Information Technology Reference
In-Depth Information
impedance, while the polarization ellipses and principal directions are indetermi-
nate, since any magnetic field is transformed to a quasi-orthogonal electric field.
Take the 2D-model with the strike along the
x
-axis. Here
Z
xx
=
Z
yy
=
0 and
Z
,
Z
⊥
. With (2.46), (2.49), (2.50) we get
Z
,
2
=
Z
⊥
Z
xy
=
Z
yx
=−
1
=
or
Z
,
2
=
Z
⊥
1
=
0.
The principal values of the tensor [
Z
] coincide with the longitudinal and the trans-
verse impedances, while the principal directions are the longitudinal and transverse
ones. The electric eigenfields are linearly polarized along the principal directions.
At a single observation site, the Swift-Eggers method exposes the orientation of
two-dimensional structures, though cannot distinguish between the longitudinal and
transverse direction.
The similar situation is in the axially symmetric 3D-model. Here the tangential
and radial impedances are the principal values of the tensor [
Z
], while the tangen-
tial and radial directions are its principal directions. The ellipticity of the electric
eigenfields is zero. They are linearly polarized along principal directions.
Asymmetric 3D-structures manifest themselves in the elliptic polarization of the
electric eigenfields (
and
1
=
0
,
2
=
/
2or
1
=
/
2
,
2
=
0aswellas
1
,
2
=
1
,
2
=
0) and in the violation of the perpendicularity of their
|
1
−
2
|
=
/
ellipses (
2). A special case is a quasi-symmetric 3D-structure with
ske
w
=
0 and
ske
w
=
0. If
Z
xx
+
Z
yy
=
0, then it follows from (2.52) that
S
B
=−
1. Hence the electric eigenfields
E
τ
1
,
P
E
1
P
E
2
E
τ
2
are quasi-orthogonal and
|
1
−
2
| =
/
2.
Using the Swift-Eggers method, we can define three characeristic parameters
which reveal the lateral inhomogeneities and indicate their dimensionality:
(1) the parameter of inhomogeneity
=
1
−
2
1
+
2
N
(2
.
53)
In the 1D-model we have
N
= 0. Departure of
N
from 0 is a measure of lateral
inhomogeneity.
(2) the angular parameter of asymmetry (angular skew)
ske
w
ang
= ||
1
−
2
| −
/
2
|
.
(2
.
54)
In the 2D-model as well as in the axially symmetric and quasi-symmetric 3D-
models we have
ske
w
ang
= 0. Departure of
ske
w
ang
from 0 is a measure of geoelec-
tric asymmetry.
(3) the polarization parameter of asymmetry (polarization skew)
w
pol
=
|
1
|
+
|
2
|
2
ske
.
(2
.
55)
In the 2D-model and axially symmetric 3D-model we have
ske
w
pol
=
0 indi-
w
pol
from 0 is a
cating linear polarization of electric eigenfields. Departure of
ske
measure of geoelectric asymmetry.
