The latest version of Google's Structured Data Article Help Documentation includes author.url as a Recommended Property, described as "A link to a web page that uniquely identifies the author of the article. For example, the author's social media page, an about me page, or a bio page."
The JSON-LD code would look like this:
The author.url property should be a useful feature for authors like me who publish articles on multiple website, to help Google understand the whole of our expertise.
Google could use this information in creating author carousels in the author knowledge panels that it introduced on mobile devices in beta in June, or in some wider application.
And if it works well for Google, maybe some improvement in search ranking will trickle down to authors' websites.
One caution, though: pick, and optimize, one url to be used consistently for author.url, and use it consistently. Don't use your About page in some articles and your Linkedin profile in others.