Information Technology Reference
In-Depth Information
In bilogarithmic coordinates, we have
2log
√
T
o
h
1
.
log
A
=−
+
log2
43
o
Evidently, the
h
-line is tilted at an angle of
-a
rctan 2
=−
63
.
to the axis of
√
T
. It intersects the line
mat
√
T
h
, from which we can determine
=
1Ohm
·
A
T
h
356
T
h
(second)
1
√
2
h
=
or
h
(kilometer)
=
0
.
.
o
The remarkable property of the
h
-interval is that the depth
h
to the perfect con-
ductor can be obtained immediately from the impedance,
h
|
/
o
, without
any additional information. Applying this formula for an arbitrary layered medium,
we get at any frequency so-called
effective penetration depth h
eff
.
= |
Z
Following Weidelt
(1972), we draw analogy with a center of masses and consider
h
eff
as the depth to
the center of currents induced in the Earth:
0
0
0
∞
∞
∞
z
dH
y
dz
=
H
y
dz
dz
zj
x
dz
|
o
=
|
Z
1
o
E
x
(0)
H
y
(0)
A
o
=
h
eff
=
=
=
.
0
0
0
∞
∞
∞
j
x
dz
j
x
dz
j
x
dz
(1
.
47)
Note that in the homogeneous half-space of resitivity
the
effective penetration
depth h
eff
is proportional to the
skin-depth
:
1
√
2
=
o
,
h
eff
=
where
2
o
.
=
The
h
-interval is separated from the
S
1
-interval by a transition zone embracing
the maximum of the
A
-curve. The position of the maximum can be defined from
the approximate equation
max
0
S
1
h
2
≈
1 whence
T
max
≈
2
o
S
1
h
2
.
(1
.
48)
Thus, with
T
<<
T
max
we obtain information on
S
1
and with
T
>>
T
max
we
obtain information on
h
. The informativeness of apparent resistivities depends on
parameter
o
S
1
h
2
. Note that this parameter reflects the distribution of current
induced in the Earth. With some work it is shown that
