I would be interested in your thinking behind the idea the first curve is the largest fields. (I agree, but interested in hearing your logic).

First glance said to me "peak in early 70's, must be US". But the size is too large.

Well, I was thinking anout the discovery pattern of oil fields:


(data taken from Simmons's book)

The largest fields are also the oldest and the most accessible with high flow wells.

Given the first bump was politically driven - ie a manifestation of an external force, rather than a feature of nature or geology, I find it hard to accept that it can be explained as it being due to some natural decline in a subset of larger fields. It just doesn't make sense to me.
The 1973 and 1979 oil shocks were politically driven but not the prior strong production growth.
You left me completely confused... how does that address the problem? The decline in the 70's was politically driven, but you are claiming the decline was really due to the decline of some subset of the fields just because you can make a curve fit under the first bump. Seriously, that's not very convincing is it?
I think we are not understanding each other.

Stuart identified several time periods where the growth rate is stationary:

1891-1929         7.9%  
1929-1942         3.9%  
1942-1973         7.4%  
1973-1979         2.1%  
1979-1983         -4.0%  
1983-2004         1.5%  

Between each period, we have economic transitions, oil shocks,  wars, etc. I agree with you that the transitions in 1973 and 1979 were politically driven (OPEC embargo and the Iran crisis respectively) and not a natural decline of some subset of fields. However, prior to these two shocks, the period between 1942 and 1973 enjoyed an exceptional growth rate (7.4%) which was possible mainly because of a few giant oil fields discovered in the 40s-60s (see graph about discoveries above) that not necessarely required a mature oil infrastructure.

You could probably also make an arguement that the growth would have probably been (and indeed has been) fairly constant in the mid 7%'s if the oil had been absolutely effeciently extracted. And then argue the exceptions are due to the extreme situations in the thirties (the economic depression) and the late seventies/early eighties (embargo/politics in Iran) which "interfered" with effecient development. Then from the ninties onwards you start approaching the peak and so you might expect growth in production to slow. So the model is intact. Would that make sense?