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3. Third, we disregard the local induction in superficial inhomogeneities and apply
the local-regional decomposition with real-valued tensor of electric distortion
characterizd by local galvanic (static) effects.
These restrictions open the way to separation of local and regional effects.
Following is a cursory examination of the separation methods based on the super-
imposition models that contain local small-scale two- or three-dimensional inho-
mogeneities over a two- or three-dimensional large-scale regional structure. These
methods are: (1) the Bahr method, (2) the Groom-Bailey method, (3) the Zhang-
Roberts-Pedersen method, (4) the Chave-Smith method, and 5) the Caldwell-Bibby-
Brown method.
3.2 The Bahr and Groom-Bailey Methods
Bahr (1988) suggested a method for separating local and regional effects in
the superimposition model with local two-dimensional or three-dimensional near-
surface inhomogeneities and regional two-dimensional background (
B method
). In
this method we neglect the magnetic distortion and use the low-frequency trun-
cated decomposition (1.75), [
Z
S
]
[
e
][
Z
R
], where [
e
] is the real-valued tensor
of electric distortion and [
Z
R
] is the two-dimensional regional impedance tensor
with anti-diagonal matrix. A peculiarity of Bahr's method is that the characteristics
of local and regional effects are given in an explicit form and their separation is
performed analytically by means of simple formulae.
The basic assumptions in the Groom-Bailey method (Groom and Bailey, 1989)
are the same as in the Bahr method, but separation of local and regional effect is
performed numerically by solving an overdetermined system of equations with least
squares fitting procedure.
We begin our consideration with the Bahr method.
=
3.2.1 The Bahr Method
Writing the basic equation (1.75) in the regional coordinate system (the
x
y
-axes
are along and across the strike of the regional two-dimensional structure), we have
,
Z
xx
e
xx
0
Z
xy
2
1
−
e
xy
e
xx
1
e
xy
[
Z
S
]
=
=
=
,
(3
.
1)
2
e
yx
e
yy
−
0
Z
yx
Z
yy
2
1
−
e
yy
e
yx
2
are principal values of the regional impedance tensor (the lon-
gitudinal and transverse impedances) and
e
xx
,
1
and
where
e
yy
are components of the
real-valued tensor of electric distortion. The columns of the superimposition tensor
[
Z
S
] consist of in-phase or anti-phase components:
e
xy
,
e
yx
,
