Information Technology Reference
In-Depth Information
Resorting to intuition, the above proofs of uniqueness can be extended to the
general 3D case of MT inversions. It appears evident that the
dependence of
the impedance tensor ensures determination of the vertical variations in the con-
ductivity, whereas its
x, y
-dependence characterizes the horizontal variations in the
conductivity. Intuition suggests that measurements of the MT impedance made in
a wide frequency range along sufficiently long profiles or over a sufficiently large
area can provide information which enables the reconstruction of the geoelectric
structure of the region studied.
III.
The uniqueness of the MV inversion for a long time was open to question. It
seemed that the tipper characterizes horizontal heterogeneities of the medium, but
cannot provide information on its normal layered structure because
W
zx
−
W
zy
=
0 in a horizontally homogeneous model. However, if the medium is horizontally
inhomogeneous, the manetovariational sounding can be considered as a common
frequency sounding using the magnetic field of a local buried source. The latter
is formed by any geoelectric inhomogeneity
=
z
) filled with excess electric
current. It is evident that this current and its magnetic field depend not only on
the structure of the inhomogeneity,
(
x
,
y
,
(
x
,
y
,
z
), but also on the normal structure,
z
) of the magnetovariational
inverse problem exists and we should find out whether it is unique.
The theorem of uniqueness for the MV inversion was proven by Dmitriev
(Berdichevsky et al., 2000; Dmitriev, 2005). Let us consider a model shown in Fig.
10.3. In this model, a homogeneously layered Earth with the normal conductivity
N
(
z
). Thus, the solution
(
x
,
y
,
z
)
=
N
(
z
)
+
(
x
,
y
,
(
z
)0
≤
z
≤
D
N
(
z
)
=
D
D
≤
z
contains a 2D inhomogeneous domain
S
of conductivity
(
y
,
z
)
=
N
(
z
)
+
(
y
,
z
),
where
z
) is the excess conductivity. The inhomogeneity is striking along the
x
-axis, and the maximum diameter of its cross-section is
d
. The functions
(
y
,
N
(
z
) and
S
D
d
N
(z)
(y,z)
Fig. 10.3
A layered model
with a 2D inhomogeneous
bounded domain S
D
