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In-Depth Information
Chapter 4
The Magnetovariational Response Functions
Along with the magnetotelluric response functions originating from linear relations
between components of the electric and magnetic fields we can consider the magne-
tovariational response functions derived from linear relations between components
of the magnetic field. This consideration may significantly enhance the capabilities
of the magnetotellurics, since at low frequencies the magnetic field becomes free
of near-surface distortions and shines a nondeceptive light on the deep geoelectric
structures.
4.1 The Wiese-Parkinson Matrix
Return again to the model of inhomogeneous medium presented in Fig. 1.1. Recall
that this layered model containing a bounded inhomogeneous domain V is excited
by a plane elliptically polarized wave incident vertically on the Earth's surface.
Proceeding from (1.12) and supplementing (1.13
c,d
) with an equation for vertical
component of the magnetic field, we get
H
x
H
x
J
H
2
x
H
y
o
J
H
1
H
x
=
+
=
H
x
o
(1
+
)
+
a
x
H
y
H
y
H
x
o
J
H
2
J
H
1
y
H
y
=
+
=
+
H
y
o
(1
+
)
b
.
(4
1)
y
H
z
H
x
o
J
H
2
H
y
o
J
H
1
H
z
=
=
+
,
c
z
z
where
H
x
o
,
H
y
o
are components of the normal magnetic field on the Earth's sur-
face, and
J
H
1
J
H
2
are convolutions of excess currents with the magnetic Green
tensors. On eliminating
H
x
o
,
,
H
y
o
from 4.1
a
,
b
) and substituting them in (4.1
c
), we
obtain:
H
z
=
W
zx
H
x
+
.
W
zy
H
y
(4
2)
