“There’s literally tons of carbon here,” she said, looking around the bog, which covers several acres off a muddy oil-company road amid the vast flatness of northern Alberta.
I think this sentence could be two meaning grammatically like:
and, i don't know which picture should be a right meaning semantically.
Mostly ditto StoneyB, but let me say it a little differently.
Sometimes modifiers are grammatically ambiguous but clear from context. For example, if I said, "I saw a dog with a leash that was running", you would surely understand that to mean that the dog was running, not that the leash was running. But if I said, "I saw a dog with a leash that was a metal chain", you'd understand that the leash was a chain, not that the dog was a chain. If I said, "I saw a dog with a leash that was brown" ... now you can't be sure. Either the dog or the leash could plausibly be brown. The sentence is left ambiguous because it was poorly worded.
I'm suddenly reminded of a listing I saw in a catalog years ago for some sort of bowl that said "[whatever] bowl excellent for a cook with a round bottom suitable for beating". I'm sure the writer meant that the bowl has a round bottom and it is suitable for beating cake mixes or whatever in. But my first thought was that the cook has a round bottom suitable for spanking him or her.
In this case: It's clear that the "bog" covers "several acres", and the "several acres" are "off a muddy road". The carbon is in this area, I'd assume in the bog. So what is "amid the vast flatness"? I suppose that grammatically you could read it as the acres are in the flatness, or that the road is in the flatness, or both.
In real life, the most sensible reading is that the acres and the road are both in the vast flatness. "Vast flatness" is not something then tends to have clearly-defined borders. If someone said, "the vast flatness ends here", someone else might reply, "no, it goes a hundred miles further south than that", but they'd be unlikely to say, "no, it goes 9 inches further south than that". The end of the "vast flatness" is likely vague within several miles, at least. So it's unlikely someone would say that a road runs past a bog and the road is in the vast flatness but the bog is not, like the flatness ends exactly in the space between the road and the bog.
Note the reading of this could be very different if the phrase was something with a more clearly defined boundary than "vast flatness". Like if she had said, "covers several acres off a muddy road on land owned by XYZ Company", it's possible that the several acres are on land owned by XYZ Company and the road is not, or the road is on land owned by XYZ Company and the bog is not. I'd probably assume both the bog and road are on land owned by XYZ Company, but that's not necessarily the case.
Preposition phrases can be "stacked", just like ordinary adjectives, and the precise scope of each term can be ambiguous—is a "little red dog" a [little [red dog]] or a [[little & red] dog]?
In many cases the difference is so trivial it need not be disambiguated—does it really matter which parsing we bring to "little red dog"? In other cases, the difference is resolved by the 'world-knowledge' shared by the writer and the readers. That's the case in your example: the acres adjoin the road, which we assume to extend in both directions well beyond the acres, and both are set within ("amid") a "vast" territory—Alberta has an area of quarter-million square miles.
