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(
m
,
n
)
=
(
m
,
n
)
P
A
,
(11
.
20)
where
P
is an operator transforming resistivity-depth profile into apparent-resistivity
curve. Multiplying
(
m
,
n
)
by Zohdy's correction factor
Z
(
m
,
n
)
, we get
(
m
,
n
+
1)
Z
(
m
,
n
)
(
m
,
n
)
=
,
(11
.
21)
where
(
m
)
A
Z
(
m
,
n
)
=
.
(
m
,
n
)
A
We illustrate Zohdy's corrections by a simple example. Let the resistivity-depth
profile
(
m
,
1)
is given by (11.18). Correcting
(
m
,
1)
, we obtain the second iteration
(
m
,
2)
Z
(
m
,
1)
(
m
,
1)
=
,
where, according to (11.20) and (11.21),
(
m
)
A
Z
(
m
,
1)
(
m
,
1)
A
(
m
,
1)
=
=
P
.
(
m
,
1)
A
(
m
,
1)
A
(
m
)
A
(
m
,
1)
If
>
,
the value for
is overstated but it is reduced by Zohdy's
(
m
,
1)
A
(
m
)
A
(
m
,
1)
is understated but it is
enhancved by Zohdy's factor. It seems that we arrive at the second iteration with
diminished misfit of resistivity profile
factor. And vice versa, if
<
, the value for
(
m
,
2)
. This heuristic consideration suggests
that Zohdy's multiplications decrease the misfit of transformation.
Iterations are continued until the misfit
M
(
m
,
n
)
100 %
M
ln
(
n
)
A
=
(11
.
22)
(
m
)
A
m
=
1
becomes reasonably small. Though lacking theoretical support, this simple approach
works rather well in practice. It is typical that on 25-50 iterations we reach a misfit
of the order of 2-3%.
Figure 11.30 shows the five-layer test model. Parameters of the model are:
1
=
10 Ohm
·
m,
h
1
=
1km,
2
=
100 Ohm
·
m,
h
2
=
2km,
3
=
10 Ohm
·
m,
h
3
=
4
=
·
m,
h
4
=
.
5
=
·
.
3km,
A
-curve has
pronounced maximum and minimum corresponding to the second and third layers.
Its starting transformation made by the Molochnov-Viet scheme yields a smoothed
resistivity distribution
1Ohm
4
2km,
60 Ohm
m
The original
(
z
) with a misfit of 96% for its
A
-response. The Zohdy
