Information Technology Reference
In-Depth Information
⎧
⎨
2
2
2
1
−
e
−
g
(
|
y
|−
v
)
/
f
n
˙
1
−
|
y
| ≥
v
cot h
g
Z
⊥
(
y
)
+
f
v
2
⊥
(
y
)
=
=
2
o
⎩
2
2
cos h
g
f
1
−
n
¨
1
+
y
|
y
| ≤
v,
sin h
g
cot h
g
f
v
+
f
v
(7
.
76)
n
are locally normal apparent resistivities in the side segments and
the central segment.
Once again we see that variations in the conductance
S
1
of the upper layer may
dramatically distort the descending branches of the apparent-resistivity curves (
S-
effect) but leaves almost undistorted their ascending branches. Let
n
and ¨
where ˙
o
S
1
h
2
>>
1
o
S
1
h
2
>>
1. Then in the
S
1
-interval (within the ascending branch of the
⊥
-curves), we have
and
≈
, whence
⎧
⎨
1
S
1
Z
N
=
|
y
| ≥
v
Z
⊥
(
y
)
≈
⎩
1
S
1
Z
N
=
|
y
| ≤
v
(7
.
77)
⎧
⎨
1
o
(
S
1
)
2
Z
⊥
(
y
)
n
=
|
| ≥
v
˙
y
2
⊥
(
y
)
=
≈
⎩
1
o
(
S
1
)
2
o
n
=
¨
|
y
| ≤
v.
In this approximation, the transverse impedance and apparent resistivity do not
depart from their locally normal values.
Now pass on to the
h-
interval. Let
o
S
1
h
2
<<
1 and
o
S
1
h
2
<<
1. Then,
⊥
-curves, we have
f
≈
f
≈
within the descending branch of the
1 and
≈
1,
whence
⎡
⎤
⎧
⎨
S
1
S
1
⎣
1
−
⎦
Z
N
e
−
(
|
y
|−
v
)
/
d
1
−
S
1
S
1
|
y
| ≥
v
cot h
d
1
+
⎡
⎤
Z
⊥
(
y
)
≈
(7
.
78)
⎩
S
1
S
1
⎣
1
−
⎦
1
sin h
d
y
d
Z
N
1
−
S
1
cos h
|
y
| ≤
v
cot h
d
S
1
+
