appendix2.tex

\chapter{Methods for Constraining Paleopoles for Tectonic Plates in Chapter 3}\label{appen4chp3}

(All the datasets used for Chapter~\ref{chap:Reliab} are openly accessible from
\url{https://github.com/f-i/making\_of\_reliable\_APWPs}.)

A polygon can be drawn around a set of paleomagnetic data, whose sampling sites
we believe belong to a specific plate or rigid block. Each such plate tectonic
polygon is assigned with an unique identification code, which is called Plate
ID\@. Then the {\em Spatial Join\/} technique~\citep{J07} helps join attributes,
especially Plate ID, from the polygon to the paleomagnetic data based on the
spatial relationship allowing data within this polygon to be extracted from the
whole raw large dataset without splitting a subset just for a specific plate.
That allows us to quickly select subsets of the database based on geographic
constraints just as easily as for age. Of course, the boundary of this polygon
must be reasonably along a tectonic boundary. Regions like those close to the
plate boundaries are usually tectonically active (e.g.\ local rotations), so we
should also be careful when we deal with the paleopoles derived from this type
of locations.

\section{120\textendash0 Ma North America}

\begin{figure}[!ht]
\includegraphics[scale=.75]{../../paper/tex/GeophysJInt/figures/Appendix/101.pdf}
  \caption[Final filtered datasets for analysis on 120\textendash0 Ma North
America]{The final filtered datasets (red triangle-inside-circles) for later
analysis on 120\textendash0 Ma North America. Those poles that had been
influenced by local tectonic rotations are shown as white
circles.}\label{fig_NAfinal}
\end{figure}

The data-constraining polygons are from the recently published plate
model~\citep{Y18} (Fig.~\ref{fig_NAfinal}). North American craton (Plate ID 101)
polygon in the plate model~\citep{Y18}, including its children 108
(Avalon/Acadia block) and 109 (Piedmont block) polygons for 120\textendash0 Ma,
is used to select the sampling sites of the paleopoles for North America.
According to the plate model rotation data~\citep{Y18}, 108 is fixed to 101
during the geologic period from Cretaceous to the present day. 109 is also fixed
to 101 since ${\sim}300$ Ma~\citep{C14}. Then in order to be compared with the
FHM (120\textendash0 Ma)~\citep{M93,M99}, the paleopoles with age ranging
120\textendash0 Ma are further selected through constraining the lower magnetic
age ``LOMAGAGE $<=$ 135'' (here it is not 120 but 135, because for the lower
resolution case when the window length is 30 Myr, the Age Position Picking
method will include those data with their lower magnetic age between 120 Ma and
135 Ma). In addition, the RESULTNO=6007 dataset should also be included
according to a published plate kinematic model~\citep{Mc06}
with a relatively higher resolution of polygons and
rotations, although the dataset is in the PlateID=178 polygon. In the end, 193
datasets in total are extracted (both white circles and red
triangle-inside-circles in Fig.~\ref{fig_NAfinal}).

\begin{figure}[!ht]
  \includegraphics[scale=.75]{../../paper/tex/GeophysJInt/figures/Appendix/501.pdf}
  \caption[Final filtered datasets for analysis on 120\textendash0 Ma India]{The
    final filtered datasets (red triangle-inside-circles) for later analysis on
    120\textendash0 Ma India. Those poles that had been influenced by local
    tectonic rotations are shown as white circles. The rifts, faults and
    detachments (red lines) around India are used to filter out those data that
    are influenced by local tectonic rotations.}\label{fig_INfinal}
\end{figure}

Also based on this model of southwestern North America since 36 Ma~\citep{Mc06},
part of the paleopoles constrained by the four small western terranes whose
Plate IDs are also 101 (white circles in Fig.~\ref{fig_NAfinal}) in fact had gone through regional
rotations and here are removed. However, the poles with age younger than 10 Ma
located within the largest western 101 terrane (on the south of the smallest
western 101 terrane; corresponding to the RANGE\_ID=74 polygon in the
model~\citep{Mc06}) should be included. So finally 135 of the 193 datasets remain
(Fig.~\ref{fig_NAfinal}). Spatially North American paleomagnetic data are mainly
from the western and eastern margins of the plate.

\section{120\textendash0 Ma India}

Plate ID 501 polygons in the recently published Plate Model~\citep{Y18} also
include the two small polygons of the northern ``Lesser Himalayan passive
margin of Greater Indian Basin'' and ``Tethyan Himalayan microcontinent of
Greater India'' (Fig.~\ref{fig_INfinal}). The polygons are used to select the
sampling sites of the paleopoles for India (Fig.~\ref{fig_INfinal}).

Based on the model of the tectonic interactions between India, Arabia and Asia
since the Jurassic~\citep{G15} (Fig.~\ref{fig_INfinal}), part of the paleopoles
constrained by the north two small terranes whose Plate IDs are also 501 in fact
had gone through regional rotations and here are removed. So finally 75 datasets
are left (Fig.~\ref{fig_INfinal}). Spatially Indian paleomagnetic data are more
evenly distributed on the India plate than North American and Australian poles.

\begin{figure}[!ht]
\includegraphics[scale=.75]{../../paper/tex/GeophysJInt/figures/Appendix/801.pdf}
\caption[Final filtered datasets for analysis on 120\textendash0 Ma
Australia]{The final filtered datasets (red triangle-inside-circles) for later
analysis on 120\textendash0 Ma Australia. Those poles that had been influenced
by local tectonic rotations are shown as white circles. The Plate ID 850 helps
increase the amount of qualified datasets for 100\textendash0
Ma.}\label{fig_AUfinal}
\end{figure}

\section{120\textendash0 Ma Australia}

Plate ID 801 polygon in the recently published Plate Model~\citep{Y18}, including
its children 675 (Sumba block) and 684 (Timor block) polygons for
120\textendash0 Ma (Fig.~\ref{fig_AUfinal}), is used to select the sampling
sites of the paleopoles for Australia. According to the plate model rotation
data~\citep{Y18}, 675 and 684 are fixed to 801 during the geologic period from
${\sim}145$ Ma to the present.

On the southeast of the main Australia plate (the blue polygon in
Fig.~\ref{fig_AUfinal}), there is a triangle-shaped small polygon 850
(Tasmania block) which is fixed to 801 since ${\sim}100$ Ma according to
the~\citet{Y18} rotation data. With that attribute, 850 contributes more data
younger than ${\sim}100$ Ma for the later analysis. Ultimately the final 99 extracted
datasets is shown in Fig.~\ref{fig_AUfinal}.

\begin{landscape}
\footnotesize
\setlength\LTleft{-7mm}
\setlength{\tabcolsep}{1pt}
  \begin{longtable}{@{}lllllllllllll>{\scriptsize}p{3.1cm}@{}}
\caption{Rotation parameters for making three reference paths}\label{tab:rot}\\
\toprule
Moving-Fixed & Chron & Age (Ma) & Lat (\degree) & Long (\degree) & Rot (\degree) & $\hat{\kappa}$ & a & b & c & d & e & f & Source \\* \midrule
\endfirsthead%
\multicolumn{14}{c}%
{{\bfseries Table \thetable\ continued from previous page}} \\
\toprule
Moving-Fixed & Chron & Age (Ma) & Lat (\degree) & Long (\degree) & Rot (\degree) & $\hat{\kappa}$ & a & b & c & d & e & f & Source \\* \midrule
\endhead%
\bottomrule
\endfoot%
\endlastfoot%
NAm-Nubia & 1no & 0.78 & 79.2 & 40.2 & 0.18 & 1 & 7.41E-9 & -5.77E-9 & 4.29E-9 & 5.93E-9 & -3.35E-9 & 5.15E-9 & Demets et al. 2010 \\
NAm-Nubia$\dagger$ & 2An & 2.7 & 78.8 & 38.3 & 0.65 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Cande et al. 1995 Shephard et al. EPSL2012 Gurnis et al. CG2012 \\
NAm-Nubia$\dagger$ & 5n.1ny & 9.74 & 80.98 & 22.82 & 2.478 & 2.46 & 4.72E-5 & -4.05E-5 & 2.79E-5 & 4.35E-5 & -2.9E-5 & 2.06E-5 & Muller et al. 1999 \\
NAm-Nubia$\dagger$ & 5n.2o & 10.949 & 81 & 22.9 & 2.85 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gaina et al. 2013 \\
NAm-Nubia$\dagger$ & 6ny & 19.05 & 80.89 & 23.28 & 5.244 & 1.96 & 6.13E-5 & -4.97E-5 & 3.56E-5 & 5.2E-5 & -3.59E-5 & 2.68E-5 & Muller et al. 1999 \\
NAm-Nubia$\dagger$ & 6no & 20.131 & 80.6 & 24.4 & 5.54 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gaina et al. 2013 \\
NAm-Nubia$\dagger$ & 8n.1ny & 25.82 & 79.34 & 28.56 & 7.042 & 2.53 & 1.71E-4 & -1.71E-4 & 1.24E-4 & 1.96E-4 & -1.41E-4 & 1.04E-4 & Muller et al. 1999 \\
NAm-Nubia$\dagger$ & 13ny & 33.058 & 75.99 & 5.98 & 9.767 & 1.19 & 8.32E-5 & -8.47E-5 & 5.97E-5 & 1.03E-4 & -7.14E-5 & 5.21E-5 & Muller et al. 1999 Gaina et al. 2013 \\
NAm-Nubia$\dagger$ & 16ny & 35.343 & 75.3 & 3.1 & 10.68 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gaina et al. 2013 \\
NAm-Nubia$\dagger$ & 18n1ny? & 38.43 & 74.54 & 0.19 & 11.918 & 1.65 & 1.98E-4 & -2.08E-4 & 1.43E-4 & 2.41E-4 & -1.64E-4 & 1.16E-4 & Muller et al. 1999 \\
NAm-Nubia$\dagger$ & 18n.2no & 40.13 & 74.5 & -1.2 & 12.61 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gaina et al. 2013 \\
NAm-Nubia$\dagger$ & 20ny & 42.5 & 74.38 & -2.8 & 13.56 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Muller et al. 1993 Shephard et al. 2012 \\
NAm-Nubia$\dagger$ & 20no & 43.789 & 74.3 & -3.6 & 14.09 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gaina et al. 2013 \\
NAm-Nubia$\dagger$ & 21ny & 46.26 & 74.23 & -5.01 & 15.106 & 1.19 & 1.8E-4 & -2.03E-4 & 1.36E-4 & 2.68E-4 & -1.8E-4 & 1.26E-4 & Muller et al. 1999 \\
NAm-Nubia$\dagger$ & 21no & 47.906 & 74.9 & -4.6 & 15.61 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gaina et al. 2013 \\
NAm-Nubia$\dagger$ & 22ny & 49.037 & 75.29 & -4.26 & 15.95 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Muller et al. 1993 Shephard et al. 2012 \\
NAm-Nubia$\dagger$ & 22no & 49.714 & 75.9 & -3.5 & 16.15 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gaina et al. 2013 \\
NAm-Nubia$\dagger$ & 24n.1ny & 52.364 & 77.34 & -1.61 & 16.963 & 3.08 & 2.65E-4 & -3.13E-4 & 2.07E-4 & 4.05E-4 & -2.67E-4 & 1.8E-4 & Muller et al. 1999 Gaina et al. 2013 \\
NAm-Nubia$\dagger$ & 25ny & 55.904 & 80.64 & 6.57 & 17.895 & 1.26 & 1.19E-4 & -1.36E-4 & 8.64E-5 & 1.87E-4 & -1.18E-4 & 7.87E-5 & Muller et al. 1999 Gaina et al. 2013 \\
NAm-Nubia$\dagger$ & 30ny & 65.58 & 82.74 & 2.93 & 20.84 & 1.07 & 9.12E-5 & -1.07E-4 & 6.64E-5 & 1.58E-4 & -9.83E-5 & 6.45E-5 & Muller et al. 1999 \\
NAm-Nubia$\dagger$ & 31ny & 67.735 & 82.3 & -1.8 & 21.53 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gaina et al. 2013 \\
NAm-Nubia$\dagger$ & 32n.2ny & 71.59 & 81.35 & -8.32 & 22.753 & 1.33 & 1.23E-4 & -1.62E-4 & 9.7E-5 & 2.42E-4 & -1.46E-4 & 9.1E-5 & Muller et al. 1999 \\
NAm-Nubia$\dagger$ & 33ny & 73.619 & 81.11 & -10.64 & 23.74 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Muller et al. 1993Shephard et al. 2012 \\
NAm-Nubia$\dagger$ & 33no & 79.075 & 78.64 & -18.16 & 26.981 & 1.85 & 4.09E-5 & -4.02E-5 & 2.34E-5 & 5.73E-5 & -3.48E-5 & 2.38E-5 & Muller et al. 1999 \\
NAm-Nubia$\dagger$ & 34ny & 83.5 & 76.81 & -20.59 & 29.506 & 1.82 & 6.2E-5 & -4.83E-5 & 2.47E-5 & 6.96E-5 & -4.29E-5 & 3.07E-5 & Muller et al. 1999\_2008 Gaina et al. 2013 \\
NAm-Nubia$\dagger$ & $\mathord{?}$ & 89.9 & 74.33 & -22.65 & 33.86 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Muller\_Roest1992 Muller et al. 2008 Shephard et al. 2012 \\
NAm-Nubia$\dagger$ & $\mathord{?}$ & 94.1 & 72.0 & -24.39 & 36.49 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Muller\_Roest1992 Muller et al. 2008 Shephard et al. 2012 \\
NAm-Nubia$\dagger$ & $\mathord{?}$ & 100 & 69.42 & -23.52 & 40.46 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Muller\_Roest1992 Muller et al. 2008 Shephard et al. 2012 \\
NAm-Nubia$\dagger$ & $\mathord{?}$ & 106.9 & 68.08 & -22.66 & 45.36 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Muller\_Roest1992 Muller et al. 2008 Shephard et al. 2012 \\
NAm-Nubia$\dagger$ & $\mathord{?}$ & 118.1 & 66.21 & -21.0 & 53.19 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Muller\_Roest1992 Muller et al. 2008 Shephard et al. 2012 \\
NAm-Nubia$\dagger$ & 34no & 120.6 & 65.9 & -20.5 & 54.56 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gaina et al. 2013 \\
Nubia-Mantle & interpol & 0 & 57.728 & -51.2596 & 0 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & interpol & 10 & 57.728 & -51.2596 & -1.3645 & 3.3043 & 9.495E-5 & -6.072E-6 & 1.085E-5 & 2.8857E-5 & -2.436E-5 & 6.987E-5 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & interpol & 20 & 40.412 & -23.4948 & -3.611 & 2.545 & 1.57E-4 & 4.682E-6 & 2.293E-5 & 8.242E-5 & -6.609E-5 & 1.49E-4 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & interpol & 30 & 49.42 & -61.8981 & -5.795 & 3.172 & 8.149E-5 & 2.568E-5 & -6.617E-6 & 8.819E-5 & -5.922E-5 & 8.762E-5 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & interpol & 40 & 44.555 & -55.735 & -7.4188 & 0.7337 & 7.166E-4 & -5.577E-5 & -2.8646E-4 & 1.5166E-4 & -5.034E-5 & 2.725E-4 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & interpol & 50 & 8.836 & -34.845 & -12.431 & 0.826 & 6.97E-4 & 2.808E-5 & -3.607E-4 & 1.587E-4 & -1.04E-4 & 3.44E-4 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & interpol & 60 & 14.244 & -40.32 & -13.725 & 2.081 & 1.496E-3 & 3.451E-4 & -5.396E-4 & 7.096E-4 & -2.723E-4 & 5.502E-4 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & interpol & 70 & 26.518 & -47.4563 & -14.604 & 0.65 & 8.564E-4 & 1.195E-4 & -3.269E-4 & 2.863E-4 & -1.276E-4 & 4.452E-4 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & interpol & 80 & 26.85 & -46.9249 & -17.705 & 0.473 & 7.972E-4 & 1.314E-4 & -3.436E-4 & 2.874E-4 & -1.396E-4 & 3.485E-4 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & interpol & 90 & 7.2356 & -33.7327 & -22.745 & 0.692 & 6.805E-4 & 2.6E-5 & -1.336E-4 & 1.834E-4 & -2.302E-4 & 6.163E-4 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & interpol & 100 & 10.826 & -46.482 & -26.59 & 1.308 & 3.705E-4 & 2.897E-6 & 5.225E-5 & 4.458E-4 & 3.313E-5 & 3.037E-4 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & interpol & 110 & 5.063 & -34.8933 & -31.787 & 0.475 & 6.694E-4 & 1.7826E-4 & -1.243E-5 & 1.875E-4 & 6.704E-5 & 4.335E-4 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & interpol & 120 & 22.488 & -37.2224 & -30.632 & 66.181 & 1.436E-3 & 4.318E-5 & 1.78E-3 & 1E-3 & 1.134E-3 & 4.44E-3 & O'Neill et al. 2005fixedHotspots \\
Nubia-Mantle & None & 0 & 46.19 & -87.86 & 0 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & O'Neill et al. 2005moving \\
Nubia-Mantle & None & 10 & 46.19 & -87.86 & -1.92 & 0.92 & 9.94E-5 & -3.8E-6 & -1.18E-6 & 2.84E-5 & -2.3E-5 & 8.68E-5 & O'Neill et al. 2005moving \\
Nubia-Mantle & None & 30 & 43.54 & -69.67 & -6.05 & 3.31 & 9.89E-5 & 2.14E-5 & -3.56E-5 & 8.19E-5 & -6.45E-5 & 1.18E-4 & O'Neill et al. 2005moving \\
Nubia-Mantle & None & 40 & 44.56 & -54.31 & -8.08 & 0.6 & 6.39E-4 & -9.58E-5 & -3.09E-4 & 1.54E-4 & -2.27E-5 & 3.49E-4 & O'Neill et al. 2005moving \\
Nubia-Mantle & None & 50 & 36.97 & -58.9 & -10.26 & 1.24 & 7.6E-4 & -1.29E-4 & -4.44E-4 & 1.65E-4 & -1.35E-5 & 4.53E-4 & O'Neill et al. 2005moving \\
Nubia-Mantle & None & 60 & 23.73 & -42.14 & -12.53 & 2.31 & 1.61E-3 & 8.69E-5 & -6.22E-4 & 6.07E-4 & -2.63E-4 & 7.51E-4 & O'Neill et al. 2005moving \\
Nubia-Mantle & None & 90 & 14.6 & -33.26 & -16.24 & 2.47 & 5.47E-4 & -9.38E-5 & 5.78E-6 & 1.18E-4 & -7.96E-5 & 5.36E-4 & O'Neill et al. 2005moving \\
Nubia-Mantle & None & 100 & 14.4 & -29.63 & -20.08 & 3.25 & 2.41E-4 & -1.79E-5 & 1.48E-5 & 3.16E-4 & -1.69E-5 & 1.92E-4 & O'Neill et al. 2005moving \\
Nubia-Mantle & None & 120 & 17.03 & -27 & -29.72 & 9.06 & 7.81E-4 & 3.73E-4 & 4.38E-4 & 6.44E-4 & 4.17E-4 & 5.87E-4 & O'Neill et al. 2005moving \\
Ind-Somalia & 1no & 0.781 & 19.57 & 27.97 & -.347 & 1 & 1.99E-6 & 3.41E-6 & 1.86E-9 & 6.82E-6 & 6.01E-7 & 4.67E-7 & Bull et al. 2010 \\
Ind-Somalia & 2ny & 1.778 & 21.59 & 30.83 & -.755 & 1 & 4.26E-7 & 6.51E-7 & -4.44E-8 & 1.32E-6 & 1.74E-7 & 2.11E-7 & Bull et al. 2010 \\
Ind-Somalia & 2An.1ny & 2.581 & 22.48 & 30.6 & -1.074 & 1 & 2.94E-6 & 4.33E-6 & -6.73E-7 & 7.77E-6 & -7.56E-9 & 9.55E-7 & Bull et al. 2010 \\
Ind-Somalia & 2An.3no & 3.596 & 18.7 & 34.62 & -1.642 & 1 & 4.51E-6 & 7.3E-6 & -5.4E-7 & 1.42E-5 & 7.06E-7 & 1.35E-6 & Bull et al. 2010 \\
Ind-Somalia & 3n.1ny & 4.187 & 22.11 & 28.45 & -1.74 & 1 & 4.31E-6 & 7.11E-6 & -2.86E-7 & 1.34E-5 & 5.49E-7 & 8.8E-7 & Bull et al. 2010 \\
Ind-Somalia & 3n.4no & 5.235 & 22.05 & 31.64 & -2.181 & 1 & 2.18E-6 & 3.53E-6 & -3.32E-7 & 6.89E-6 & 1.84E-7 & 6.19E-7 & Bull et al. 2010 \\
Ind-Somalia & 3An.1ny & 5.89 & 22.89 & 28.11 & -2.333 & 1 & 6.98E-6 & 1.15E-5 & -1.71E-6 & 2.29E-5 & -3.39E-7 & 2.37E-6 & Bull et al. 2010 \\
Ind-Somalia & 3An.2no & 6.57 & 21.32 & 30.92 & -2.748 & 1 & 2.41E-6 & 4.68E-6 & -5.41E-10 & 9.68E-6 & 4.53E-7 & 4.53E-7 & Bull et al. 2010 \\
Ind-Somalia & 4n.1ny & 7.43 & 22.61 & 30.57 & -2.982 & 1 & 5.75E-6 & 1.17E-5 & -2.81E-7 & 2.68E-5 & 1.7E-6 & 1.92E-6 & Bull et al. 2010 \\
Ind-Somalia & 4n.2no & 8.07 & 22.01 & 30.79 & -3.281 & 1 & 4.62E-6 & 8.01E-6 & -1.16E-6 & 1.58E-5 & -6.77E-7 & 1.4E-6 & Bull et al. 2010 \\
Ind-Somalia & 4Any & 8.67 & 22.48 & 30.77 & -3.489 & 1 & 4.46E-6 & 6.32E-6 & -1.54E-6 & 1.36E-5 & 1.13E-6 & 3.14E-6 & Bull et al. 2010 \\
Ind-Somalia & 4Ano & 9.03 & 22.59 & 30.78 & -3.685 & 1 & 1.45E-6 & 1.82E-6 & -6.92E-7 & 3.84E-6 & 3.34E-7 & 1.33E-6 & Bull et al. 2010 \\
Ind-Somalia & 5n.1ny & 9.74 & 23.59 & 30.49 & -3.89 & 1 & 3.08E-6 & 4.97E-6 & -2.38E-7 & 1.01E-5 & 1.36E-6 & 1.63E-6 & Bull et al. 2010 \\
Ind-Somalia & 5n.2no & 10.95 & 23.62 & 29.3 & -4.311 & 1 & 4.43E-6 & 7.25E-6 & -1.58E-7 & 1.58E-5 & 2.01E-6 & 1.56E-6 & Bull et al. 2010 \\
Ind-Somalia & 5An.2no & 12.4 & 23.8 & 29.26 & -4.879 & 1 & 3.39E-6 & 5.42E-6 & -5.85E-7 & 1.04E-5 & 5.02E-7 & 1.44E-6 & Bull et al. 2010 \\
Ind-Somalia & 5ADno & 14.607 & 24.6 & 29.14 & -5.76 & 1 & 2.83E-6 & 6.13E-6 & 4.51E-7 & 1.4E-5 & 1.29E-6 & 3.29E-7 & Bull et al. 2010 \\
Ind-Somalia & 5Cn.1ny & 16.01 & 24.8 & 29.3 & -6.399 & 1 & 1.27E-6 & 2.26E-6 & -1.7E-7 & 5.7E-6 & 4.81E-7 & 5.08E-7 & Bull et al. 2010 \\
Ind-Somalia & 5Dny & 17.235 & 24.83 & 30.29 & -7.149 & 1 & 1.76E-6 & 2.98E-6 & -2.06E-7 & 6.53E-6 & 6.03E-7 & 7.15E-7 & Bull et al. 2010 \\
Ind-Somalia & 5Eny & 18.28 & 24.77 & 30.27 & -7.637 & 1 & 2.47E-6 & 5.44E-6 & 3.58E-7 & 1.32E-5 & 1.44E-6 & 5.17E-7 & Bull et al. 2010 \\
Ind-Somalia & 6no & 20.13 & 25.41 & 30.6 & -8.469 & 1 & 3E-5 & 3.6E-5 & -1.63E-5 & 6.11E-5 & -7.2E-6 & 1.81E-5 & Bull et al. 2010 \\
Ind-Somalia & 13no & 33.55 & -19.35 & -137.7 & 16.05 & 1 & 3.85E-5 & 5.31E-5 & -2.14E-5 & 1.05E-4 & -1.84E-5 & 2.19E-5 & Calculated \\
Ind-Somalia & 18n.2no & 40.13 & -19.48 & -135.85 & 19.31 & 1 & 4.06E-5 & 6.05E-5 & -2.33E-5 & 1.31E-4 & -2.52E-5 & 2.37E-5 & Calculated \\
Ind-Somalia & 20ny & 42.54 & -19.94 & -136.28 & 20.23 & 1 & 3.74E-5 & 4.99E-5 & -2.03E-5 & 9.48E-5 & -1.51E-5 & 2.08E-5 & Calculated \\
Ind-Somalia & 20no & 43.79 & -20.44 & -136.77 & 20.63 & 1 & 3.73E-5 & 4.98E-5 & -2.03E-5 & 9.5E-5 & -1.52E-5 & 2.1E-5 & Calculated \\
Ind-Somalia & 21ny & 46.26 & -19.6 & -137.27 & 21.82 & 1 & 3.73E-5 & 4.94E-5 & -2.02E-5 & 9.33E-5 & -1.46E-5 & 2.08E-5 & Calculated \\
Ind-Somalia & 21no & 47.91 & -19.49 & -138.01 & 22.9 & 1 & 3.7E-5 & 4.87E-5 & -1.99E-5 & 9.13E-5 & -1.41E-5 & 2.05E-5 & Calculated \\
Ind-Somalia & 22no & 49.71 & -19.63 & -140.64 & 24.1 & 1 & 3.72E-5 & 4.96E-5 & -2.01E-5 & 9.42E-5 & -1.48E-5 & 2.07E-5 & Calculated \\
Ind-Somalia & 23n.2no & 51.74 & -17.83 & -142.26 & 26.82 & 1 & 3.8E-5 & 5.26E-5 & -2.09E-5 & 1.06E-4 & -1.75E-5 & 2.15E-5 & Calculated \\
Ind-Somalia & 24n.3no & 53.35 & -17.69 & -144.8 & 28.76 & 1 & 3.86E-5 & 5.46E-5 & -2.13E-5 & 1.14E-4 & -1.9E-5 & 2.17E-5 & Calculated \\
Ind-Somalia & 25ny & 55.9 & -17.68 & -147.99 & 31.52 & 1 & 4.13E-5 & 6.48E-5 & -2.29E-5 & 1.52E-4 & -2.53E-5 & 2.29E-5 & Calculated \\
Ind-Somalia & 26ny & 57.55 & -16.81 & -148.61 & 33.86 & 1 & 3.91E-5 & 5.72E-5 & -2.14E-5 & 1.25E-4 & -2E-5 & 2.16E-5 & Calculated \\
Ind-Somalia & 27ny & 60.92 & -15.03 & -149.25 & 38.15 & 1 & 3.97E-5 & 5.93E-5 & -2.15E-5 & 1.34E-4 & -2.02E-5 & 2.15E-5 & Calculated \\
Ind-Somalia & 28ny & 62.5 & -14.48 & -149.55 & 40.23 & 1 & 4.93E-5 & 9.58E-5 & -2.61E-5 & 2.74E-4 & -3.79E-5 & 2.38E-5 & Calculated \\
Ind-Somalia & 29no & 64.75 & -15.39 & -152.91 & 42.42 & 1 & 3.92E-5 & 5.79E-5 & -2.08E-5 & 1.32E-4 & -1.79E-5 & 2.1E-5 & Calculated \\
Ind-Somalia & 34ny & 83 & 21.571 & 21.698 & -52.702 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Rowan and Rowley2016 \\
Ind-Nubia$\ddagger$ & synthetic & 83 & 22.16 & 19.22 & -52.74 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gibbons et al. 2013 Muller et al. 2017 \\
Ind-Nubia$\ddagger$ & synthetic & 100 & -23.19 & -152.79 & 55.76 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gibbons et al. 2013 Muller et al. 2017 \\
Ind-Nubia$\ddagger$ & synthetic & 106 & -23.19 & -152.79 & 55.76 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gibbons et al. 2013 Muller et al. 2017 \\
Ind-Nubia$\ddagger$ & synthetic & 120.6 & -24.58 & -153.92 & 54.51 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Gibbons et al. 2013 Muller et al. 2017 \\
Somalia-Nubia & 1no & 0.78 & -33.83 & 34.4 & 0.04602 & 1 & 3.737E-9 & 3.426E-9 & -8.39E-10 & 3.957E-9 & -8.03E-10 & 6.66E-10 & Demets et al. 2017 replace 2010 inverted DoF from 2010 \\
Somalia-Nubia & 2A.2no & 3.22 & -44.7 & 2.8 & 0.27048 & 1 & 4.29E-9 & 1.26E-9 & -5.01E-9 & 1.62E-9 & -1.44E-9 & 7.19E-9 & Horner-Johnson et al. 2005 \\
Somalia-Nubia & 5n.2no & 10.95 & -27.4 & 43.28 & 0.4 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Rowan and Rowley2016 \\
Somalia-Nubia & 6no & 20.13 & -27.4 & 43.28 & 0.8 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Rowan and Rowley2016 \\
Somalia-Nubia & C7.2m & 25.01 & -27.4 & 43.28 & 1 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Rowan and Rowley2016 \\
Somalia-Nubia & C34 & 85 & -27.4 & 43.28 & 1 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Rowan and Rowley2016 \\
Somalia-Nubia & $\bigstar$ & 120 & -27.4 & 43.28 & 1 & 1 & 1E-15 & 1E-15 &
1E-15 & 1E-15 & 1E-15 & 1E-15 & Inferred From Global\_ EarthByte\_230\textendash0Ma\_ GK07\_AREPS.rot \\
Australia-EAnt & 1no & 0.78 & 11.3 & 41.8 & -.49374 & 1 & 2.605E-8 & 1.846E-8 & 9.725E-9 & 2.184E-8 & 1.785E-9 & 1.031E-8 & Demets et al. 2010errInverted \\
Australia-EAnt & 2An.1ny & 2.58 & -11.164 & -139.7 & 1.655 & 5.33 & 2.81E-7 & -3.35E-7 & 2.6E-7 & 5.15E-7 & -4.87E-7 & 9.06E-7 & Cande and Stock2004 \\
Australia-EAnt & 3An.1ny & 5.89 & -11.591 & -139.23 & 3.83 & 2.12 & 2.94E-7 & -3.9E-7 & 3.19E-7 & 6.27E-7 & -5.83E-7 & 8.97E-7 & Cande and Stock2004 Krijgsman et al. 1999 Age From Meckel2005 \\
Australia-EAnt & 5n.2no & 10.95 & -11.896 & -142.058 & 6.79 & 1.02 & 1.36E-7 & -1.71E-7 & 5.56E-8 & 3.05E-7 & -1.89E-7 & 4.47E-7 & Cande and Stock2004 \\
Australia-EAnt & 6no & 20.13 & -13.393 & -145.63 & 12.051 & 1.06 & 1.61E-7 & -1.85E-7 & 2.56E-8 & 3E-7 & -1.59E-7 & 4.22E-7 & Cande and Stock2004 \\
Australia-EAnt & 8o & 26 & -13.79 & -146.43 & 15.92 & 0.95 & 1.68E-7 & -2.05E-7 & 1.05E-7 & 3.57E-7 & -2.72E-7 & 5.04E-7 & Granot and Dyment2018 \\
Australia-EAnt & 8n.2no & 26.55 & -13.805 & -146.444 & 15.919 & 1.01 & 1.95E-7 & -2.24E-7 & 5.79E-8 & 3.71E-7 & -2.39E-7 & 5.9E-7 & Cande and Stock2004 \\
Australia-EAnt & 10n.2no & 28.75 & -13.58 & -146.016 & 17.319 & 1.17 & 2.32E-7 & -2.56E-7 & 8.48E-8 & 3.94E-7 & -2.77E-7 & 7.51E-7 & Cande and Stock2004 \\
Australia-EAnt & 12no & 30.94 & -13.396 & -145.623 & 18.89 & 0.75 & 2.6E-7 & -3.14E-7 & 5.53E-8 & 5.18E-7 & -3.1E-7 & 9.82E-7 & Cande and Stock2004 \\
Australia-EAnt & 13no & 33.55 & -13.451 & -145.623 & 20.495 & 1.07 & 2.44E-7 & -3.26E-7 & 1.49E-7 & 5.56E-7 & -3.43E-7 & 6.93E-7 & Cande and Stock2004 \\
Australia-EAnt & 17n.3no & 38.11 & -14.65 & -146.525 & 22.882 & 0.49 & 6.88E-7 & -8.39E-7 & -2.51E-7 & 1.34E-6 & -1.37E-7 & 1.31E-6 & Cande and Stock2004 \\
Australia-EAnt & 20no & 43.79 & 14.92 & 32.5 & -24.51 & 0.74 & 6.3E-7 & -1E-7 & 1.68E-6 & 1.87E-6 & -3.1E-6 & 6.76E-6 & Whittaker et al. 2007\_2013 \\
Australia-EAnt & 21ny & 46.26 & 13.42 & 33.83 & -24.62 & 5.32 & 1.328E-5 & -2.024E-5 & 8.2E-7 & 3.203E-5 & -2.28E-6 & 5.76E-6 & Whittaker et al. 2013\_replace2007 \\
Australia-EAnt & 24n.3no & 53.35 & 10.48 & 35.17 & -25.24 & 0.11 & 3.38E-7 & -2.17E-7 & 4.29E-7 & 4.84E-7 & -1.139E-6 & 4.281E-6 & Whittaker et al. 2013\_replace2007 \\
Australia-EAnt & 27ny & 60.92 & 9.22 & 35.42 & -25.43 & 0.17 & 3.09E-7 & -1.93E-7 & 3.6E-7 & 5.07E-7 & -1.206E-6 & 4.474E-6 & Whittaker et al. 2013\_replace2007 \\
Australia-EAnt & 31no & 68.74 & 7.89 & 35.75 & -25.61 & 0.19 & 3.11E-7 & -1.85E-7 & 3.23E-7 & 4.95E-7 & -1.158E-6 & 4.303E-6 & Whittaker et al. 2013\_replace2007 \\
Australia-EAnt & 32n.1ny & 71.07 & 6.67 & 36.14 & -25.75 & 0.14 & 2.5E-7 & -1.82E-7 & 3.25E-7 & 4.82E-7 & -1.087E-6 & 3.991E-6 & Whittaker et al. 2013\_replace2007 \\
Australia-EAnt & 33no & 79.08 & 4.53 & 36.64 & -26.13 & 0.13 & 2.52E-7 & -1.79E-7 & 2.97E-7 & 4.75E-7 & -1.031E-6 & 3.788E-6 & Whittaker et al. 2013\_replace2007 \\
Australia-EAnt & 34ny & 83.5 & 1.02 & 37.28 & -26.62 & 0.13 & 5.37E-7 & -6E-9 & -6.56E-7 & 5.73E-7 & -8.19E-7 & 2.356E-6 & Williams et al. 2011 Whittaker et al. 2013replace2007 \\
Australia-EAnt & QZB & 96 & -12.69 & 46.58 & -29.06 & 1.03 & 3.53E-6 & -4.06E-6 & 8.19E-6 & 6.09E-6 & -1.35E-5 & 3.571E-5 & Whittaker et al. 2007 \\
Australia-EAnt & Full-fit & 136. & -3.91 & 37.9 & -30.86 & 1.04 & 2.85E-6 & -2.69E-6 & 3.77E-6 & 4.01E-6 & -6.93E-6 & 1.38E-5 & Williams et al. 2011 Whittaker et al. 2013 \\
EAnt-Somalia & 1no & 0.78 & -20.58 & 115.29 & -.10062 & 1 & 3.661E-9 & 3.38E-9 & -8.209E-10 & 4.124E-9 & -1.068E-9 & 2.415E-9 & Demets et al. 2017inverted replacing 2010inverted \\
EAnt-Somalia & 2A.2no & 3.22 & 7.9 & -44.1 & 0.42826 & 1 & 7.9E-10 & 8.8E-10 & -8.2E-10 & 1.49E-9 & -1.22E-9 & 1.15E-9 & Horner-Johnson et al. 2005 \\
EAnt-Somalia & 5n.2no & 10.95 & 14.6 & -49.1 & 1.53 & 1 & 2.21E-7 & 2.36E-7 & -9.2E-8 & 3.04E-7 & -1.67E-7 & 2.45E-7 & LeMaux et al. 2002 \\
EAnt-Somalia & 6no & 20.131 & 10.8 & -46 & 2.7 & 1 & 1.028E-7 & 8.83E-8 & -2.34E-8 & 1.759E-7 & -1.347E-7 & 2.237E-7 & Patriat et al. 2008 \\
EAnt-Somalia & 8n.2no & 26.554 & 14.3 & -46.9 & 3.91 & 1 & 1.484E-7 & 1.489E-7 & -9.66E-8 & 2.58E-7 & -2.458E-7 & 3.702E-7 & Patriat et al. 2008 \\
EAnt-Somalia & 13ny & 33.06 & 16.2 & -44.7 & 5.66 & 1 & 8.56E-7 & 6.73E-7 & -1.66E-7 & 6.9E-7 & -3.74E-7 & 5.82E-7 & Patriat et al. 2008 \\
EAnt-Somalia & 13no & 33.55 & 12.69 & -44.61 & 5.67 & 0.59 & 5.71E-7 & 5.12E-7 & 5.63E-7 & -2.35E-7 & -2.53E-7 & 3.99E-7 & Cande et al. 2010basic \\
EAnt-Somalia & 18n.2no & 40.13 & 13.8 & -43.75 & 7.05 & 0.63 & 6.6E-7 & 5.69E-7 & 5.56E-7 & -1E-9 & -7.9E-8 & 6.8E-7 & Cande et al. 2010basic \\
EAnt-Somalia & 20ny & 42.54 & 11.84 & -42.32 & 7.53 & 0.93 & 2.36E-7 & 1.91E-7 & 2.31E-7 & -2.28E-7 & -2.63E-7 & 5.98E-7 & Cande et al. 2010all \\
EAnt-Somalia & 20no & 43.79 & 11.84 & -42.16 & 7.87 & 0.78 & 1.64E-7 & 1.23E-7 & 1.79E-7 & -1.95E-7 & -2.42E-7 & 4.97E-7 & Cande et al. 2010all \\
EAnt-Somalia & 21ny & 46.26 & 11.29 & -41.54 & 8.49 & 0.55 & 1.89E-7 & 1.6E-7 & 2.24E-7 & -2.76E-7 & -3.25E-7 & 6.86E-7 & Cande et al. 2010all \\
EAnt-Somalia & 21no & 47.91 & 9.82 & -40.7 & 8.83 & 1.86 & 2.26E-7 & 1.98E-7 & 2.67E-7 & -3.69E-7 & -4E-7 & 8.38E-7 & Cande et al. 2010all \\
EAnt-Somalia & 22no & 49.71 & 9.19 & -40.63 & 9.21 & 1.4 & 2.73E-7 & 2.54E-7 & 3.7E-7 & -4.7E-7 & -5.4E-7 & 1.084E-6 & Cande et al. 2010all \\
EAnt-Somalia & 23n.2no & 51.74 & 9.31 & -41.53 & 9.61 & 0.74 & 2.78E-7 & 2.77E-7 & 4.22E-7 & -4.41E-7 & -5.38E-7 & 9.45E-7 & Cande et al. 2010withSWIR \\
EAnt-Somalia & 24n.3no & 53.35 & 10.16 & -43.3 & 9.96 & 0.72 & 4.74E-7 & 4.34E-7 & 5.65E-7 & -7.41E-7 & -7.62E-7 & 1.398E-6 & Cande et al. 2010withSWIR \\
EAnt-Somalia & 25ny & 55.9 & 9.86 & -45.24 & 10.49 & 0.52 & 1.149E-6 & 1.375E-6 & 1.932E-6 & -2.016E-6 & -2.601E-6 & 3.954E-6 & Cande et al. 2010withSWIR \\
EAnt-Somalia & 26ny & 57.55 & 10.64 & -47.47 & 10.78 & 1.35 & 1.267E-6 & 1.409E-6 & 1.747E-6 & -1.885E-6 & -2.253E-6 & 3.33E-6 & Cande et al. 2010withSWIR \\
EAnt-Somalia & 27ny & 60.92 & 7.1 & -45.8 & 11.08 & 1.15 & 1.623E-6 & 1.751E-6 & 2.193E-6 & -2.459E-6 & -2.843E-6 & 4.288E-6 & Cande et al. 2010withSWIR \\
EAnt-Somalia & 28ny & 62.5 & 4.75 & -44.79 & 11.39 & 0.66 & 1.359E-6 & 1.549E-6 & 2.054E-6 & -2.354E-6 & -2.838E-6 & 4.486E-6 & Cande et al. 2010withSWIR \\
EAnt-Somalia & 29no & 64.75 & 4.79 & -45.56 & 11.7 & 0.53 & 9.16E-7 & 9.94E-7 & 1.27E-6 & -1.651E-6 & -1.913E-6 & 3.288E-6 & Cande et al. 2010withSWIR \\
EAnt-Somalia & 34y & 83 & -1.8 & -38.7 & 17.9 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Rowan and Rowley2016 \\
EAnt-Somalia & EAn-Afr & 96 & -3.06 & -33.49 & 26.8 & 1 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & 1E-15 & Marks and Tikku 2001EPSL \\
EAnt-Somalia & M0 & 120.6 & 10.36 & 153.67 & -41.56 & 1 & 1E-15 & 1E-15 & 1E-15
& 1E-15 & 1E-15 & 1E-15 & Muller et al. 2008G3 \\* \bottomrule
\let\thefootnote\relax\footnote{Rotations for the plate pairs are given as
motion of the `Moving' plate relative to the `Fixed' plate. The covariance
matrix is given by the formula $\frac{1}{\hat{\kappa}}\left( {\begin{array}{ccc}
   a & b & c\\
   b & d & e\\
   c & e & f\\ \end{array}} \right)$ where the values of a–f are given in
   radians$^2$.}
\let\thefootnote\relax\footnote{Lat, Pole Latitude; Long, Pole Longitude; Rot,
Angle of Rotation.}
\let\thefootnote\relax\footnote{$\dagger$ Northwestern Africa; $\ddagger$
Madagascar; $\bigstar$ No real relative plate motions before 85 Ma.}
\end{longtable}
\end{landscape}

\begin{longtable}[c]{@{}llllll@{}}
\caption{Calculated North American, Indian and Australian reference APWPs (5
  Myr interval) in the hotspot references, FHM and MHM}\label{tab:refAPWP}\\
\toprule
Longitude (\degree) & Latitude (\degree) & Age (Ma) & Azimuth (\degree) & SemiMajor (\degree) & SemiMinor (\degree) \\* \midrule
\endfirsthead%
\multicolumn{6}{c}%
{{\bfseries Table \thetable\ continued from previous page}} \\
\toprule
Longitude (\degree) & Latitude (\degree) & Age (Ma) & Azimuth (\degree) & SemiMajor (\degree) & SemiMinor (\degree) \\* \midrule
\endhead%
\bottomrule
\endfoot%
\endlastfoot%
\multicolumn{6}{c}{North America, FHM} \\
-179 & 90 & 0 & 0 & 0 & 0 \\
-174.331 & 89.61 & 5 & 113.946 & 0.7802 & 0.4368 \\
-175.024 & 89.266 & 10 & 117.593 & 1.446 & 0.7937 \\
-143.465 & 88.579 & 15 & 145.472 & 1.287 & 0.8165 \\
-135.153 & 87.731 & 20 & 137.589 & 1.58 & 1.1 \\
-164.308 & 86.976 & 25 & 148.751 & 2.48 & 1.109 \\
173.098 & 86.207 & 30 & 127.221 & 1.698 & 1.286 \\
168.608 & 85.861 & 35 & 95.3017 & 1.95 & 1.066 \\
165.88 & 85.483 & 40 & 95.9912 & 3.886 & 1.736 \\
-167.954 & 83.693 & 45 & 130.354 & 2.862 & 1.303 \\
-154.176 & 80.461 & 50 & 137.487 & 3.578 & 1.613 \\
-155.85 & 79.001 & 55 & 138.82 & 3.588 & 2.14 \\
-158.209 & 78.156 & 60 & 121.46 & 4.859 & 3.176 \\
-162.178 & 78.169 & 65 & 132.308 & 3.69 & 2.3 \\
-168.366 & 78.755 & 70 & 124.638 & 4.342 & 2.501 \\
-170.935 & 78.245 & 75 & 119.072 & 2.643 & 1.541 \\
-176.092 & 78.137 & 80 & 119.419 & 4.383 & 2.572 \\
-171.38 & 76.706 & 85 & 132.099 & 2.771 & 1.327 \\
-169.766 & 75.087 & 90 & 137.193 & 3.709 & 1.367 \\
174.157 & 74.423 & 95 & 121.558 & 2.234 & 1.625 \\
159.46 & 72.443 & 100 & 30.8058 & 2.898 & 2.683 \\
162.224 & 71.777 & 105 & 85.1415 & 2.323 & 1.746 \\
164.338 & 70.753 & 110 & 94.224 & 4.13 & 2.26 \\
151.714 & 72.571 & 115 & 67.3948 & 4.635 & 2.58 \\
137.618 & 73.573 & 120 & 50.9863 & 7.344 & 4.06 \\
\multicolumn{6}{c}{North America, MHM} \\
-179 & 90 & 0 & 0 & 0 & 0 \\
167.448 & 89.222 & 5 & 93.9164 & 0.79 & 0.4434 \\
166.095 & 88.489 & 10 & 97.1675 & 1.692 & 0.9353 \\
170.16 & 87.697 & 15 & 98.0275 & 1.43 & 0.9188 \\
171.448 & 86.871 & 20 & 88.655 & 1.876 & 1.31 \\
174.498 & 85.977 & 25 & 126.491 & 2.586 & 1.186 \\
169.985 & 85.437 & 30 & 119.932 & 1.758 & 1.246 \\
169.891 & 85.352 & 35 & 102.791 & 1.88 & 1.024 \\
170.954 & 85.237 & 40 & 107.055 & 3.863 & 1.725 \\
167.564 & 84.214 & 45 & 112.528 & 2.921 & 1.197 \\
170.182 & 82.928 & 50 & 112.937 & 3.648 & 1.478 \\
-171.618 & 81.501 & 55 & 132.2 & 3.788 & 1.974 \\
-161.291 & 79.974 & 60 & 133.697 & 4.997 & 2.988 \\
-159.451 & 79.35 & 65 & 145.708 & 3.812 & 2.029 \\
-159.851 & 79.359 & 70 & 148.362 & 3.806 & 1.859 \\
-161.687 & 79.597 & 75 & 143.166 & 2.488 & 1.432 \\
-166.266 & 80.301 & 80 & 138.098 & 3.482 & 2.166 \\
-172.202 & 80.986 & 85 & 137.839 & 2.606 & 1.301 \\
179.532 & 81.68 & 90 & 133.098 & 3.09 & 1.22 \\
173.853 & 81.911 & 95 & 133.027 & 2.015 & 1.363 \\
166.329 & 81.647 & 100 & 5.23552 & 2.217 & 1.972 \\
162.461 & 80.565 & 105 & 75.9178 & 1.931 & 1.578 \\
158.682 & 79.369 & 110 & 77.4283 & 2.952 & 1.897 \\
152.419 & 78.189 & 115 & 65.0493 & 3.113 & 1.663 \\
147.766 & 76.872 & 120 & 60.0476 & 4.742 & 2.28 \\
\multicolumn{6}{c}{India, FHM} \\
-179 & 90 & 0 & 0 & 0 & 0 \\
-68.4652 & 88.2 & 5 & 16.7724 & 0.7074 & 0.4826 \\
-71.7616 & 86.461 & 10 & 18.9733 & 1.121 & 0.6732 \\
-74.4272 & 83.942 & 15 & 7.15217 & 1.135 & 0.8127 \\
-72.6 & 81.043 & 20 & 170.291 & 1.79 & 1.302 \\
-68.5899 & 79.462 & 25 & 156.305 & 1.443 & 0.9811 \\
-65.2017 & 77.644 & 30 & 149.031 & 1.644 & 1.019 \\
-62.0848 & 74.819 & 35 & 11.5526 & 2.123 & 1.469 \\
-60.3729 & 72.289 & 40 & 25.2625 & 4.021 & 2.311 \\
-66.2619 & 67.566 & 45 & 19.1795 & 2.617 & 1.427 \\
-71.1592 & 61.003 & 50 & 14.6201 & 3.698 & 1.915 \\
-72.6213 & 54.419 & 55 & 178.977 & 3.233 & 2.035 \\
-72.3461 & 47.845 & 60 & 175.474 & 4.797 & 3.071 \\
-73.3224 & 42.441 & 65 & 173.455 & 3.449 & 2.173 \\
-73.2032 & 40.393 & 70 & 0.136912 & 4.265 & 2.488 \\
-73.7248 & 36.782 & 75 & 178.704 & 2.678 & 1.58 \\
-73.9922 & 33.116 & 80 & 178.443 & 4.208 & 2.503 \\
-74.3076 & 26.836 & 85 & 2.40753 & 2.507 & 1.247 \\
-73.0955 & 22.961 & 90 & 7.5674 & 3.89 & 1.434 \\
-74.2136 & 23.036 & 95 & 5.96566 & 2.234 & 1.625 \\
-75.3342 & 23.09 & 100 & 107.925 & 2.806 & 2.598 \\
-75.2387 & 19.342 & 105 & 157.362 & 2.323 & 1.746 \\
-75.3615 & 15.893 & 110 & 161.764 & 4.555 & 2.492 \\
-73.9386 & 17.277 & 115 & 144.671 & 4.635 & 2.58 \\
-72.6048 & 18.789 & 120 & 139.637 & 6.026 & 3.332 \\
\multicolumn{6}{c}{India, MHM} \\
-179 & 90 & 0 & 0 & 0 & 0 \\
-79.4273 & 88.505 & 5 & 4.28395 & 0.723 & 0.4801 \\
-83.6684 & 87.013 & 10 & 5.28613 & 1.444 & 0.8494 \\
-85.8127 & 85.284 & 15 & 178.968 & 1.288 & 0.9161 \\
-82.7702 & 83.243 & 20 & 169.091 & 2.016 & 1.52 \\
-74.1526 & 80.865 & 25 & 158.372 & 1.528 & 1.127 \\
-68.475 & 78.19 & 30 & 150.59 & 1.621 & 1.093 \\
-64.1437 & 75.027 & 35 & 14.2827 & 2.02 & 1.489 \\
-61.7224 & 72.127 & 40 & 30.0739 & 3.974 & 2.402 \\
-64.3999 & 70.211 & 45 & 30.2175 & 2.618 & 1.439 \\
-67.989 & 66.547 & 50 & 29.2119 & 3.662 & 1.833 \\
-70.4059 & 57.978 & 55 & 15.7185 & 3.324 & 2.08 \\
-70.4049 & 49.361 & 60 & 13.6689 & 4.86 & 3.013 \\
-71.6567 & 42.727 & 65 & 11.0741 & 3.433 & 2.166 \\
-71.5409 & 39.451 & 70 & 19.6466 & 3.506 & 1.922 \\
-71.2003 & 36.142 & 75 & 14.9621 & 2.512 & 1.501 \\
-70.7182 & 32.834 & 80 & 9.68229 & 3.3 & 2.132 \\
-70.5195 & 29.586 & 85 & 11.9972 & 2.322 & 1.231 \\
-68.3816 & 28.507 & 90 & 16.0164 & 2.807 & 1.109 \\
-66.7679 & 26.262 & 95 & 20.8345 & 2.015 & 1.363 \\
-65.2692 & 23.983 & 100 & 79.6564 & 1.972 & 1.753 \\
-66.2778 & 21.878 & 105 & 151.058 & 1.931 & 1.578 \\
-67.3405 & 20.117 & 110 & 152.924 & 2.704 & 1.738 \\
-68.211 & 18.388 & 115 & 143.392 & 3.113 & 1.663 \\
-68.9914 & 16.631 & 120 & 139.979 & 4.007 & 1.927 \\
\multicolumn{6}{c}{Australia, FHM} \\
-179 & 90 & 0 & 0 & 0 & 0 \\
-41.4449 & 87.036 & 5 & 54.1118 & 0.689 & 0.3796 \\
-45.0416 & 84.256 & 10 & 49.038 & 0.7835 & 0.4258 \\
-50.6502 & 81.119 & 15 & 38.1494 & 1.117 & 0.7248 \\
-53.2369 & 77.974 & 20 & 30.9554 & 1.476 & 1.028 \\
-53.2848 & 76.256 & 25 & 16.07 & 1.106 & 0.869 \\
-51.2849 & 74.267 & 30 & 167.746 & 1.167 & 0.8867 \\
-50.2873 & 71.435 & 35 & 40.8833 & 1.936 & 1.056 \\
-50.5986 & 69.481 & 40 & 42.2012 & 3.984 & 1.782 \\
-55.5547 & 66.545 & 45 & 37.3027 & 2.536 & 1.191 \\
-58.9951 & 64.115 & 50 & 33.5829 & 3.654 & 1.676 \\
-57.5828 & 63.706 & 55 & 23.0261 & 3.095 & 1.867 \\
-57.2977 & 63.671 & 60 & 16.0634 & 4.463 & 2.843 \\
-55.5565 & 64.436 & 65 & 20.5328 & 3.214 & 1.989 \\
-51.9574 & 65.69 & 70 & 29.6999 & 4.312 & 2.465 \\
-51.2245 & 65.722 & 75 & 30.9868 & 2.626 & 1.529 \\
-50.5474 & 65.686 & 80 & 32.5267 & 4.471 & 2.657 \\
-51.107 & 63.469 & 85 & 39.4428 & 2.511 & 1.249 \\
-48.3618 & 61.873 & 90 & 48.1966 & 3.89 & 1.435 \\
-43.0424 & 64.33 & 95 & 53.4492 & 2.241 & 1.629 \\
-41.1958 & 67.209 & 100 & 154.896 & 2.871 & 2.661 \\
-42.376 & 65.281 & 105 & 21.3797 & 2.327 & 1.752 \\
-43.2223 & 63.352 & 110 & 23.2216 & 4.278 & 2.343 \\
-34.22 & 63.817 & 115 & 12.2265 & 4.637 & 2.583 \\
-24.9452 & 64.093 & 120 & 13.5957 & 6.936 & 3.836 \\
\multicolumn{6}{c}{Australia, MHM} \\
-179 & 90 & 0 & 0 & 0 & 0 \\
-43.8522 & 87.468 & 5 & 49.83 & 0.7027 & 0.3808 \\
-48.2655 & 85.095 & 10 & 44.0171 & 1.459 & 0.7801 \\
-52.7796 & 82.828 & 15 & 37.4668 & 1.275 & 0.8358 \\
-55.2364 & 80.568 & 20 & 33.5627 & 1.731 & 1.21 \\
-55.4555 & 77.907 & 25 & 25.7336 & 1.268 & 0.9666 \\
-53.2917 & 75.002 & 30 & 1.25275 & 1.156 & 0.9391 \\
-51.8626 & 71.779 & 35 & 45.6379 & 1.863 & 1.018 \\
-51.898 & 69.415 & 40 & 46.9976 & 4.026 & 1.803 \\
-52.3541 & 68.985 & 45 & 48.9107 & 2.568 & 1.132 \\
-51.6966 & 69.015 & 50 & 51.1423 & 3.548 & 1.462 \\
-51.9822 & 66.573 & 55 & 42.7177 & 3.232 & 1.823 \\
-53.4926 & 64.622 & 60 & 36.3825 & 4.516 & 2.731 \\
-52.8722 & 64.191 & 65 & 40.5529 & 3.247 & 1.883 \\
-50.5454 & 64.244 & 70 & 49.5822 & 3.279 & 1.689 \\
-48.1673 & 64.106 & 75 & 49.0042 & 2.465 & 1.426 \\
-45.9043 & 63.879 & 80 & 46.2523 & 3.33 & 2.149 \\
-41.6854 & 63.431 & 85 & 55.6345 & 2.326 & 1.233 \\
-33.6915 & 62.706 & 90 & 67.5618 & 2.814 & 1.113 \\
-28.7281 & 61.005 & 95 & 77.4292 & 2.028 & 1.373 \\
-26.8608 & 60.554 & 100 & 135.582 & 2.143 & 1.914 \\
-26.3797 & 60.593 & 105 & 26.4611 & 1.942 & 1.585 \\
-25.8665 & 60.575 & 110 & 27.2651 & 2.877 & 1.85 \\
-25.2025 & 60.386 & 115 & 17.2151 & 3.118 & 1.669 \\
-24.4723 & 60.146 & 120 & 13.2747 & 4.514 & 2.173 \\* \bottomrule
\end{longtable}

\begin{figure}
  \centering
  \includegraphics[width=.95\textwidth]{../../paper/tex/GeophysJInt/figures/draper1.pdf}
  \caption[Regression of $\mathcal{CPD}$ on average number of paleopoles per
    window for Wt 1]{Regression of equal-weight $\mathcal{CPD}$ on average
    number of paleopoles per window for Wt 1. Continued from
    Fig.~\ref{fig-regr}.}\label{fig-regr1}
\end{figure}

\begin{figure}
  \centering
  \includegraphics[width=.95\textwidth]{../../paper/tex/GeophysJInt/figures/draper2.pdf}
  \caption[Regression of $\mathcal{CPD}$ on average number of paleopoles per
    window for Wt 2]{Regression of equal-weight $\mathcal{CPD}$ on average
    number of paleopoles per window for Wt 2.  Continued from
    Figs.~\ref{fig-regr} and~\ref{fig-regr1}.}\label{fig-regr2}
\end{figure}

\begin{figure}
  \centering
  \includegraphics[width=.95\textwidth]{../../paper/tex/GeophysJInt/figures/draper3.pdf}
  \caption[Regression of $\mathcal{CPD}$ on average number of paleopoles per
    window for Wt 3]{Regression of equal-weight $\mathcal{CPD}$ on average
    number of paleopoles per window for Wt 3.  Continued from
    Figs.~\ref{fig-regr},~\ref{fig-regr1} and~\ref{fig-regr2}.}\label{fig-regr3}
\end{figure}

\begin{figure}
  \centering
  \includegraphics[width=.95\textwidth]{../../paper/tex/GeophysJInt/figures/draper4.pdf}
  \caption[Regression of $\mathcal{CPD}$ on average number of paleopoles per
    window for Wt 4]{Regression of equal-weight $\mathcal{CPD}$ on average
    number of paleopoles per window for Wt 4.  Continued from
    Figs.~\ref{fig-regr},~\ref{fig-regr1},~\ref{fig-regr2}
    and~\ref{fig-regr3}.}\label{fig-regr4}
\end{figure}

\begin{figure}
  \centering
  \includegraphics[width=.95\textwidth]{../../paper/tex/GeophysJInt/figures/draper5.pdf}
  \caption[Regression of $\mathcal{CPD}$ on average number of paleopoles per
    window for Wt 5]{Regression of equal-weight $\mathcal{CPD}$ on average
    number of paleopoles per window for Wt 5.  Continued from
    Figs.~\ref{fig-regr},~\ref{fig-regr1},~\ref{fig-regr2},~\ref{fig-regr3}
    and~\ref{fig-regr4}.}\label{fig-regr5}
\end{figure}