I would have to do some research to be for sure! I figure there are several ways of achieving the look!!
It appears to look somewhat like a case hardening process! Take a look at this link!
Image: guns-pictures.drippic.com
Color case hardening (sometimes referred to as case-hardening, case color hardening, or surface hardening) is a heat treating process and one of the earliest ways of hardening lower-grade steel. Originally, this process used bone charcoal heated to an exact temperature. Afterwards, the parts were removed from the furnace and quenched.
Color Case Hardening - Turnbull Restoration
www.turnbullrestoration.com/restoration-services/color-case-hardening/
It could be a careful etching using two different solutions of ferric acid! I have been told if you use ferric acid to etch something copper it ruins the ferric acid, except for use on a copper objects. I have been told that anything you etch after that will retain the copper residue! Sooooooooo working on that theory if you purposely exposed ferric acid to a lot of copper. The following items would be etched and copper would be left on them.
Also another method may be the following. There is a product called Birchwood Casey's Plumb brown. It is meant to give a browning instead of a bluing. It is used on period correct muzzle loaders barrels and their furniture to mimic an old weapon that was exposed to the elements. However if you fail to shake/mix it up and paint it on after heating the piece you will see more of a copper look rather than brown!
I have never tried to mimic the look but I would start with trial and error working with the afore mentioned processes. Testing to see if I could get the look!! Anyway that is where I would start trying to get that kind of a look!!

You would definitely want to have the process nailed before you attempted it. The maker made a top shelf Tomahawk and the other is just gravy!!