The Magnetization of Sedimentary Rocks: Processes and their Interpretation - Paleomagnetism of Sedimentary Rocks: Process and Interpretation - page 128

measure an infi nite number of samples, lies within the
95% confi dence limits of the mean obtained by your
markedly smaller dataset. The smaller the confi dence
limits the better but, whatever their size, they quantify
at what level of confi dence a paleomagnetic result can
be used to determine a vertical axis rotation, the posi-
tion of a plate or continent in the past or the variations
of the secular variation of the geomagnetic fi eld.
Tauxe (2010) has pointed out that many directional
distributions measured for paleomagnetic samples are
non-Fisherian. She has championed and pioneered the
statistical analysis of paleomagnetic directions using
bootstrap techniques that can be designed so they
do not make any assumptions about the directional
distribution of the paleomagnetic data. In bootstrap
analysis, the observed data distribution is resampled
thousands of times by a computer randomly selecting
different points from the original dataset. An estimate
of the mean direction and its confi dence limits are
derived from the scatter of the means calculated from
the multiple resampling of the dataset. In order for the
technique to work well, the initial dataset needs to be
large enough to withstand the multiple resamplings.
One way that paleomagnetic directional distribu-
tions are non-Fisherian is when they are elliptical.
Elliptical distributions are better statistically analyzed
with the Kent (1982) distribution that is the elliptical
analogue of the Fisher distribution. However, both
Fisher and Kent distributions assume that the direc-
tional distributions are one polarity. Obviously paleo-
magnetic directional distributions come in two fl avors
of reversed and normal polarity. Most geologists handle
the statistical analysis of bi-modal distributions by
inverting one of the polarity distributions through the
origin to create a distribution of one polarity. There is
always some ambiguity in this approach however, par-
ticularly if the results are scattered, since it is hard to
unequivocally determine the polarity of a very diver-
gent direction.
For these types of distributions, it is best to use
Bingham (1974) statistics that can handle bi-modal
direction distributions. However, Bingham statistics
assume that the two modes are antipodal, i.e. exactly
opposite to each other in direction; because of over-
printing or inadequate sampling of secular variation,
this is not always the case.
There are therefore advantages and drawbacks for
using each type of statistics for analysis. Fisher and
Bingham statistics are both widely used in paleomag-

netic data analysis. Recently, bootstrapping of paleo-
magnetic data has been gaining ground. Tauxe (2010)
gives more detailed coverage of different kinds of paleo-
magnetic data statistical analysis.
Most workers have found that thermal demagnetiza-
tion does a much better job than alternating fi eld
demagnetization in removing the multiple secondary
magnetizations in ancient (early Tertiary, Mesozoic,
Paleozoic, or Precambrian) sedimentary rocks and
so, for most modern paleomagnetism studies, it is the
demagnetization technique of choice. Alternating
fi eld demagnetization works well on young lake and
marine sediments that are diffi cult to heat because of
their high organic or water content. Alternating fi eld
demagnetization also works well on young glacial sedi-
ments that usually contain freshly eroded magnetite
liberated by intense mechanical weathering and not
appreciably affected by chemical alteration.
There are two common cases when thermal demag-
netization is problematic. If a sedimentary rock con-
tains secondary iron sulfi des, formed by reduction
diagenesis, the sulfi des often oxidize to magnetite at
heating near to the Curie Point of the iron sulfi des
( c. 300°C). The magnetite formed is usually unstable
magnetically and its magnetization masks the magnet-
ization of any stable, depositional magnetite present in
the rock that has higher unblocking temperatures
than the iron sulfi des, making it diffi cult to isolate
the initial depositional remanence carried by the
primary magnetite. Therefore, simple heating of an
iron - sulfi de-bearing rock above the 300°C sulfi de Curie
temperature does not necessarily isolate the magneti-
zation of the depositional magnetite in a rock. The
instability of the secondary magnetite formed during
heating is probably because it is very fi ne grained and
superparamagnetic.
The other case where thermal demagnetization does
not work particularly well is the removal of secondary
overprinting caused by lightning strikes. Lightning
strikes and the resulting huge currents through the
ground produce correspondingly very high magnetic
fi elds and strong natural IRMs. IRMs are diffi cult to
remove by thermal demagnetization, and so it is best to
avoid sampling localities struck by lightning. High
exposed ridges are particularly prone to lightning
strikes. Sometimes slowly sweeping a fi eld compass
along the ground near a potential sampling site and
watching for large defl ections of the compass needle
is a good way to identify, and avoid, places probably