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Thus, both the methods rest on the identical decompositions, but differ in
parametrization and technology. Comparison between (3.18) and (3.30) suggests
that the Bahr method with its analytical formulae and the Groom-Bailey method
with its least squares fitting procedure offer the same information about local and
regional structures (regional strike, phases and apparent amplitudes of principal
regional impedances, deflection angles or twist and shear angles). The special merit
of the Bahr method is that it suggests some auxiliary parameters (
skew
B
,
) that
help to estimate the applicability of the truncated local-regional decomposition with
a real-valued electric distortion tensor and a two-dimensional regional impedance.
But the Groom-Bailey method has the advantage that due to the least squares fitting
procedure it may provide better stability of the local-regional decomposition.
To illustrate the Bahr and Groom-Bailey methods numerically, we turn back to
the superimposition model shown in Fig. 1.11. Here a local conductive body L
in the form of vertical cylinder is superimposed upon a regional conductive two-
dimensional prism R. Let
,
1
=100 Ohm
·
m,
h
1
=0.1km,
L
=10Ohm
·
m,
a
=0.1km,
m,
h
2
=10km,
2
=
3
=0.
The problem was solved by the hybrid method given in Sect. 1.3.4. Calculations
were carried out for the observation site O in the immediate neighborhood of the
conductive cylinder (
r
=0.11km,
∞
,
h
2
= 100 km,
R
=10Ohm
·
h
= 10 km, v = 200 km,
=45
◦
).
Figure 3.5 depicts the longitudinal and transverse apparent-resistivity and
impedance-phase curves computed from the regional impedance in the absence of
the local near-surface inhomogeneity. The effect of the buried conductive prism is
clearly visible in longit
ud
inal curves
=45
o
,
. Special
a
ttention must be given to
and
the phase curves. At
√
T
<
0
,
√
T
and
√
T
1s
1
/
2
3s
1
/
2
100 s
1
/
2
.
≈
>
the phases of
longitudinal and transverse impedances virtually coincide.
Consider some characteristic parameters, which define the applicability of the
Bahr and Groom-Bailey decompositions. These parameters are: (1) Swift's
skew
s
,
(1.60), (2) Bahr's
skew
B
, (1.61), (3) phase difference
(difference between longitu-
dinal and transverse phases calculated directly from the superimposition impedance
[
Z
S
]), (3.21). Appart from these parameters, we also consider a model parameter
q
measuring the contribution of the local magnetic anomaly:
5
+
h
xy
+
h
yx
+
h
yy
−
1
2
2
2
2
q
=
0
.
5
m
=
0
.
|
h
xx
−
1
|
,
(3
.
35)
where
q
is a calibrated Euclidean norm of difference [
m
]
=
[
h
]
−
[
I
] between the
magnetic distortion matrix [
h
] and the identity matrix [
I
]
Recall that local-regional
Bahr's and Groom-Bailey's methods are applicable providing that
skew
B
and
q
are
sufficiently small, while
.
is sufficiently large.
Figure 3.6 shows all these parameters versus
√
T. At high frequencies (
√
T
<
0.1
s
1/2
) the regional two-dimensional structure does not manifest itself, and the
superimposition model acts as an axisymmetric model containing only a verti-
cal near-surface cylinder. Here
skew
S
and
skew
B
come close to zero, while mag-
netic distortion is rather large (
q
>
0.3). However at intermediate frequencies
