Estimation of Finite Population Properties When Sampling is without Replacement and Proportional to Magnitude

Abstract Geologists often evaluate aggregate volumes of discovered plus undiscovered oil and/or gas in a petroleum basin by use of geologic-volumetric methods. Although sophisticated geological reasoning may be employed, the essential idea behind these methods is simple: estimate (a) the volume of hydrocarbon bearing sediment in the basin, (b) the amount of hydrocarbons present per unit volume of sediment, and (c) the fraction of hydrocarbons present per unit volume that is technologically recoverable. The product of (a) and (b) is interpretable as a point estimate of the sum of amounts of oil and gas in place in individual oil and gas deposits (fields) in the basin. The product of (a), (b), and (c) is a point estimate of amounts of oil and gas recoverable from all individual deposits in the basin.