Absolute URLs omitting the protocol (scheme) in order to preserve the one of the current page

is this URL format safe to use for all
browsers.

I can’t say anything for sure, but you should be able to test it in different browsers.

And is it a standard?

Technically, it is called “network-path reference” according to RFC 3986. Here is the scheme for it:

  relative-ref  = relative-part [ "?" query ] [ "#" fragment ]

  relative-part = "//" authority path-abempty
                / path-absolute
                / path-noscheme
                / path-empty

There is a problem though, when used on a <link> or @import, IE7 and IE8 download the file.

Here is a post written by Paul Irish on the subject:

• The protocol-relative URL