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[
S
] and [
A
]
this decomposition is unique (Groom and Bailey, 1989). It has a simple physi-
cal interpretation. The factor
g
plays a part of the scaling parameter. The tensors
[
T
]
Without going into detail we note that for all real-valued
g
,
[
T
]
,
[
A
] describe elementary distortions of the regional electric field
E
R
τ
,
[
S
]
,
.
Figure 3.4a shows a family of unit regional electric fields
E
R
τ
linearly polarized
in different directions. Here vectors 1,3 are oriented in the principal directios of the
tensor [
Z
R
], i.e. along and across the strike of the regional structure, while vectors
2,4 bisect these principal directions.
The effect of the tensor [
T
] is shown in Fig. 3.4b. This tensor rotates all vectors
through a clockwise angle
t
=
arctan
t
.
It is said to be the
twist tensor.
The angle
t
is the
twist angle
.
The effect of the tensor [
S
] is shown in Fig. 3.4c. It looks like shear deformation.
By analogy with the theory of deformation this tensor is said to be the
shear tensor
.
It causes maximum angular changes in vectors 1,3 and does not change vectors 2,4.
Vector 1 is deflected clockwise by an angle
s
=
arctan
s
, and vector 2 by the same
angle, but counter-clockwise. The angle
s
is the
shear angle
.
The effect of the tensor [
A
] is shown in Fig. 3.4d. This tensor stretches the longi-
tudinal and transverse components of electric vectors by different factors, creating
a pattern of “anisotropy”. It is said to be the
anisotropy tensor.
Thus the factorization (3.23) reduces the distortions of regional electric field to
scale change and shear, twist and anisotropy deformations.
Reverting to the truncated decomposition (1.75), we write
[
Z
S
]
g
[
T
][
S
][
A
][
Z
R
]
=
(3
.
24)
Fig. 3.4
Transformation of unit electric fields (
a
)bythetwist(
b
), shear (
c
) and anisotropy (
d
)
tensors
