Turn off superscript when all authors have same affiliation (elsarticle)

Question

I'm using the elsarticle class, which adds superscripts to link the author to their affiliation. However, all of the authors for my paper have the same affiliation, so it looks a little weird for them all to have the superscript "a" (as shown below).

\documentclass{elsarticle}

\author[su]{Jane Doe\corref{cor1}}
\ead{jdoe@someuniversity}
\author[su]{Joe Bloggs}
\ead{jbloggs@someuniversity}

\cortext[cor1]{Corresponding author}

\address[su]{Department of Underwater Basket-weaving, Some University}

\begin{document}

\maketitle

\end{document}

Is there a way to turn this off? I experimented with leaving off the [su] tags, but that results in all the authors getting an asterisk marking them as corresponding authors!

EDIT: Here's a complete example:

\documentclass[preprint,12pt]{elsarticle}

\journal{Some Journal}

\begin{document}

\begin{frontmatter}

\title{My Article}

\author[su]{Jane Doe\corref{cor1}}
\ead{jdoe@someuniversity}
\author[su]{Joe Bloggs}
\ead{jbloggs@someuniversity}

\cortext[cor1]{Corresponding author}

\address[su]{Department of Underwater Basket-weaving, Some University}

\begin{abstract}

Abstract

\end{abstract}

\begin{keyword}
test
\end{keyword}

\end{frontmatter}

\section{Introduction}

Blah blah blah

\end{document}
\endinput

Answer 1

Here's a way to achieve your output:

\documentclass{elsarticle}

\author{Jane Doe\corref{cor1}}
\ead{jdoe@someuniversity}
\author{Joe Bloggs\corref{}}
\ead{jbloggs@someuniversity}

\cortext[cor1]{Corresponding author}

\address{Department of Underwater Basket-weaving, Some University}

\begin{document}

\maketitle

\end{document}

Providing an empty \corref{} to the non-corresponding author removes the unwanted asterisk.

Answer 2

As you have found, elsarticle provides two ways of adding the authors - with and without a label (pages 4 and 5 of the documentation). If the label is omitted, then the authors before the \address will have the same affiliation. The asterisk denotes the corresponding author. Its repetition is a known bug which may be fixed with etoolbox:

\documentclass[preprint,10pt,3p]{elsarticle}

\usepackage{etoolbox}
\makeatletter
    \patchcmd{\@author}{\global\let\@fnmark\@empty}{\global\let\@fnmark\@empty\global\let\@corref\@empty}{}{\@latex@error{Failed to patch \string\@author for \string\@corref reset}}
\makeatother

\journal{}

\begin{document}

\begin{frontmatter}
\title{Title of my paper \tnoteref{label1}}
\tnotetext[label1]{A note to the title}

\author{Jane Doe\corref{cor1}}
\ead{jdoe@someuniversity}
\author{Joe Bloggs}
\ead{jbloggs@someuniversity}

\cortext[cor1]{Corresponding author}
\address{Department of Underwater Basket-weaving, Some University}

\begin{abstract}
  Abstract
\end{abstract}

\begin{keyword}
keyword1, keyword2
\end{keyword}
\end{frontmatter}

\section{Introduction}
\end{document}