Geology Reference
In-Depth Information
Fig. 6.8
Determination of
the inclination and
declination uncertainty
from the confidence cone
'
95
Fig. 6.9
Colatitude error,
dp
, and relationship
between declination
uncertainty, •
D
,and
trasversal uncertainty in the
paleopole direction,
dm
direction in terms of confidence limits for the
inclination and the declination, as illustrated in
Fig.
6.8
. From simple trigonometry, we have
that:
The colatitude error
dp
can be calculated using
the dipole equation (
6.40
). It results:
dI
•I
D
'
95
d™
d™
2'
95
1
C
3cos
2
I
dp
D
dI
D
tan '
95
cos I
2
'
95
1
C
3cos
2
™
•I
D
'
95
I
tan •D
D
(6.48)
1
D
(6.52)
where the second of these equations is usually
expressed in the approximated form:
The pair (
dp
,
dm
) is called
oval of 95
%
confi-
dence about the paleopole
. In an alternative ap-
proach, each site direction is converted first into a
virtual geomagnetic pole
(VGP). Then, the result-
ing set of VGPs is considered as a Fisher distribu-
tion and analyzed using the technique described
above. In this instance, conventions require that
the precision parameter and the 95 % confidence
cone be indicated by the capital symbols
K
and
A
95
, respectively (e.g., Van der Voo
1993
). It can
be shown that the approximate relation between
the confidence cone
A
95
and the uncertainties
dp
and
dm
is:
'
95
cosI
•D
Š
(6.49)
These uncertainties can be easily converted
into a confidence oval about the paleopole, with
mutually orthogonal semi-axes
dp
and
dm
,as
illustrated in Fig.
6.9
. Applying the spherical law
of sines we obtain:
sin dm
sin ıD
D
sin p
(6.50)
A
95
p
dpdm
(6.53)
Therefore,
'
95
sin p
cos I
Paleopoles
are
fundamental
quantities
dm
Š
•D sin p
D
(6.51)
in
the
application
of
paleomagnetism
to
