting
Z
⊥
(
y
) into equation
(7.35) valid for the mantle descending branch of the apparent-resistivity curves (the
h
-interval), we get
Fig. 8.20
Two-dimensional
model with the cosine relief
of the asthenosphere surface