chapter1.tex

\chapter{Introduction}\label{chap:Intro}
\textit{The first chapter introduces paleomagnetism-based paleogeographic
reconstruction technique and highlights the motivation of the research conducted
in the thesis.}
\vfill
\minitoc\newpage

\section{Background and Motivation}

Reconstructing past paleogeographies, especially the motion of plates and their
interactions through time, is a key component of understanding the Earth's
geological history, including deciphering tectonics (e.g.\ supercontinent
reconstruction), paleo-climate history, and the evolution of life. Since the
advent of plate tectonics, it has been the background for nearly all geologic
events. In addition, plate reconstructions form the basis of global or regional
geodynamic models.

\subsection{Techniques Used in Relative and Absolute Plate Motion Studies}

The earliest quantitative effort to model plate kinematics was fitting conjugate
passive margins of the Atlantic~\citep{B65,W07}. They showed that the Atlantic
could be closed using a single Euler pole (using Euler's theorem on rotation).
Then it became fitting conjugate isochrons based on best-fitting marine magnetic
anomaly and fracture zone data~\citep{M71}, which minimizes the misfit area
between two isochrons. The \emph{Hellinger} method~\citep{H81} is a more
advanced and generalised method which also fits conjugate isochrons based on
best-fitting marine magnetic anomaly and fracture zone data, which minimizes the
sum of the misfits of conjugate data points that belong to common isochron
segments~\citep{W07}. These conjugate-line-fitting techniques are relatively
accurate for quantitative analysis. However they give relative, not absolute,
motions between plates, because plate motions can't be tied into absolute
location on Earth's surface, since both plates are likely moving. In addition,
they are limited to survey data from the seafloor, with a maximum age of no more
than ${\sim}200$ Ma~\citep{M08}.

Reference frames are a means of describing the motion of geologic features
(e.g.\ tectonic plates) on the surface of the Earth, relative to a common point
or ``frame''~\citep{Sh12}. An absolute reference frame is a frame that can be
treated as fixed relative to the Earth's geographic reference frame. In reality,
it's impossible to find a truly absolute reference frame, so we are actually
looking for a frame that has limited (and hopefully known) motion, which
approximates as ``fixed'' over geologically useful timescales and provides the
most complete descriptions of plate motions. A commonly used absolute reference
frame is the ``Fixed-hotspot model''~\citep{M93,M99}, covering ages from
${\sim}132$ Ma to present-day, which assumes that the linear volcanic chains
found on most oceanic plates are artifacts of absolute plate motions over a
upwelling plume from the deep mantle, which is assumed to be relatively fixed.
The advantage of this ``Fixed-hotspot model'' is that it is fairly
straightforward if the assumption of fixed hotspots is correct. However, this
model is limited to plates with well-dated volcanic hotspot chains~\citep[e.g.\
the Ninetyeast Ridge on the Indian Ocean floor and the Walvis Ridge in the
southern Atlantic Ocean, see][]{O05} and dating can be difficult~\citep[e.g.\
diffuse volcanic centers possibly related to large diameter plume conduits could
cause the existence of time reversals, see][]{O05}. As for not well-dated
hotspot tracks, for example, only about 5\textperthousand\ of the seamounts
(thought to be volcanic) in the Pacific are thought be be related to hotspot
volcanism and radiometrically dated~\citep[39 per cent of these ages are less
than 10 Ma, see][]{H07}. In addition, the fixed-hotspot model is mostly confined
to existing oceanic or thin continental crust because older oceanic lithosphere
has been largely destroyed by subduction and old, thick continental crust mostly
removed by erosion~\citep{C13}. Last, but not least, hotspots can be susceptible
to drift that may be caused by changes in sub-lithospheric mantle
flow~\citep{T09}. Generally, however, the drift rate is considered to be an
order of magnitude less than the rate of plate motions, so only becomes
significant over timescales of ${\sim}50$ Myr or more~\citep{O05,T07}. To
overcome this source of error, the ``Moving-hotspot model''~\citep{O05} uses
mantle convection modeling to predict hotspot drift. This approach has achieved
some apparent success, e.g.\ by getting motions in the Indo-Atlantic and Pacific
hotspot clusters to agree with each other, but it's very dependent on the mantle
convection model used. Hybrid models attempt to overcome the shortcomings of
each reference frame by combining them, e.g.\ combining a fixed-hotspot frame
from 100 Ma to 0 Ma~\citep{M93} with a moving-hotspot frame from
${\sim}132$\textendash100 Ma~\citep{O05}~\citep[Hybrid hotspot model,
see][]{Sh12}, combining a moving-hotspot frame from 100\textendash0
Ma~\citep{O05} with a paleomagnetic model (which reflects plate motion relative
to the magnetic dipole axis but cannot provide paleolongitudes because of the
axial symmetry of the Earth's magnetic dipole field)~\citep{T08} from
140\textendash100 Ma~\citep[Hybrid paleomagnetic model, see][]{Sh12}, and
combining a moving-hotspot frame from 120\textendash100 Ma~\citep{O05} with a
true polar wander (TPW) corrected paleomagnetic model~\citep{S08} from
100\textendash0 Ma~\citep[Hybrid TPW-corrected model, see][]{Sh12}.

Recently another absolute reference frame ``Subduction reference
model''~\citep{v10} tries to connect orogenies/sutures/subduction complexes on
the Earth surface with their corresponding subducted slabs in the mantle.
Assuming that these remnants sank vertically through the mantle, the absolute
location at which they were subducted can be reconstructed. In this way, this
model mainly imposes a longitude correction on the above mentioned ``Hybrid
TPW-corrected model'', and can theoretically give past absolute locations of
plates back to ${\sim}260$ Ma based on the estimated age of the oldest slab
remnants that can be reliably located in the mantle. While the ``Subduction
reference model'' allows for reconstructions between ${\sim}260$ Ma and 140 Ma,
older than the other absolute models can predict, the model is strongly
dependent on the vertical subduction assumption and resolution of seismic
tomography models, so its uncertainty is high. Above all, importantly, if we can
describe the absolute motion of one or a few key plates, the techniques for
establishing the relative plate motions described in the second paragraph above
can be used to construct plate circuits that allow a full kinematic description
of plate tectonics to be developed.

As we can see, all of these above reconstruction methods are limited to recent
geological history. For most of Earth history, concretely for times before
${\sim}170$ Ma, the age of the oldest magnetic anomaly identification,
paleomagnetism is the only accepted quantitative method for reconstructing plate
motions and past paleogeographies.

\subsection{Application of Paleomagnetism to Plate
Tectonics}\label{sec:applPlateTec}

\begin{figure}[!ht]
  \centering
    \includegraphics[width=0.88\textwidth]{../sphinx/source/I/fig/GAD.pdf}
  \captionsetup{width=.95\textwidth}
  \caption[Geocentric axial dipole model]{GAD model: Inclination (angle I =
    $\tan^{-1}(2\tan\lambda)$) of the Earth's magnetic field and how it varies
    with latitude, redrawn from~\citet{B92,T08,T20}. Magnetic dipole M is placed
    at the center of the Earth and aligned with the rotation axis; $\lambda$ is
    the geographic latitude, and $\theta$ is the
    colatitude.}\label{Fig:chap_intro_gad}
\end{figure}

The geomagnetic field is generated by the convective flow of a liquid
iron-nickel alloy in the outer core of the Earth. It is largely dipolar and can
be represented by a dipole that points from the north magnetic pole to the south
pole. However, the geomagnetic field varies in strength and direction over
decadal\textendash{}millennial timescales due to quadropole and octopole
components of the field. The most spectacular variations in direction are
occasional polarity reversals (normal polarity: the same as the present
direction of the field; or the opposite, i.e.\ reverse polarity). Over a period
of a few thousand years, the magnetic axis slowly migrates around the Earth's
rotational (geographic) axis (secular variation), but when averaged over 10,000
year timescales, higher order components of the field are thought to largely
cancel out and the position of the magnetic poles aligns with the geographic
poles. This is the geocentric axial dipole (GAD) hypothesis. In a GAD field, at
the north magnetic pole the inclination (angle with respect to the local
horizontal plane, see for example angle I in Fig.~\ref{Fig:chap_intro_gad}) of
the field is +90\degree\ (straight down), at the Equator the field inclination
is 0\degree\ (horizontal) pointing north and at the south magnetic pole the
inclination is -90\degree\ (straight up) (Fig.~\ref{Fig:chap_intro_gad}).
Another direction parameter of the Earth's magnetic field is declination. It is
the angle with respect to the geographic meridian, which is 0\degree\ everywhere
in a time-averaged GAD field.

Magnetic remanence is the magnetization left behind in a ferromagnetic substance
in the absence of an external magnetic field~\citep{T20}. The remanent
magnetisation of rocks can preserve the direction and intensity of the
geomagnetic field when the rock was formed, e.g.\ in the process of cooling,
ferromagnetic materials in the lava flow are magnetized in the direction of the
Earth's magnetic field, so the local direction of the field vector is locked in
solidified lava. We are often interested in whether the geomagnetic pole has
changed, or whether a particular plate/terrane has rotated with respect to the
geomagnetic pole~\citep{T20}. By measuring the direction of the remanent
magnetisation, we can calculate a virtual geomagnetic pole (VGP) to represent
the geomagnetic pole of an imaginary geocentric dipole which would give rise to
the observed remanent declination and inclination. Collection of VGPs (or
site-mean directions) allow calculating a ``paleomagnetic pole'', also known as
paleopole, at the formation level. Commonly a paleopole is a \emph{Fisherian}
mean~\citep{F53} of VGPs with a spatial uncertainty. A paleopole that plots away
from the present geographic poles is assumed to be due to plate motions since
the lava was solidified, which causes the paleopole to move with the
plate~\citep{T08}. Based on measurements of the remanent inclination, the
ancient latitude $\lambda$ for a plate can be calculated when the rock formed
from the dipole formula $\tan(I) = 2 \times\tan(\lambda)$
(Fig.~\ref{Fig:chap_intro_gad}). In addition, the remanent declination provides
information about the rotation of a plate. Ideally, as a time average, a
paleopole (which can be calculated from declination, inclination and the current
geographic location of the sampling site) for a newly formed rock will
correspond with the geographic north or south pole. To perform a reconstruction
with paleopoles we therefore have to calculate the rotation (Euler) pole and
angle which will bring the paleopole back to the geographic north or south pole,
and then rotate the plate by the same amount of angle using the same Euler pole.
This is how paleomagnetism can be used to reconstruct past positions of a plate.
In our example (Fig.~\ref{Fig:chap_intro_reconstructpole}), a ${\sim}155$ Ma
paleopole (latitude=52.59\degree{}N, longitude=91.45\degree{}W) will be restored
to the geographic pole by an Euler rotation of pole (0\degree, 178.55\degree{}E)
with angle 37.41\degree, which rotates the sampling site from its present
position of (0\degree, 25\degree{}E) to the Africa paleo-continent at
(15.7\degree{}S, 20.11\degree{}E). So Africa must have drifted northwards since
the Late Jurassic.

\begin{figure}[!ht]
  \centering
    \includegraphics[width=0.88\textwidth]{../sphinx/source/I/fig/af.pdf}
  \captionsetup{width=.95\textwidth}
  \caption[The hemispheric ambiguity and absolute paleolongitude indeterminacy
  with a single paleomagnetic pole (paleopole)]{Reconstruction of Africa with
  its ${\sim}155$ Ma paleopole. The red polygon is today's position of Africa,
  while the blue and green ones shows its reconstructed position at ${\sim}155$
  Ma, if the pole was North and South pole, respectively. Dashed green polygon
  illustrates the ambiguity of paleolongitude from paleomagnetic data alone
  (sites at same latitude but different longitudes record the same Declination
  and Inclination in a GAD field).}\label{Fig:chap_intro_reconstructpole}
\end{figure}

However, there are 2 problems with using paleopoles for constraining finite
rotations~\citep{T20}. First, if only one paleopole is given alone without any
geologic context, its polarity can be ambiguous, i.e.\ an upward inclination may
be due to being located in the southern hemisphere during a normal polarity
chron, or in the northern hemisphere during a reversed polarity chron (cf.\ the
solid blue and solid green Africa in Fig.~\ref{Fig:chap_intro_reconstructpole}).
In other words, we can't know if it's North pole or South pole, especially for
paleomagnetic data with Precambrian and early Paleozoic ages. Returning to the
example above, if the ${\sim}155$ Ma paleopole (52.59\degree{}N,
91.45\degree{}W) was formed during a period of reversed polarity, then it needs
to be rotated to the South pole rather than the North pole. The necessary Euler
rotation of pole (0\degree, 1.45\degree{}W) and angle 142.59\degree\ rotates the
sampling site (0\degree, 25\degree{}E) on Africa to (15.7\degree{}N,
23.01\degree{}W) indicating southward motion since the Late Jurassic. Second,
because in a GAD field the declination equals zero everywhere
(Fig.~\ref{Fig:chap_intro_reconstructpole}), paleomagnetic data doesn't register
longitudinal motions of plates (the Euler pole for a plate moving purely to the
east or west is at the geographic poles, so preserved paleopoles will experience
zero rotation), which means we can position a plate at any longitude we wish
subject to other geological constraints (cf.\ the solid and dashed green Africa
in Fig.~\ref{Fig:chap_intro_reconstructpole}).

The data source used in this thesis is \emph{Global Paleomagnetic
Database} (GPMDB) Version 4.6b~\cite[updated in 2016 by the Ivar Giaever
Geomagnetic Laboratory team, in collaboration with Pisarevsky]{M96,P05}, which
includes 9514 paleopoles for ages of 3,500 Ma to the present published from 1925
to 2016. GPMDB has been published in two ways: (1) IAGA GPMDB 4.6 online query:
\url{http://www.ngu.no/geodynamics/gpmdb/}, which is now closed; (2) Microsoft
Access system in \emph{.mdb} format at NOAA's National Geophysical Data Center
\url{https://www.ngdc.noaa.gov/geomag/paleo.shtml}~\citep{P03}
and CESRE's Paleomagnetism and Rock Magnetism project
\url{https://wiki.csiro.au/display/cmfr/Palaeomagnetism+and+Rock+Magnetism},
which is later updated to 4.6b by Ivar Giaever Geomagnetic Laboratory
\url{http://www.iggl.no/resources.html\#data}.

An apparent polar wander path (APWP) is composed of poles of different ages
from different sampling sites on the same stable (non-deforming) continent,
chained together to form a record of motion relative to the fixed magnetic pole
over geological time. It represents a convenient way of summarizing
paleomagnetic data for a plate instead of producing paleogeographic maps at
each geological period~\citep{T08}. As a preliminary study, the \emph{North
American Craton} (NAC) is chosen as a research object to develop techniques we
want to think about. The NAC is one of best studied cratons in paleomagnetism
with the GPMDB 4.6b containing 2160 paleopoles published since 1948
(Fig.~\ref{Fig:chap_intro_nacpole}). If we observe the latitudes, longitudes and
age distribution of the NAC paleopoles (Fig.~\ref{Fig:chap_intro_nacpole}), we
actually can identify the general trend of its APWP\@. However, converting this
data into a reliable, well-defined APWP can be challenging, due to the following
issues:

\subsection{Fact 1: Not All Regions on the Earth Surface Are
Solid}\label{sec:f1}

If we consider the modern North American continent, the region west of the
Rockies is actively deforming. Paleomagnetic data from such areas are likely to
reflect local tectonic processes such as block rotation rather than rigid plate
motions, and should be excluded. For example, the Rockies Mountain area was not
included in my data selecting polygon (the transparent yellow area in
Fig.~\ref{Fig:chap_intro_nacpole}). In order to investigate a specific craton or
terrane or block's past paleogeographic motion, choosing an appropriate
subregion without active tectonics, e.g.\ rotation, uplift or rifting, to select
data is often required. Such tectonics-free regions are usually called rigid.
However, the difficulty of defining such tectonic boundaries makes appropriate
spatial and temporal choices very difficult, particularly further in the
geological past when cratonic configurations and active plate boundaries were
very different to today. This leads to a question: What is the best way to
constrain the data for a specific plate or block? The solution proposed in this
thesis is described in Appendix~\ref{appen4chp3}.

\subsection{Fact 2: Not All Data Are Created Equal}\label{sec:f2}

APWPs are generated by combining paleopoles for a particular rigid block over
the desired age range to produce a smoothed path. However, the NAC dataset
illustrates that uncertainties in the age and location of different paleopoles
in the GPMDB can vary greatly (Fig.~\ref{Fig:chap_intro_nacpole}).

\subsubsection{Age Uncertainty}\label{sec:ageu}

Although remanent magnetizations are generally assumed to be primary, many
events can cause remagnetisation (in which case the derived pole is `younger'
than the rock). If an event that has occurred since the rock's formation that
should affect the magnetisation (e.g.\ folding, thermal overprinting due to
igneous intrusion, etc.) can be shown to have affected it, then it constrains
the magnetisation to have been acquired before that event. Recognising or ruling
out remagnetisations depends on these field tests, which are not always
performed or possible. Even a passed field test may not be useful if field test
shows magnetisation acquired prior to a folding event tens of millions of years
after initial rock formation.

The most obvious characteristic we can observe from the NAC paleomagnetic data
(Fig.~\ref{Fig:chap_intro_nacpole}) is that some paleopoles have very large age
ranges, e.g.\ more than 100 Myr. The magnetization age should be some time
between the information of the rock and folding events. There are also others
where we have similar position but the age constraint is much narrower, e.g.\ 10
Myr window or less. Obviously the latter kind of data is more valuable than the
one with large age range.

\begin{figure}[H]
  \centering
  \includegraphics[width=1\textwidth]{../../pps/poster/fig/na.pdf}
  \captionsetup{width=1\textwidth}
  \caption[All published paleomagnetic data from North America]{Much
    paleomagnetic data has been collected from the North American Craton. For
    younger geologic times, do we really need so much data to reconstruct
    accurately just like modern-day plate motions? The image shows distribution
    of all published paleopoles of the NAC over time, which are compiled from
    GPMDB 4.6b~\citep{P05} and PALEOMAGIA~\citep{V14}.}\label{Fig:chap_intro_nacpole}
\end{figure}

\subsubsection{Position Uncertainty}\label{sec:posu}

The uncertainties of paleopole latitudes and longitudes are plotted as 95\%
confidence ellipses (cf.\ the transparent red ovals in
Fig.~\ref{Fig:chap_intro_nacpole}), which also vary greatly in magnitude. All
paleopoles have some associated uncertainties due to measurement error and the
nature of the geomagnetic field. More uncertainties can be added by too few
samples, sampling spanning too short a time range to approximate a GAD field,
failure to remove overprints during demagnetisation, etc.

\subsubsection{Data Consistency}\label{sec:datcons}

Paleopoles of a rigid plate or block should be continuous time series. For a
rigid plate, two paleopoles with similar ages shouldn't be dramatically
different in location. We want to look at the consistency of the NAC and India's
data over smaller time periods, so the data is binned over a small time interval
(e.g.\ 2 Myr) to see whether the paleopoles in each time interval overlap within
their uncertainty ellipses, as they should. Sometimes, this is the case
(Fig.~\ref{Fig:chap_intro_na6462agemean}). Sometimes we have further separated
poles with close ages (Fig.~\ref{Fig:chap_intro_in97agemean}).

\begin{figure*}[!ht]
  \captionsetup[subfigure]{labelformat=empty,aboveskip=-6pt,belowskip=-6pt}
  \centering
  \begin{subfigure}[htbp]{.49\textwidth}
    \captionsetup{skip=0pt}  % local setting for this subfigure
    \centering
    \includegraphics[width=1.01\linewidth]{../sphinx/source/I/fig/na6462.pdf}
    \caption{North America: 64\textendash62 Ma (mean age)}\label{Fig:chap_intro_na6462agemean}
  \end{subfigure}
  \begin{subfigure}[htbp]{.49\textwidth}
    \captionsetup{skip=0pt}
    \centering
    \includegraphics[width=1.01\linewidth]{../sphinx/source/I/fig/in97.pdf}
    \caption{India: 9\textendash7 Ma (mean age)}\label{Fig:chap_intro_in97agemean}
  \end{subfigure}
  \caption[Example of AMP moving averaging effects]{Overlapping and further
    separated paleopoles of the NAC\@ and India. The oval ellipses are their
    95\% confidence uncertainties. The labels are their result number given in
    GPMDB 4.6b.}\phantomsection\label{Fig:chap_intro_ma-amp}
\end{figure*}

There are a number of possible causes for these outliers, including:

\paragraph{Lithology}

For this poor consistency of data (Fig.~\ref{Fig:chap_intro_in97agemean}), it is
potentially because of different inclinations or declinations. The first thing
we should consider about is their lithology. We want to check if the sample rock
are igneous or sedimentary, because sediment compaction can result in
anomalously shallow inclinations~\citep{T20}. In addition, we also can check if
the rock are redbeds or non-redbeds. Although whether redbeds record a detrital
signal or a later \emph{chemical remanent magnetization} is still somewhat
controversial, both sedimentary rocks and redbeds could lead to inconsistency in
direction compared to igneous rocks. For this case, all the three paleopoles
(Fig.~\ref{Fig:chap_intro_in97agemean}) are from sedimentary rocks. In addition,
pole 1136 and 1137 (Result Number in GPMDB 4.6b)'s source rocks also contain
redbeds~\citep{O82}, although the authors did not mention about the potential
inclination shallowing. For pole 7095, although the source rocks do not contain
redbeds, the authors did mention about possible inclination shallowing due to
haematite grains~\citep{G94}.

\paragraph{Local Rotations}

As discussed previously, local deformation between two paleomagnetic localities
invalidates the rigid plate assumption and could lead to inconsistent paleopole
directions. All the three paleopoles (Fig.~\ref{Fig:chap_intro_in97agemean})
contain signals of local rotations~\citep{O82,G94}, e.g.\ pole 7095 has a signal
which suggests the presence of a counter-clockwise local rotation of the Tinau
Khola section~\citep{G94}, and therefore do not reflect motions of the whole
rigid India plate in this case. So the discordance is likely due to local
deformation (Fig.~\ref{Fig:chap_intro_in97agemean}), and we would ideally
want to exclude or correct such poles from our APWP calculation.

\paragraph{Other Factors}

In Fig.~\ref{Fig:chap_intro_ma-amp}, mean pole age (centre of age uncertainty)
has just been binned. If any of the paleopoles have large age uncertainties,
they could be different ages from each other and sample entirely different parts
of the APWP\@. Conversely, if any of the paleopoles have too few samples, or
were not sampled over enough time to average to a GAD field, a discordant pole
may be due to unreduced secular variation, because in order to average errors in
orientation of the samples and scatter caused by secular variation, a
``sufficient'' number of individually oriented samples from ``enough'' sites
must be satisfied~\citep{v90,B02,T20}. For example, pole 1136
(Fig.~\ref{Fig:chap_intro_in97agemean}) is from only 4 sampling sites, pole 1137
is from only 3 sites and number of pole 7095's sampling sites is not even given
in the GPMDB 4.6b.

\subsubsection{Data Density}\label{sec:datden}

As we go back in time, we have lower quality and lower density (or quantity) of
data, for example, Precambrian or Early Paleozoic paleopoles are relatively
fewer than Middle-Late Phanerozoic ones, and most of them are not high-quality,
e.g.\ larger uncertainties in both age and location
(Fig.~\ref{Fig:chap_intro_nacpole}). The combination of lower data quality with
lower data density means that a single `bad' paleopole (with large uncertainties
in age and/or location) can much more easily distort the reconstructed APWP,
because there are few or no `good' paleopoles to counteract its influence.

Data density also varies between different plates. For example, we have a
relatively high density of paleomagnetic data for the NAC, but few paleopoles
exist for Greenland and Arabia. Based on mean age (mean of lower and upper
magnetic ages), for 120\textendash0 Ma, GPMDB 4.6b has more than 130 paleopoles
for the NAC, but only 17 for Greenland and 24 for Arabia.

\subsubsection{Publication Year}\label{sec:puby}

The time when the data was published should also be considered, because
paleomagnetic measuring methodology, technology and equipment have been improved
since the early $20^{th}$ century. For example, stepwise demagnetisation, which
is the most reliable method of detecting and removing secondary overprints, has
only been in common use since the mid 1980s.

In summary, not all paleopoles are created equal, which leads to an important
question: how to best combine poles of varying quality into a coherent and
accurate APWP\@? Paleomagnetists have proposed a variety of methods to filter
so-called ``bad'' data, or give lower weights to those ``bad'' data before
generating an APWP, e.g.\ two widely used methods: the V90 reliability
criteria~\citep{v90} and the BC02 selection criteria~\citep{B02}. Briefly, the
V90 criteria for paleomagnetic results includes seven criteria: (1) Well
determined rock age and that magnetization age is the same is presumed; (2) At
least 25 samples reported with \emph{Fisher} precision $\kappa$~\citep{F53} greater
than 10 and $\alpha$95 less than 16\degree; (3) Detailed demagnetisation results
reported; (4) Passed field tests; (5) Tectonic coherence with continent and good
structural control; (6) Identified antipodal reversals; (7) Lack of similarity
with younger poles~\citep{T92}. Compared with V90, the BC02 criteria suggests
stricter filtering, e.g.\ using only poles with at least 6 sampling sites and 36
samples, each site having $\alpha$95 less than 10\degree\ in the Cenozoic and
15\degree\ in the Mesozoic. There are many potential ways to weight the data set
which could obviously greatly influence the final result, and we want to test
this. But there has been limited study of how effective these
filtering/weighting methods are at reconstructing a `true' APWP, and for most
studies after a basic filtering of `low quality' poles, the remaining poles are,
in fact, treated equally.

\section{Objectives}

Our overarching aims are to develop rigorous, consistent and well-documented
methods of reconstructing plate motions using paleomagnetic data, and to
investigate the limits of paleomagnetic data on reconstructing individual plate
motions.

\subsection{Motivation and General Approach}

How has plate tectonics evolved over geologic history, in terms of average plate
velocities, numbers of plates and so on? The only quantitative data we have
prior to ${\sim}170$ Ma are paleomagnetic data. We know there are limitations to
paleomagnetic data, because we can't constrain the longitudes of paleo-plates
very well. When we look back through geologic history, how much good
paleomagnetic data do we have, and how well does it reconstruct `true' plate
motions? We don't know well the effects of data quality and density, which
generally degrades further back in geologic history, on producing reliable
APWPs. For the past ${\sim}130$\textendash200 Myr we have the highest density of
paleomagnetic data and also independent plate motion data from reconstructions
of ocean spreading combined with hotspot reference frames. These independent
data sources can help constrain plate motions in more accurate ways. This allows
us to ask the question: What path-generating method and how much paleomagnetic
data do we need actually to reconstruct accurately known modern-day plate
motions? If we can handle that, we can go back in time. For a certain density of
paleomagnetic data that we have, how reliably can we talk about what's going on
in the past given the much lower data distribution? It might turn out we don't
need very much data to say something reasonably and reliably. We can test this
by looking at the last 0\textendash120 Ma where we can compare paleomagnetically
derived plate motions with other more accurate methods of paleogeographic
reconstruction. This does not only include the work of developing tools and
algorithms to generate those paleomagnetically derived plate motions (to use
paleomagnetic data to reconstruct APWP parameters that are known from other
sources like ocean basins and hotspots), but also need us to know how good these
tools are or which one is the best algorithm (to compare paleomagnetic APWPs
with the known data sources predicted APWP). In short, this can give insights
into how well we can `know' plate motions back in the past, and what
path-generating method, data quality and density are necessary to reliably
reconstruct a `true' APWP\@.

As a preliminary analysis, some algorithms were made to separate/calculate out
so-called good paleomagnetic data (at any particular time period for a
particular craton, like here from ${\sim}120$ Ma to the present day for the
NAC, India and Australia). We are interested in what makes `good' data, how we
can identify them and filter them out from the database, and how sometimes `bad'
data are only bad in the sense that it is poorly constrained in age or position
or any other parameter, in which cases it might be possible to include it by
e.g., weighting. A weighted mean pole can be calculated for a time interval with
`better' (more likely to be reliable) paleopoles counting more than `worse'. For
example, a paleopole with small $\alpha$95 and very well constrained age is more
likely to reflect APWP position at the selected age point than a paleopole with
large $\alpha$95 and very broad age range. Then an algorithm that compares
similarity between paleomagnetic APWP and known-data-predicted APWP and also
gives scores should be developed. So that best path-generating method and data
quality are used to make a reliable paleomagnetic APWP\@. The validity of this
algorithm should also be tested.

\subsection{Research Questions or Hypotheses}

Questions 1\textendash2 focus on method development, whereas 3 starts
using them for plate tectonic research in modern geologic era, potentially
further back in geological time.

\subsubsection{Question 1}

What is the best way to turn a collection of individual paleopoles, with
different age constraints and uncertainties, into a smoothed APW path? This
question, in fact, is about how to (1) choose a data-constraining polygon that
represents a solid continent during a certain period; (2) pick (or bin) data
within a certain window for \emph{Fisher} statistical~\citep{F53} calculation; (3) do
weighting for picked data according to different uncertainties or other kinds of
standards of qualifications; (4) if the derived APWP is still not smoothed
enough when compared with a reference path, is further smoothing necessary? Our
goal here actually is to get a reliable result, i.e.\ a path generated to
approximate the `real' APWP with appropriate uncertainties.

\subsubsection{Question 2}

Based on the consequences from the algorithms we developed, we can do research
on why some algorithms are good, others bad for all plates? Why some algorithm
performs well for a plate or two but not others?

\subsubsection{Question 3}

What kind of dataset (in terms of data density and quality) is needed to
accurately reconstruct a known APWP, or a shared APWP between two cratons? If
Some criteria could be established for this. Does it provide any insights into
past reconstructions of plate motions (e.g., Rodinia)?

\bigskip
In summary, this thesis starts the research from studying modern paleomagnetic
datasets to attempt to find a general or even universal methodology that also
could be applied onto deep-time paleopoles.