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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
 
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