Geology Reference
In-Depth Information
1984 by two important articles of Livermore and
colleagues (Livermore et al.
1983
,
1984
). These
authors confirmed that the best substitute for the
dipole equation was the following expression,
which can be determined easily from (
6.64
)
retaining only dipole, quadrupole, and octupole
components:
with coefficients
g
2
and
g
3
, respectively. This
study confirmed the existence of non-dipole
components for the time interval between 130 Ma
(early Barremian) and the present day, although
the octupole component was negligible for times
older than 26 Ma. The study of Coupland and
VanderVoo(
1980
) was followed in 1983 and
2
g
2
3 cos
2
™
1
C
2g
3
cos ™
5 cos
2
™
3
g
1
sin ™
C
3g
2
sin ™ cos ™
C
3
2g
1
cos ™
C
tan I
D
(6.70)
3
2
g
3
sin ™.5cos
2
™
1/
This formula is usually written in the form:
2
g
2
=g
1
3 cos
2
™
1
C
2
g
3
=g
1
cos™
5 cos
2
™
3
sin ™
C
3
g
2
=g
1
sin ™ cos ™
C
3
2 cos™
C
tan I
D
(6.71)
2
g
3
=g
1
sin ™.5cos
2
™
1/
3
which evidences more clearly the dependence
of the inclination from the ratios
G
2
g
2
/
g
1
and
G
3
g
3
/
g
1
. Livermore and colleagues
found that
G
2
D
0.045
˙
0.015 for the last
35 Myrs, while
G
2
Š
0.10 between 40 and
60 Ma (Paleocene - Eocene), and it attained
negative values between
0.07 and
0.10 during
the Cretaceous and the Jurassic. Regarding the
octupole component, these authors suggested
the possibility that
G
3
Š
0.02 for the last
5 Myrs, although they questioned that this
result may be due to data errors. The effect
of low-order non-dipolar components on the
observed magnetic inclinations is illustrated in
Fig.
6.42
. We note that both the quadrupole
and octupole components determine
shallower
inclinations
in the
northern
hemisphere.
However, in the southern hemisphere inclinations
are
always
steeper only in the case of dipole-
quadrupole fields, because when the octupole
components have sufficiently large magnitude the
inclination will be shallower in both hemispheres.
Inclinations considerably shallower than those
predicted from APW paths were effectively
observed in central Asia (e.g., Si and Van der
Vo o
2001
and references therein).
On the basis of these observations, Si and Van
der Voo (
2001
) proposed a paleomagnetic field
geometry with negligible quadrupole component
and significant octupole component (
G
3
0.06)
for the time interval between the late Cretaceous
and the Tortonian. The difference between
inclination anomalies associated with quadrupole
and octupole components is illustrated in
Fig.
6.43
. We note that an octupole inclination
anomaly is antisymmetric with respect to the
Equator, whereas a quadrupole anomaly is always
negative and has its maximum at the Equator.
In another paper, Van der Voo and Torsvik
(
2001
) used a data set of N. American and
European paleopoles with ages between 300 and
40 Ma, comparing the observed paleolatitudes
with theoretical values predicted on the basis
of the dipole equation. These authors assumed
a paleomagnetic field geometry formed by a
GAD field plus a zonal octupole component,
obtaining
G
3
D
0.1. In a successive study, Torsvik
and Van der Voo (
2002
) confirmed this value
using stable Gondwana paleopoles. One of
the major issues addressed by these authors
was associated with the classic fits of Pangaea
(known as Pangaea
A
1 configurations, e.g., Van
