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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
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