Dancingbeard, In 1968, an imaginary line was drawn straight eastwards across the North Sea from the Scotland/England border near Berwick. This marked the areas allocated to each of the countries as regards law/crime. For example, if a crewman murdered the skipper of a trawler north of the line, he would be charged and tried under Scots law, whereas - had he committed the crime south of the line - he would be charged and tried under English law.
In 1999, another such line was drawn, which marked the areas allocated to each of the countries as regards fisheries specifically. This time, instead of heading directly due east, the line went off in a north-easterly direction, as you say. However, it finished up level with Dundee at the median north/south line. Have you heard of any recent discoveries south of Dundee?
If Scotland votes for independence, either one of these existing ‘legal’ lines or another line altogether will have to be agreed on as the border between which part of the North Sea is under Scottish jurisdiction and which part is under English jurisdiction as far as OIL is concerned. In other areas of the world, the median line is the one generally employed, as has happened with the European countries which have exclusive areas in the eastern part of the North Sea.
If you imagine the second line I mentioned - the same line you yourself mention - puts most of the oil in England’s sector if Scotland becomes independent, either (a) your geography is rather faulty or (b) you’ve failed to notice that the southern North Sea is where supplies are beginning to fade.
As a matter of interest, it is generally accepted that over 90% of the oil revenue which has accrued to the UK Treasury during the last 40 years or so came from what would have been “Scotland’s area”, whichever of the existing lines was chosen. In other words, if independence happened, virtually all of that money would find its way into the Treasury in Edinburgh and practically none of it would go to Westminster! Remember, too, that - as I've already pointed out - England would have no access to the productive areas of the North Atlantic, which is where the oil future lies.
(As a further matter of interest, the same would be true of all the revenue generated by Scotland’s whisky distilleries!)