<onlineresource xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://www.globe.gov/"/">
Specifically I needed both the "xmlns:xlink" attribute and the "xlink:href" attribute. At first I tried to trick LINQ-to-SQL into giving me those attributes using .AddAttribute("xmlns:xlink", xlinkUrl), but that did not work (because the API does not allow that kind of cheating).
The final solution was short and easy, but it was not straightforward until I knew how to do it. This solution is now stable and works correctly. Here it is:
XNamespace xlinkNamespace = "http://www.w3.org/1999/xlink";
XDocument doc = new XDocument(
new XAttribute(XNamespace.Xmlns + "xlink", "http://www.w3.org/1999/xlink"),
new XAttribute(xlinkNamespace + "href", "http://localhost:1558/GenericWMS/WMS.ashx")