That would require a large-scale fluvial erosion event over a long period of time in order to carve the canyon out. Some type of large-scale value l-system noise could do it if it were available. You might get away with it using regular erosion but the erosion size would have to be not only very long but very wide, deep and tapered at there ends then the small-scale erosion can be mixed in with the canyon like smaller sediment channels and water channels for example. As far as animating it, i have yet to see how technically it is done in any software. Again you might have to grow using a branched channel noise as if the tree branches were digging there way through the terrain therefore creating the canyon time scale. Something like Houdini might do that as it has a built in l-system noise that can be animated in many ways.
