Geoscience Reference
In-Depth Information
Geomagnetic
North
Figure 3.5.
A cross
section through the Earth,
illustrating the
components of the dipole
field at a location P on the
surface. O is the centre of
the Earth,
θ
the colatitude
of P,
Z
and
H
are the
vertical and horizontal
components of
B
and
I
is
the angle of inclination.
H
B
I
P
Z
θ
O
It follows immediately that, at any point on the Earth's surface, the expression
B
r
has the constant value 4
B
0
.
B
0
is most simply visualized in practice
as being the equatorial field of the best-fitting dipole field (see Eq. (3.9)). The
strength of the field at the poles is about 6
+
4
B
2
θ
10
−
5
teslas (T) or 6
10
4
nanoteslas
×
×
(nT) (1 weber m
−
2
10
−
5
T(Fig. 3.1(a)).
In geomagnetic work, the inward radial component of the Earth's field is
usually called
Z
(it is the downward vertical at the Earth's surface) and is positive.
The horizontal magnitude (always positive) is called
H
.
Thus, for a dipole,
=
1 T), and at the equator it is about 3
×
Z
(
R
,
θ
,
φ
)
=−
B
r
(
R
,
θ
,
φ
)
(3.14)
H
(
R
,
θ
,
φ
)
=|
B
θ
(
R
,
θ
,
φ
)
|
(3.15)
At the surface of the Earth the angle between the magnetic field and the
horizontal is called the
inclination I
(Fig. 3.5):
Z
H
tan
I
=
(3.16)
Substituting for
B
r
and
B
θ
from Eqs. (3.12) and (3.13)gives
2 cos
θ
sin
θ
=
2 cot
θ
=
2 tan
λ
=
tan
I
(3.17)
). Equation (3.17) makes it a simple
matter to calculate the magnetic latitude, given the angle of inclination, and vice
versa. Mariners use the angle of inclination for navigational purposes.
The angle of
declination
is the azimuth of the horizontal component of the
magnetic field. It is measured in degrees east or west of north. Mariners call
it the variation or magnetic variation of the compass.
4
where
λ
is the magnetic latitude (
λ
=
90
−
θ
Figure 3.3(b) illustrates
4
The magnetic compass was a Chinese invention. Declination was described by Shen Kua in 1088.
