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effects reduce the distortion of the ascending branches of the longitudinal apparent-
resistivity curves, but distort their descending branches.
In our consideration the inclusion
elongation e
b
(aspect ratio) can
be used as a parameter that controls an accuracy of the two-dimensional approxima-
tion of the three-dimensional inclusions. Considering an inclusion elongated in the
x
=
a
/
b
,
a
>
direction, we introduce the following decompositions of the apparent resistivi-
ties observed over the inclusion:
−
p
xy
xy
(2
D
)int e
S
1
-interval
xy
(3
D
)
=
p
xy
xy
(2
D
) n e
h
-interval
(7
.
130)
p
yx
S
yx
(2
D
)int e
S
1
-interval
yx
(3
D
)
=
p
yx
yx
(2
D
) n e
h
-interval
.
S
h
S
h
Here
xy
(2
D
)
,
xy
(2
D
)
,
yx
(2
D
)
,
yx
(2
D
) are the two-dimensional apparent
p
yx
are the factors characteriz-
ing their three-dimensional distortions. According to (7.122) and (7.126),
, and
p
xy
,
p
xy
,
p
yx
,
resistivities, obtained at
e
→∞
4
o
(
S
1
+
xy
(2
D
)
xy
(2
D
)
=
o
h
2
=
S
1
)
2
=
o
h
2
S
1
S
1
2
(7
.
131)
1
o
(
S
1
)
2
S
yx
(2
D
)
h
yx
(2
D
)
=
and
1)
2
1)
2
(
e
+
(
e
+
p
xy
=
p
xy
=
e
2
S
1
/
S
1
)
2
(
e
+
2
+
S
1
/
S
1
1
+
(7
.
132)
1)
2
1)
2
(
e
+
(
e
+
p
yx
=
p
yx
=
S
1
)
2
.
e
2
S
1
/
S
1
/
S
1
(
e
+
1
+
+
2
The factors
p
xy
,
p
xy
,
p
yx
,
p
yx
tend to 1, as the elongation
e
tends to
(the ellip-
tic cylinder degenerates into a two-dimensional prism). Naturally the departure
of
p
xy
,
∞
p
yx
from 1 is a measure of the inclusion three-dimensionality.
Assume that the elliptic inclusion can be considered as quasi-two-dimensional,
provided 0
p
xy
,
p
yx
,
p
xy
,
p
xy
,
p
yx
,
p
yx
.
9
≤
≤
1
.
1, that is, if the longitudinal and trans-
verse apparent resistivities,
xy
and
yx
, differ from the two-dimensional apparent
yx
(2
D
) at most by 10%. Thus, in view
of (7.132), we can derive the simple estimates for the quasi-two-dimensionality of
resistive and conductive elliptic inclusions (Table 7.2). The most favorable estimates
xy
(2
D
)
xy
(2
D
) and
yx
(2
D
)
resistivities
,
,
