I think your best bet is to have an image that doesn't actually have a background color included in it. and preferably have it in svg format. (most companys have their logos available in svg as its infinitely resizeable). And so then you would just set the color of your AppBar to black, and add "Geoprobe" svg (or png as a backup).
This will make sure that it's resizeable on wider devices and stuff (vs just an image thats stretched)