Information Technology Reference
In-Depth Information
The question of physical validity of the Tikhonov-Cagniard model seemed to be
the controversial one. The discussion was opened by Wait (1954, 1962) and Price
(1962, 1967). They referred to the strong horizontal nonuniformity of the external
magnetic field and pointed to the necessity of serious limitations for MT sound-
ing. These limitations have been removed by Dmitriev and Berdichevsky (1979)
and Berdichevsky and Dmitriev (2002). They showed that the Tikhonov-Cagniard
model covers a broad class of magnetotelluric fields with anyhow fast but quasi-
linear variations of
H
over distances comparable to the threefold field-penetration
depth. This considerably extends the boundaries of practical applicability of
the MT sounding. Moreover, in that class of fields the Tikhonov-Cagniard
impedance may be determined by the
gradient magnetovariational sounding
(Berdichevsky et al., 1969; Schmucker, 1970; Weidelt, 1978; Berdichevsky and
Dmitriev, 2002):
H
z
Z
=−
i
o
y
.
(1
.
3)
H
x
/
x
+
H
y
/
The experiments carried out in the late 1950s showed that the real magnetotel-
luric field may dramatically differ from (1.2). The impedance
Z
was being deter-
mined with large (occasionally very large!) scatter. What's more, it depended on the
direction of the measurement axes
x
y
.
Berdichevsky (1960, 1963) and Cantwell (1960) attributed these effects to the
influence of lateral inhomogeneity of the Earth's layers and went from the scalar
impedance measurements to the tensor ones. The validity of the tensor approach
has been confirmed by extensive magnetotelluric observations over many years.
Behind the tensor approach is the long-standing question on the existence and
nature of linear algebraic relations between horizontal components of the elec-
tromagnetic field in inhomogeneous media. Would we have to consider the mag-
netotelluric linear relationships as a postulate verified by statistics of numerous
observations? Or, more properly, can we turn to the common principles of clas-
sic electrodynamics and derive the linear relations directly from the Maxwell
equations?
The general theory of this question has been suggested by Berdichevsky and
Zhdanov (1984). They proved that the existence of invariant linear relationships with
coefficients reflecting the Earth's conductivity is a special property of the electro-
magnetic field stemming from the structure of its generators. Electromagnetic fields
having this property are said to be fields of algebraic type. Considering fields of
algebraic type we can deduce the linear relationships between the field components
directly from the equations of Maxwell's electrodynamics. The form of these rela-
tionships depends on the number of degrees of freedom characterizing the primary
field.
In our topic we will follow the work by Berdichevsky and Dmitriev (1997) and
use a field excited by a primary plane wave propagating vertically from the iono-
sphere. This is the simplest field of algebraic type having two degrees of freedom
corresponding to two different polarizations of the primary plane. We are going to
,
