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11.2 Stratifying the Geoelectric Background
At this stage we perform some rough one-dimensional estimates stratifying the geo-
electric background. Two appropriate techniques can be used: the Occam inver-
sion provided by smoothing stabilizer (Constable et al., 1987; Parker, 1994) or the
Zohdy transformation, suggested originally for the resistivity method (Zohdy, 1989;
Andreeva et al., 1991; Hobbs and Dumitresku, 1997; Berdichevsky and Dmitriev,
2002). We shall restrict our consideration to Zohdy's transformation. The key advan-
tage of this approach is that it yields immediately the stable
S
−
distribution. So, we
get a firm and pictorial basis for geoelectric stratification.
Magnetotelluric modification of Zohdy's transformation has its origin in the
Molochnov-Viet transformation (Berdic
he
vsky and Dmitriev, 2002), which trans-
lates the apparent-resistivity curve
A
(
√
T
)into a resistivity-depth profile
(
z
):
⎧
⎨
A
(
√
T
)
1
2
A
(
√
T
)
d
log
√
T
A
(
√
T
)
d
log
√
T
1
2
d
log
d
log
+
for
≤
0
(
√
T
)
=
A
(
√
T
)
1
−
2
A
(
√
T
)
d
log
√
T
A
(
√
T
)
d
log
√
T
⎩
1
2
d
log
d
log
−
for
≥
0
A
(
√
T
)
T
2
z
(
√
T
)
h
eff
(
√
T
)
=
=
.
π
o
(11
.
18)
Simplicity of the Molochnov-Viet transformation is achieved at the cost of a
severe sacrifice in its accuracy. An apparent-resis
tiv
ity curve calculated from
(
z
)
A
(
√
T
). We can reduce this difference
by means of
it
erative procedure involving
Zohdy corrections
.
Let
may dramatically differ from the initial curve
A
(
√
T
) be given on a sufficiently dense grid
T
m
,
m
∈
[0
,
M
]:
A
(
T
m
)
(
m
)
A
=
.
At
n
th iteration we have
(
n
)
(
√
T
m
)
(
m
,
n
)
(
n
)
(
z
(
m
)
)
=
=
A
(
√
T
m
)
T
m
2
z
(
√
T
m
)
.
z
(
m
)
(11
19)
=
=
π
o
(
n
A
(
√
T
m
)
(
m
,
n
)
A
=
and