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way is that a number of unknown parameters in the decomposition (4.75) is
vastly larger than a number of known parameters determined from the field
observation.
4.5.1 The Zhang-Pedersen-Mareschal-Chouteau Method
Zhang and his workmates (Zhang et al., 1993) assume that the local and regional
effects in the Wiese-Parkinson matrix are uncorrelated. Then they apply (4.75)
and (4.78), and define the local and regional Wiese-Parkinson matrices [
W
L
] and
[
W
R
]
[
W
L
] using the observed impedance tensor [
Z
S
] and the least-
squares estimates of [
t
] obtained through minimizing the misfit
[
W
S
]
=
−
t
zy
Z
yx
t
zy
Z
yy
2
2
W
zx
−
t
zx
Z
xx
−
W
zy
−
t
zx
Z
xy
−
q
=
+
,
(4
.
80)
where letters with tilde denote realizations normalized to the standard deviations of
W
zx
and
W
zy
. The accuracy of such decomposition depends on to what extent the
assumption that the local and regional effects are uncorrelated is true.
4.5.2 The Ritter-Banks Method
Another approach has been suggested by Ritter and Banks (1998). This approach
rests on the decomposition
=
[
W
R
]
[
h
z
][
Z
R
]
H
R
H
z
=
H
z
+
H
z
+
τ
=
[
W
S
]
H
R
τ
,
(4
.
81)
[
W
S
]
=
[
W
R
]
+
[
W
L
]
,
[
W
R
][
h
]
[
W
R
]
[
W
L
]
following
from
(4.72)
and
(4.73).
Here
=
and
=
[
W
L
][
h
] are the regional and local Wiese-Parkinson matrices defined
at low frequencies when the distortion matrix [
h
z
] is real-valued and frequency-
independent. Thus, along with (4.79) we have the linear relations between
components of the local Wiese-Parkinson matrix and the regional impedance
tensor:
[
h
z
][
Z
R
]
=
h
zx
Z
xx
+
h
zy
Z
yx
,
W
zx
=
(4
.
82)
h
zx
Z
xy
+
h
zy
Z
yy
.
W
zy
=
In the Ritter-Banks method we examine a model that contains a two-dimensional
local inhomogeneity against a two-dimensional regional background. The regional
and local strike angles are
L
counted clockwise from the
x
-axis. This is the
same (2D+2D)-superimposition model as in the Zhang-Roberts-Pedersen method
described in Sect. 3.3. According to (4.81),
R
and
