\documentclass{article}
\begin{document}

This is a test1.
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This is a test1.
This is a test1.
This is a test1.
This is a test1.
This is a test1.
This is a test1.
This is a test1.
This is a test1.
This is a test1.
\begin{table}
%\begin{center}
\begin{minipage}[t]{0.49\textwidth}
  \begin{center}
  \begin{tabular}{|c|r|r|}
    \hline
    DDD      &   E           & FF${}^1$     \\ \hline
    GG       & HHH${}^2$     & I            \\ \hline
  \end{tabular}
  \caption{Vertical electric.}
  \label{Efield}  
  \end{center}
\end{minipage}
\hfill
\begin{minipage}[t]{0.49\textwidth}
  \begin{center}
  \begin{tabular}{|c|r|r|}
  \hline
  DDD      &   E           & FF${}^1$     \\ \hline
  GG       & HHH${}^2$     & I            \\ \hline
  \end{tabular}
  \caption{Vertical electric field.}
  \label{Efield1}
  \end{center}
\end{minipage}
%\end{center}
\end{table}

\begin{table}
%\begin{center}
\begin{minipage}[b]{0.49\textwidth}
  \begin{center}
  \begin{tabular}{|c|r|r|}
    \hline
    DDD      &   E           & FF${}^1$     \\ \hline
    GG       & HHH${}^2$     & I            \\ \hline
  \end{tabular}
  \caption{Vertical electric.}
  \label{Efield}
  \end{center}
\end{minipage}
\hfill
\begin{minipage}[b]{0.49\textwidth}
  \begin{center}
  \begin{tabular}{|c|r|r|}
  \hline
  DDD      &   E           & FF${}^1$     \\ \hline
  GG       & HHH${}^2$     & I            \\ \hline
  \end{tabular}
  \caption{Vertical electric field.}
  \label{Efield1}
  \end{center}
\end{minipage}
%\end{center}
\end{table}

\end{document}