"Attanasi, E.D., and Root, D.H., 1994, The enigma of oil and gas field growth: American Association of Petroleum Geologists Bulletin, v. 78, no. 3, p. 321-332."
If I plot the raw data as a scatter plot which shows only fractional increases per year since the year of discovery it looks like the chart below. Note that this plot does not visualize the "multiplier" approach which A&R choose to do; IMO they do this rather unwisely, because it accentuates bad early estimates. The "fractional" approach provides an accepted statistical way to look at this kind of data which avoids amplifying regions with poor statistics.
I also put in a 20-point moving average filter to guide the eye (not weighted by size of field). Notice that in the sweet spot right in the middle of the chart, where we get the best statistics, the "reserve growth" fluctuates around 1% per year. You can see some growth for fields for fields older than ~80 years, but those have have worse sampling statistics than the rest. The latest data also exhibits poor sampling statistics.
Basically this approach demonstrates how you extrapolate assumed stationary data correctly.
Now, I ask the question how 1% reserve growth of mature fields will effectively compensate the 5% to 20% depletion rate per year routinely estimated for many fields?