Which is better style:
(1) This picture is copyright of John Smith.
(2) This picture is copyright John Smith.
Please explain ...
"The copyright for this picture is held by (or belongs to) John Smith."
I do not consider either of the two options you offered as being in good form.
A brief look with the Ngram viewer and online with the google finds that the locution
X is copyright of Y,
(where X is some work and Y is a claimant) is a fairly common usage for
Y holds the copyright to X
or
the copyright of Y belongs to X.
For instance, the American Society of Civil Engineers warns in its publication Education and continuing development for the civil engineer (1990) that
LOTUS 1-2-3 is copyright of LOTUS Development Corporation.
Of course, literally speaking, the work isn't its copyright, but usage trumps literal-mindedness.
It's harder to search for "is copyright" without the following of, but this form was likely influenced by the US copyright notice,
© 2012 Y
which was mandatory for published works before 1989, and in which the circle-c symbol could be replaced with the word Copyright.
There is a preferred format for claiming copyright on a work:
Copyright year owner
For example:
Copyright 2016 John Smith
If you're referring to a work by someone else, then don't. Unless you have permission or one of the rare, misunderstood exemptions, you're violating their copyright.
BTW--You don't need to add anything to own the copyright, you're simply notifying people to bolster your claims later.
If you are John Smith and you want to declare your copyright on a photo you created, you use one of these synonymous phrases:
… replacing the year with the year in which the photo was created.
However, if you are not John Smith and you want to apply a photo credit to a photo that was taken by John Smith — for example, in a publication you are editing — you should use one of these synonymous phrases:
If John Smith asked you to include his copyright notice in the photo credit, you may want to use a combination: “Photo by John Smith © 2016 John Smith.” The duplication is necessary because in some cases, the person who took the photo does not own the copyright. For example: “Photo by John Smith © 2016 The New York Times.”
If you are declaring the copyright on a sound recording rather than a photograph, you also need to include the “sound recording copyright” to make the declaration valid worldwide. It looks like this: “℗ 2016 John Smith” and you will also see that combined with the copyright symbol, especially if the author also wrote music or a speech that is the content of the sound recording, like this: “© ℗ 2016 John Smith.”
Ideally, you use the actual glyphs for “©” and “℗” but you can also write “(c)” and “(p)” and lawyers like it just fine.