@@ -105,7 +105,7 @@ \section{Introduction}
105105any change to the integration method.
106106
107107\begin {figure }
108- \centreing
108+ \centering
109109\includegraphics [width=0.6\linewidth ]{figures/tesseroid-uieda.pdf}
110110\caption {
111111 A tesseroid (spherical prism) in a geocentric spherical coordinate system, with a
@@ -367,7 +367,7 @@ \subsection{Adaptive Discretization}
367367\subsection {Density-based Discretization Algorithm }
368368
369369\begin {figure* }
370- \centreing
370+ \centering
371371\includegraphics [width=\linewidth ]
372372 {figures/density-based-discretization-algorithm.pdf}
373373\caption {
@@ -600,7 +600,7 @@ \subsection{Linear Density}
600600shell (determined by the thickness).
601601
602602\begin {figure* }
603- \centreing
603+ \centering
604604\includegraphics [width=\linewidth ]{figures/linear-D.pdf}
605605\caption {
606606 Differences between the gravitational fields generated by the tesseroid model
@@ -705,7 +705,7 @@ \subsubsection{$D$-$\delta$ space exploration}
705705to the exponential case.
706706
707707\begin {figure }
708- \centreing
708+ \centering
709709\includegraphics [width=0.5\linewidth ]
710710 {figures/grid-search.pdf}
711711\caption {
@@ -727,7 +727,7 @@ \subsubsection{$D$-$\delta$ space exploration}
727727\subsubsection {Delta ratio determination }
728728
729729\begin {figure* }
730- \centreing
730+ \centering
731731\includegraphics [width=\linewidth ]{figures/exponential-delta.pdf}
732732\caption {
733733 Numerical error for different exponential density functions and values of the delta
@@ -779,7 +779,7 @@ \section{Application to the Neuqu\'en Basin}
779779to 5000m of depth \citep {Howell2005 }.
780780
781781\begin {figure* }
782- \centreing
782+ \centering
783783\includegraphics [width=\linewidth ]{figures/neuquen-basin.pdf}
784784\caption {
785785 Gravitational effects of the Nequ\' en sedimentary basin modelled
@@ -894,7 +894,7 @@ \section{Analytical Solutions for Spherical Shell}
894894\label {sec:shell }
895895
896896\begin {figure }
897- \centreing
897+ \centering
898898\includegraphics [width=0.5\linewidth ]{figures/spherical-shell.pdf}
899899\caption {
900900 Spherical shell with inner and outer radii $ R_1 $ and $ R_2 $ , respectively.
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