\documentclass[12pt]{article}
\usepackage[english]{babel}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath}
\usepackage{graphicx}
\begin{document}
\begin{table}[h]
\begin{minipage}{0.5\linewidth}
\centering
\caption{Values for granite Elastic modulus (E) for sonic velocity data (Block) generated using Monte Carlo simulation with uncertainty in poisson ratio $\nu$ and Density $\rho$}
\begin{tabular}{|c|c|}
\hline
Parameter & Value \\
\hline
E & 31.51 \\
\hline
$\sigma$ & 5.06 \\
\hline
\end{tabular}
\label{table:MCEsonic}
\end{minipage}
\begin{minipage}{0.5\linewidth}
\centering
\caption{Values for granite Elastic modulus (E) for Ultrasonic velocity data (Block) generated using Monte Carlo simulation with uncertainty in poisson ratio $\nu$ and Density $\rho$} \quad
\begin{tabular}{|c|c|}
\hline
Parameter & Value \\
\hline
E & 32.20 \\
\hline
$\sigma$ & 2.16 \\
\hline
\end{tabular}
\label{table:MCEultrasonic}
\end{minipage}
\end{table}
\end{document}
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\documentclass[12pt]{article}
\usepackage[english]{babel}
\usepackage[utf8x]{inputenc}
\usepackage{subcaption}
\usepackage{booktabs}
\begin{document}
\begin{minipage}{0.45\linewidth}
\centering
\captionof{table}{Values for granite Elastic modulus (E) for sonic velocity data (Block) generated using Monte Carlo simulation with uncertainty in poisson ratio $\nu$ and Density $\rho$}\label{table:MCEsonic}
\begin{tabular}{cc}
\toprule
Parameter & Value \\
\midrule
E & 31.51 \\
$\sigma$ & 5.06 \\
\bottomrule
\end{tabular}
\end{minipage}\hfil
\begin{minipage}{0.45\linewidth}
\centering
\captionof{table}{Values for granite Elastic modulus (E) for Ultrasonic velocity data (Block) generated using Monte Carlo simulation with uncertainty in poisson ratio $\nu$ and Density $\rho$} \label{table:MCEultrasonic}
\begin{tabular}{cc}
\toprule
Parameter & Value \\
\midrule
E & 32.20 \\
$\sigma$ & 2.16 \\
\bottomrule
\end{tabular}
\end{minipage}
\begin{table}
\caption{Values for granite Elastic modulus (E) for \ref{E-sonic}~sonic and \ref{E-Usonic}~Ultrasonic velocity data (Block) generated using Monte Carlo simulation with uncertainty in poisson ratio $\nu$ and Density $\rho$}
\begin{minipage}{0.45\textwidth}
\centering
\subcaption{sonic velocity\label{E-sonic}}
\begin{tabular}{cc}
\toprule
Parameter & Value \\
\midrule
E & 31.51 \\
$\sigma$ & 5.06 \\
\bottomrule
\end{tabular}
\end{minipage}\hfil
\begin{minipage}{0.45\textwidth}
\centering
\subcaption{ultrasonic velocity\label{E-Usonic}}
\begin{tabular}{cc}
\toprule
Parameter & Value \\
\midrule
E & 32.20 \\
$\sigma$ & 2.16 \\
\bottomrule
\end{tabular}
\end{minipage}
\end{table}
\end{document}
Please note, how the tables are numbered. captionof is not a floating-environment, but table is. In my example the enumeration "seems" to be confused. You have to take care of things like that.
Table 3 shares the caption and is using subcaptions instead.
The smart way: Calm down and take a deep breath, read posts and provided links attentively, try to understand and ask if necessary.
In general vertical rules should be avoided because they disturb the reading flow (not only in tables). But you can do the following for an optical separation.
Decrease the width of the {minipage} environments and simply insert filling space by \hfill as Johannes already suggested.
Use the TeX primitive \vrule in combination with filling space by \hfill. The vertical rule will be calculated in dependence of the surrounding objects.
\documentclass[12pt]{article}
\usepackage[T1]{fontenc}
\usepackage{caption} % customized captions
\usepackage{booktabs} % good looking tables
\usepackage{siunitx} % SI units and aligned tabular material
\begin{document}
\begin{table}[!htb]
\begin{minipage}{0.45\linewidth}
\centering
\caption{Values for granite elastic modulus (E) for sonic velocity data (block) generated using Monte Carlo simulation with uncertainty in Poisson ratio $\nu$ and density $\rho$}
\begin{tabular}{
c
S[table-format=2.2]
}\toprule
Parameter & {Value} \\ \midrule
E & 31.51 \\
$\sigma$ & 5.06 \\ \bottomrule
\end{tabular}
\label{table:MCEsonic}
\end{minipage}
\hfill\vrule\hfill
\begin{minipage}{0.45\linewidth}
\centering
\caption{Values for granite elastic modulus (E) for ultrasonic velocity data (block) generated using Monte Carlo simulation with uncertainty in Poisson ratio $\nu$ and density $\rho$} \quad
\begin{tabular}{
c
S[table-format=2.2]
}\toprule
Parameter & {Value} \\ \midrule
E & 32.20 \\
$\sigma$ & 2.16 \\ \bottomrule
\end{tabular}
\label{table:MCEultrasonic}
\end{minipage}
\end{table}
\end{document}
For the other improvements you should study the manuals of the involved packages.
NEW: TikZ book now 40% off at Amazon.com for a short time.
And: Currently, Packt sells ebooks for $4.99 each if you buy 5 of their over 1000 ebooks. If you choose only a single one, $9.99. How about combining 3 LaTeX books with Python, gnuplot, mathplotlib, Matlab, ChatGPT or other AI books? Epub and PDF. Bundle (3 books, add more for higher discount): https://packt.link/MDH5p