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In-Depth Information
In closing we will consider two special cases.
1. The (3D + 3D)-superimposition model contains a regional three-dimensional
axisymmetric structure overlapped by the local near-surface three-dimensional
inhomogeneity. In that case we have the same basic equation (3.1), so that the
Bahr method can be applied to find the radial and tangential directions as well as
phases of the radial and tangential principal impedances.
2. The horizontally layered one-dimensional medium contains only the local near-
surface three-dimensional inhomogeneity. In this model, the low-frequency trun-
cated decomposition takes the form
e
xx
0
e
xy
Z
N
−
e
xy
Z
N
e
xx
Z
N
[
Z
S
]
=
=
,
(3
.
22)
e
yx
e
yy
−
Z
N
0
−
e
yy
Z
N
e
yx
Z
N
where
Z
N
is the normal (one-dimensional) impedance. Here, all the components
of the impedance tensor [
Z
S
] are in-phase or anti-phase depending on the sign of
components of the distortion tensor [
e
]
.
3.2.2 The Groom-Bailey Method
Another decomposition technique to separate local and regional effects has been
suggested by Groom and Bailey (1989).
The basic assumptions in the Groom-Bailey method (
GB method
)arethesame
as in the Bahr method. The superimposition model containing a local two- or three-
dimensional inhomogeneity over a two-dimensional regional structure is considered
and the truncated low-frequency decomposition (3.1), [
Z
S
]
[
e
][
Z
R
], with the
real-valued electric distortion tensor [
e
] and anti-diagonal regional tensor [
Z
R
]is
applied.
Using the regional coordinate system with
x
- and
y
-axes along and across the
strike of the regional structure, we represent the distortion tensor [
e
] as the product
of a real-valued scalar
g
and real-valued tensors [
T
]
=
,
[
S
], [
A
]:
=
,
.
[
e
]
g
[
T
][
S
][
A
]
(3
23)
where
1
1
s
s
1
1
−
t
+
a
0
01
[
T
]
=
N
T
,
[
S
]
=
N
S
,
[
A
]
=
N
A
.
t
1
−
a
and
1
1
1
N
T
=
√
1
t
2
,
N
S
=
√
1
s
2
,
N
A
=
√
1
a
2
.
+
+
+
