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3.5 The Caldwell-Bibby-Brown Method
The above techniques necessitate the two-dimensionality (or axial symmetry) of
the regional background. Several approaches have been suggested to remove this
constraint (Zhang et al., 1993; Utada and Munekane, 2000). The most intriguing
approach was put forward by Caldwell et al. (2002a, b, 2004) and Bibby et al.
(2005). Using the Caldwell-Bibby-Brown technique (
CBB method
), we analyze the
phase tensor.
3.5.1 The Phase Tensor
Similar to the Bahr and Groom-Bailey methods, the Caldwell-Bibby-Brown method
is based on the truncated low-frequency decomposition (1.75) neglecting the local
magnetic distortions.
The idea of this elegant technique, which opens up fresh opportunities for sepa-
ration of local and regional effects, is the following.
According to (1.75), [
Z
S
]
[
e
][
Z
R
] where [
Z
S
] and [
Z
R
] are the superimpo-
sition and regional impedances, and [
e
] is the real-valued tensor of the local electric
distortions. Applying this decomposition, we write
=
[
Z
R
]
[Re
Z
R
]
i
[Im
Z
R
]
=
+
,
[
Z
S
]
[Re
Z
S
]
i
[Im
Z
S
]
[
e
][Re
Z
R
]
i
[
e
][Im
Z
R
=
+
=
+
,
]
(3
.
56)
whence
[Re
Z
S
]
[
e
][Re
Z
R
]
[Im
Z
S
]
[
e
][Im
Z
R
]
=
,
=
.
(3
.
57)
] as the product of inverse of [Re
Z
S
]by
Let us introduce a real-valued tensor [
[Im
Z
S
]:
S
]
[Re
Z
S
]
−
1
[Im
Z
S
]
[Re
Z
R
]
−
1
[
e
]
−
1
[
e
][Im
Z
R
]
[
]
=
[
=
=
xx
xy
(3
.
58)
[Re
Z
R
]
−
1
[Im
Z
R
]
R
]
=
=
[
=
,
yx
yy
where
Re
Z
yy
Im
Z
xx
−
Re
Z
xy
Im
Z
yx
Re
Z
yy
Im
Z
xx
−
Re
Z
xy
Im
Z
yx
xx
=
Re
Z
xy
Re
Z
yx
=
Re
Z
xy
Re
Z
yx
,
Re
Z
xx
Re
Z
yy
−
Re
Z
xx
Re
Z
yy
−
