Information Technology Reference
In-Depth Information
The real tippers show a remarkable property: over a wide range of sufficiently
low frequencies they are directed away from zones of higher conductivity (current
concentration) and towards zones of lower conductivity (current deconcentration).
So, maps of real tippers may be most helpful in locating geoelectrical structures,
their tracing, their classifying by conductivity. This property of real tippers is a direct
consequence of the Bio-Savart law. Let us demonstrate this with a simple example
(Fig. 4.3). Assume that the infinitely long rectilinear horizontal direct current flows
along the
x
-axis trough an underground point C. At symmetrical surface points O
1
and O
2
we observe magnetic fields
H
(1)
and
H
(2)
with components
J
cos
J
sin
J
cos
J
sin
H
(1)
y
H
(1)
z
H
(2)
y
H
(2)
z
=
,
=−
r
,
=
,
=
r
,
2
r
2
2
r
2
is the angle made by
H
(1)
,
H
(2)
with the Earth's surface. Thus, the tippers calculated from these magnetic
fields are
where
r
is the distance between O
1
,O
2
and C, while
H
(1)
z
H
(1)
H
(2)
z
H
(2)
W
(1)
W
(2)
=
1
y
=−
1
y
,
=
1
y
=
1
y
.
tan
tan
y
y
Clearly they are directed away from the buried current.
The relations between the real and imaginer tippers can be illustrated by a
simple two-dimensional model consisting of three layers: sediments (
1
), resis-
tive lithosphere (
2
=∞
) and highly conductive mantle (
3
=
0). The sediments
1
). The model is excited by the
E
-
polarized field. Fi
gure 4.4 p
resents the tippers Re
W
and Im
W
for different
1
<<
contain a rectangular conductive inclusion (
λ
1
/
h
1
,
2
1
/
o
is the wavelength in sediments. Within the
S
1
-interval
where
λ
1
=
2
(
60), the real and imaginary tippers point away from the conduc-
tive inclusion center. On the transition to the
h
-interval (
λ
1
/
h
1
=
30
,
45
,
λ
1
/
h
1
=
100
,
150), the
PLAN
Re W
(1)
Re W
(2)
H
(1)
x
O
1
O
2
α
α
y
z
H
(2)
r
r
Fig. 4.3
Magnetic field of the
infinitely long rectilinear
direct current flowing
through a buried point C
C
CROSS-SECTION
