Format a version for the EarthArxiv (#63)

Use the Latex article class instead of GJI and insert the self-archiving
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Add citation information for version of record and its DOI.
Add DOI link and citation to README.
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Author: leouieda

README.md

@@ -7,8 +7,18 @@ Mario E. Gimenez,
 Leonardo Uieda
 
 This paper has been accepted for publication in *Geophysical Journal International*.
+The version of record
 
-An archived version of this repository is available at 
+> Soler, S. R., Pesce, A., Gimenez, M. E., & Uieda, L., 2019. Gravitational field
+> calculation in spherical coordinates using variable densities in depth, 
+> *Geophysical Journal International*, 
+> doi:[10.1093/gji/ggz277](https://doi.org/10.1093/gji/ggz277)
+
+is available online at: [doi.org/10.1093/gji/ggz277](https://doi.org/10.1093/gji/ggz277)
+
+**This repository contains the data and code used to produce all results and figures shown
+in the paper.**
+An archived version of this repository is available at
 [doi.org/10.6084/m9.figshare.8239622](https://doi.org/10.6084/m9.figshare.8239622)
 
 We introduce a novel methodology for gravity forward modeling in spherical coordinates
@@ -148,9 +158,9 @@ All source code is made available under a BSD 3-clause license.  You can freely
 use and modify the code, without warranty, so long as you provide attribution
 to the authors.  See `LICENSE.md` for the full license text.
 
-Data and the results of numerical tests are available under the 
+Data and the results of numerical tests are available under the
 [Creative Commons Attribution 4.0 License (CC-BY)](https://creativecommons.org/licenses/by/4.0/).
 
-The manuscript text and figures are not open source. The authors reserve the 
+The manuscript text and figures are not open source. The authors reserve the
 rights to the article content, which has been accepted for publication in
 Geophysical Journal International.

manuscript/manuscript.tex

@@ -1,38 +1,71 @@
-%\documentclass[extra]{gji}
-\documentclass[extra, referee]{gji}
+\documentclass[twocolumn]{article}
 
+\newcommand{\Title}{
+    Gravitational field calculation in spherical coordinates using variable
+    densities in depth
+}
+\newcommand{\Author}{S.R. Soler, A. Pesce, M.E. Gimenez, L. Uieda}
+\newcommand{\AuthorAffil}{
+    {\large
+        Santiago R. Soler$^{1,2,*}$, Agustina Pesce$^{1,2}$,
+        Mario E. Gimenez$^{1,2}$, and Leonardo Uieda$^3$
+    }
+    \\[0.4cm]
+    {\small $^1$ CONICET, Argentina}
+    \\
+    {\small $^2$ Instituto Geofísico Sismológico Volponi, Universidad Nacional de San Juan, Argentina}
+    \\
+    {\small $^3$ Department of Earth Sciences, SOEST, University of Hawai'i at M\={a}noa, USA}
+    \\
+    {\small $^*$ e-mail: [email protected]}
+}
+\newcommand{\DOI}{doi:\href{https://doi.org/10.1093/gji/ggz277}{10.1093/gji/ggz277}}
+\newcommand{\DOILink}{\href{https://doi.org/10.1093/gji/ggz277}{doi.org/10.1093/gji/ggz277}}
+
+
+\usepackage[left=0.7in,right=0.7in,top=1in,bottom=1in]{geometry}
+\setlength{\columnsep}{2\columnsep}
 \usepackage[utf8]{inputenc}
 \usepackage{timet}
 \usepackage{amsmath}
 \usepackage{graphicx}
-
+\usepackage[round]{natbib}
+\usepackage{fixltx2e}
 \usepackage{url}
 \usepackage[pdftex,colorlinks=true]{hyperref}
 \hypersetup{
     allcolors=blue,
+    pdftitle={\Title},
+    pdfauthor={\Author},
 }
-
+\usepackage{fancyhdr}
+\pagestyle{fancy}
+\fancyhf{}
+\lhead{
+    \fontsize{9pt}{12pt}\selectfont
+    \Author{}, 2019. \DOI{}
+}
+\rhead{\fontsize{9pt}{12pt}\selectfont \thepage}
+\renewcommand{\headrulewidth}{0pt}
 
 \begin{document}
 
-\title[Variable Density Tesseroids]{
-    Gravitational field calculation in spherical coordinates using variable
-    densities in depth
+\title{\Title}
+\author{\AuthorAffil}
+\date{
+    \normalsize
+    Accepted 2019 June 05. Received 2019 May 10; in original form 2018 December 29
+    \\[0.4cm]
+    This is a pre-copyedited, author-produced PDF of an article accepted for
+    publication in \textit{Geophysical Journal International} following peer review.
+    The version of record
+    ``\textit{Soler, S. R., Pesce, A., Gimenez, M. E., \& Uieda, L., 2019.
+    \Title{}, Geophysical Journal International, \DOI{}}\ ''
+    is available online at: \DOILink{}
 }
-\author[S.R. Soler, A. Pesce, M.E. Gimenez, and L. Uieda]{
-    Santiago R. Soler$^{1,2}$, Agustina Pesce$^{1,2}$,
-    Mario E. Gimenez$^{1,2}$, and Leonardo Uieda$^3$ \\
-    $^1$CONICET, Argentina.~e-mail: [email protected]\\
-    $^2$Instituto Geofísico Sismológico Volponi, Universidad Nacional de
-    San Juan, Argentina\\
-    $^3$Department of Earth Sciences, SOEST, University of Hawai‘i at
-    M\={a}noa, Honolulu, Hawaii, USA
-}
-
-
 \maketitle
 
-\begin{summary}
+\begin{abstract}
 We present a new methodology to compute the gravitational fields generated by
 tesseroids (spherical prisms) whose density varies with depth according to
 an arbitrary continuous function.
@@ -63,12 +96,11 @@
 the accuracy of the results at the expense of computational speed.
 Lastly, we apply this new methodology to model the Neuqu\'en Basin, a foreland basin in
 Argentina with a maximum depth of over 5000~m, using an exponential density function.
-\end{summary}
-
-\begin{keywords}
+\\[0.5cm]
+\textbf{Keywords:}
 Numerical modelling, Numerical approximations and analysis, Gravity anomalies
 and Earth structure, Satellite gravity
-\end{keywords}
+\end{abstract}
 
 
 \section{Introduction}
@@ -112,7 +144,7 @@ \section{Introduction}
 
 \begin{figure}
 \centering
-\includegraphics[width=0.6\linewidth]{figures/tesseroid-uieda.pdf}
+\includegraphics[width=\linewidth]{figures/tesseroid-uieda.pdf}
 \caption{
     A tesseroid (spherical prism) in a geocentric spherical coordinate system, with a
     computation point $P$ and its local north oriented Cartesian coordinate system.
@@ -267,7 +299,7 @@ \subsection{Gauss-Legendre Quadrature integration}
 included in the integration and evaluated on the Legendre polynomial roots
 (i.e.~quadrature nodes).
 
-\iftwocol{
+%\iftwocol{
 \begin{equation}
     \begin{split}
         \int\limits_{\lambda_1}^{\lambda_2}
@@ -284,21 +316,21 @@ \subsection{Gauss-Legendre Quadrature integration}
     \end{split}
 \label{eq:glq-var-dens}
 \end{equation}
-}{
-\begin{equation}
-    \int\limits_{\lambda_1}^{\lambda_2}
-    \int\limits_{\phi_1}^{\phi_2}
-    \int\limits_{r_1}^{r_2}
-    \rho(r') f(r', \phi', \lambda')
-    dr' d\phi' d\lambda' \approx
-    A
-    \sum\limits_{i=1}^{N^r}
-    \sum\limits_{j=1}^{N^\phi}
-    \sum\limits_{k=1}^{N^\lambda}
-    W_i^r W_j^\phi W_k^\lambda \rho(r_i) f(r_i, \phi_j, \lambda_k),
-\label{eq:glq-var-dens}
-\end{equation}
-}
+%}{
+%\begin{equation}
+    %\int\limits_{\lambda_1}^{\lambda_2}
+    %\int\limits_{\phi_1}^{\phi_2}
+    %\int\limits_{r_1}^{r_2}
+    %\rho(r') f(r', \phi', \lambda')
+    %dr' d\phi' d\lambda' \approx
+    %A
+    %\sum\limits_{i=1}^{N^r}
+    %\sum\limits_{j=1}^{N^\phi}
+    %\sum\limits_{k=1}^{N^\lambda}
+    %W_i^r W_j^\phi W_k^\lambda \rho(r_i) f(r_i, \phi_j, \lambda_k),
+%\label{eq:glq-var-dens}
+%\end{equation}
+%}
 
 \noindent where
 
@@ -679,8 +711,10 @@ \section{Determination of the distance-size and delta ratios}
     The horizontal dimensions of the tesseroids and the total number of
     tesseroids in the shell model are given in the latitudinal and longitudinal
     dimensions, respectively.
+    \newline
 }
 \label{tab:shell-models}
+\centering
 \begin{tabular}{rccccc}
     Thickness & Tesseroid size & Number of tesseroids \\ \hline
     0.1 km  & $30^\circ \times 30^\circ$ & $6 \times 12 = 72$ \\
@@ -691,13 +725,15 @@ \section{Determination of the distance-size and delta ratios}
 \end{tabular}
 \end{table}
 
-\begin{table}
+\begin{table*}
 \caption{
     Description of the computation grids used to characterize the accuracy of the
     numerical integration.
     Grid height is defined above the mean Earth radius.
+    \newline
 }
 \label{tab:grids}
+\centering
 \begin{tabular}{lccc}
     Name & Grid spacing & Grid region (degrees) & Grid height (km)
     \\ \hline
@@ -706,7 +742,7 @@ \section{Determination of the distance-size and delta ratios}
     Global    & $ 10^\circ$ & 180W / 180E / 90S / 90N & 0   \\
     Satellite & $ 10^\circ$ & 180W / 180E / 90S / 90N & 260 \\
 \end{tabular}
-\end{table}
+\end{table*}
 
 
 \subsection{Linear Density}
@@ -821,11 +857,11 @@ \subsection{Exponential Density}
 
 \begin{figure}
 \centering
-\iftwocol{
+%\iftwocol{
 \includegraphics[width=\linewidth]{figures/exponential-densities.pdf}
-}{
-\includegraphics[width=0.5\linewidth]{figures/exponential-densities.pdf}
-}
+%}{
+%\includegraphics[width=0.5\linewidth]{figures/exponential-densities.pdf}
+%}
 \caption{
     Exponential density functions assigned to the spherical shell models for
     $\delta$ ratio determination.
@@ -878,13 +914,13 @@ \subsubsection{$D$-$\delta$ space exploration}
 
 \begin{figure}
 \centering
-\iftwocol{
+%\iftwocol{
 \includegraphics[width=\linewidth]
     {figures/grid-search.pdf}
-}{
-\includegraphics[width=0.5\linewidth]
-    {figures/grid-search.pdf}
-}
+%}{
+%\includegraphics[width=0.5\linewidth]
+    %{figures/grid-search.pdf}
+%}
 \caption{
     Numerical error exploration in the $D$-$\delta$ space.
     The percentage difference values were obtained from the comparison between the
@@ -988,11 +1024,11 @@ \subsection{Sinusoidal Density}
 
 \begin{figure}
 \centering
-\iftwocol{
+%\iftwocol{
 \includegraphics[width=\linewidth]{figures/sine-densities.pdf}
-}{
-\includegraphics[width=0.5\linewidth]{figures/sine-densities.pdf}
-}
+%}{
+%\includegraphics[width=0.5\linewidth]{figures/sine-densities.pdf}
+%}
 \caption{
     Sinusoidal density functions assigned to the spherical shells in the $\delta$ ratio
     determination.
@@ -1110,11 +1146,11 @@ \section{Application to the Neuqu\'en Basin}
 
 \begin{figure}
 \centering
-\iftwocol{
+%\iftwocol{
 \includegraphics[width=\linewidth]{figures/neuquen-basin-densities.pdf}
-}{
-\includegraphics[width=0.5\linewidth]{figures/neuquen-basin-densities.pdf}
-}
+%}{
+%\includegraphics[width=0.5\linewidth]{figures/neuquen-basin-densities.pdf}
+%}
 \caption{
     Linear and exponential densities used to compute the gravitational fields generated
     by a tesseroid model of the Neuqu\'en sedimentary basin.
@@ -1426,10 +1462,10 @@ \subsection{Exponential density}
 
 \begin{equation}
     \begin{split}
-    V_\text{exp}(r) = \frac{4\pi G}{r} \frac{A}{k^3} \Big[
-    & \left( R_1^2 k^2 + 2 R_1 k + 2 \right) e^{- k (R_1 - R)} - \\
-    & \left( R_2^2 k^2 + 2 R_2 k + 2 \right) e^{- k (R_2 - R)}
-    \Big].
+        V_\text{exp}(r) = \frac{4\pi G}{r} \frac{A}{k^3} \Big[
+        & \left( R_1^2 k^2 + 2 R_1 k + 2 \right) e^{- k (R_1 - R)} - \\
+        & \left( R_2^2 k^2 + 2 R_2 k + 2 \right) e^{- k (R_2 - R)}
+        \Big].
     \end{split}
 \end{equation}
 
@@ -1448,10 +1484,12 @@ \subsection{Sinusoidal density}
 
 \begin{equation}
     \begin{split}
-    V_\text{sine}(r) = \frac{4\pi G}{r} \frac{A}{k^3} \Big[
-    & (2 - k^2 R_2^2) \cos(k(R_2 - R)) + 2 k R_2 \sin(k(R_2 - R)) - \\
-    & (2 - k^2 R_1^2) \cos(k(R_1 - R)) - 2 k R_1 \sin(k(R_1 - R))
-        \Big].
+        V_\text{sine}(r) = \frac{4\pi G}{r} \frac{A}{k^3} \Big[
+    & (2 - k^2 R_2^2) \cos(k(R_2 - R)) + \\
+    & 2 k R_2 \sin(k(R_2 - R)) - \\
+    & (2 - k^2 R_1^2) \cos(k(R_1 - R)) - \\
+    & 2 k R_1 \sin(k(R_1 - R))
+    \Big].
     \end{split}
 \end{equation}