[Vlasenko Fedor]

<div id="test">
  <a href="rabout.php"></a>
  <div id="aa">
    <a href="aabout.php"></a>
  </div>
  <a href=""></a>
</div>
<script>
  var links = document.querySelectorAll("a[href*='about.php']");
  for (var i = 0; i < links.length; i += 1) {
    alert(links[i].parentNode.id);
  }
</script>

или

<div id="test">
  <a href="rabout.php"></a>
  <div id="aa">
    <a href="aabout.php"></a>
  </div>
  <a href=""></a>
</div>
<script>
  var links = document.links;
  for (var i = 0; i < links.length; i += 1) {
    var link = links[i];
    if (link.href.indexOf('about.php') !== -1) {
      alert(link.parentNode.id);
    }
  }
</script>

еще парочку решений