Cubic Discovery Model follow-up

As a followup to the cubic oil discovery model post, I figured that suggesting typical numbers would help us make sense of the scale and dynamics of the discovery profile's rise and fall -- and provide a sanity check.

First, let's recall that the earth has a surface area of approximately 500 million square kilometers. Then we make the crude assumption that we can probe for oil up to 10 Km below the surface with little trouble. This gives a total volume of 5x10¹⁸ cubic meters. Under the order of magnitude estimate that it took approximately 100 years to explore all of this volume, we can deduce the initial and final volume/year sampled.

Integral (Volume/year) = Total Volume

So assuming a linear dimensional increase per year (caused by ever increasing manpower supply as well as technical improvements), we likely started out in the year 1858 sampling a volume 20 meters deep and 100 Km on a side. And then we ended in 1958 sampling a volume per year the equivalent of 2 Km deep and 100,000 Km on a side. (The volumes remain more important that the relative dimensions)

To thoroughly sanity check and perhaps validate these numbers, getting data for the actual volume per year explored would certainly help to prove or disprove the basis for the model. Barring that, the power-law increase in sampling volume seems the only reasonable explanation for why the biggest set of discoveries occurred well into the 20th century. As the probability of discovery has to scale proportionately to the sampled volume, a cubic growth remains the simplest way to defer the major discoveries until later. So the fact that the discovery model can predict the rise and fall accurately along with spanning the range of possible sampling volumes, gives us added confidence of the general validity of the model.

Bonus round: If the earth's explorable crust contains 5x10¹⁸ cubic meters, and the estimated total oil at 3 trillion barrels (0.117 cubic meters / barrel), what fractional volume does the oil displace? Answer: 0.0000000006. So, on the average, for every barrel discovered, you have to probe 1.66 million cubic meters.