Information Technology Reference
In-Depth Information
LMK
1
LMK
2
where
and
are the impedance principal values, obtained by the La
Torraca-Madden-Korringa procedure. Here
ς
>
2
. Substituting (2.88)
LMK
1
LMK
in (2.87), we get
|
1
m
|
2
LM
1
2
LM
2
2
2
m
+ |
2
m
|
SE
m
=
1
,
2
=
,
(2
.
89)
2
2
|
1
m
|
+ |
2
m
|
whence
2
<
m
1
.
LMK
SE
LMK
2
<
(2
.
90)
m
=
1
,
Clearly the LMK method has the advantage of higher sensitivity to three-
dimensional asymmetric structures.
4. In the SE method, the asymmetry of the medium violates orthogonality of the
electric eigenfields, while the electric and magnetic eigenfields are always quasi-
orthogonal. And vice versa, in the LMK method the asymmetry of the medium
violates orthogonality of the electric and magnetic eigenfields, while the electric
eigenfields as well as the magnetic eigenfields are always orthogonal. In both meth-
ods the eigenfields respond to the geoelectric asymmetry, but in a different way.
5. The SE and LMK methods offer purely mathematical procedures and discus-
sion about their physical meaning is a bit scholastic. Both methods complement
each other. The magnetotelluric eigenstate analysis can help in revealing target geo-
electric structures and establishing conditions that are most favorable for their study.
This simple idea specifies the practical significance of the eigenstate problem. Just
from this viewpoint we should judge the informativeness of different techniques
devised for eigenstate analysis.
It would be instructive to test different eigenstate techniques using synthetic data
computed for characteristic models.
Let us examine a three-layered superimposition model with a local
-shaped
resistive inclusion in the first layer (conductive sediments) and a regional two-
dimensional prismatic conductor in the second layer (resistive lithosphere). The
model is presented in Fig. 2.3. Here we can also see the apparent-resistivity and
impedance-phase curves obtained over the middle of the regional conductor in the
absence of the local
-shaped inclusion. The eigenstate determinations were done by
the Swift-Sims-Bostick, Swift-Eggers and La Torraca-Madden-Korringa methods
at 14 sites located over the
-shaped inclusion and in its vicinity.
Figure 2.4 shows the principal values
e
i
2
of the
impedance tensor [
Z
] defined by the SSB, SE, and LMK methods at
T
= 640 s
where the apparent-resistivity and impedance-phase curves distinctly reflect the
influence of the regional conductor. In the model under consideration all three
techniques yield closely related principal values: the difference in amplitudes and
phases of
e
i
ξ
1
1
= |
1
|
,
2
= |
2
|
1
,
2
at most observation sites does not exceed 5% and 3
◦
and only at a
few sites amounts up to 8-12% and 4-6
◦
. But note that
|
1
|
,
|
2
|
experience great
