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colling for conditions at infinity. In forward problem, this contradiction can be
easily removed through the embedding the observation area into the reasonably con-
structed infinite horizontally homogeneous layered medium considered as a normal
background . In the inverse problem, the normal background of the medium under
consideration is unknown and it should be chosen as a mathematical abstraction
consistent with observation data obtained at the boundary of the observation area
and a priori geological and geophysical information.
Note that using the homogeneous half-space as a normal background, we run the
risk of false structures at the periphery of the observation area. With the help of
these structures the computer tries compensate the contradictions between the real
geolectric medium and homogeneous half-space.
We believe that in the general three-dimensional case a normal background
consistent with the real medium can be introduced by the extrapolation of scalar
invariants of the measured impedance tensors, for example, the invariant Z brd (the
Berdichevsky impedance) or Z eff (the effective impedance). The idea is to adjust
the normal background to a mean value of the impedance invariants obtained at the
boundary of the observation area. This techique will be referred to as the adjustment
method . Let values of the impedance tensor [ Z ] be determined in an observation area
S 0 bounded by a contour C 0 and let [ Z ( l ) ]
L be specified at L points of
C 0 (Fig. 10.1). The average value of the invariant Z brd on the contour C 0 , i.e., on the
boundary of the observation area, is found as
,
l
=
1
,
2
...
L
L
Z ( l )
xy
Z ( l )
yx
1
L
1
L
Z brd =
log Z ( l )
ant log
brd =
ant log
log
.
(10
.
3)
2
l = 1
l = 1
Fig. 10.1 Introduction of a
normal background into the
3D interpretation model
 
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