For consistent indentation of a "somewhat list-like structure", use adjustwidth from changepage:

\documentclass{article}
\usepackage{changepage}
\begin{document}
\section{Affiliations}
\begin{adjustwidth}{1cm}{0pt}
\setlength{\parindent}{0pt}%
The American Geophysical Union.
The Seismological Society of America.
\end{adjustwidth}
\end{document}
However, I'd suggest a regular list-like structure like itemize:

\documentclass{article}
\usepackage{enumitem}
\begin{document}
\section{Affiliations}
\begin{itemize}[leftmargin=1cm]
\item The American Geophysical Union.
\item The Seismological Society of America.
\end{itemize}
\end{document}