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The Hubbert Linearization is a way to plot production data to estimate two important parameters of a Hubbert curve; the logistic growth rate and the quantity of the resource that will be ultimately recovered. The Hubbert curve is the first derivative of a Logistic function, which has been used in modeling depletion of crude oil, predicting the Hubbert peak, population growth predictions〔(【引用サイトリンク】 Projection of World Population )〕 and the depletion of finite mineral resources. The technique was introduced by Marion King Hubbert in his 1982 review paper.〔M. King Hubbert: Techniques of Prediction as Applied to the Production of Oil and Gas, in: Saul I. Gass (ed.): Oil and Gas Supply Modeling, National Bureau of Standards Special Publication 631, Washington: National Bureau of Standards, 1982, pp. 16-141.〕 The geologist Kenneth S. Deffeyes applied this technique in 2005 to make a prediction about the peak production of conventional oil. == Principle == The first step of the Hubbert linearization consists of plotting the production data (P) as a fraction of the cumulative production (Q) on the vertical axis and the cumulative production on the horizontal axis. This representation exploits the linear property of the logistic differential equation: : where ''K'' and ''URR'' are the logistic growth rate and the Ultimate Recoverable Resource respectively. We can rewrite (1) as the following: : The above relation is a line equation in the ''P/Q'' versus ''Q'' plane. Consequently, a linear regression on the data points gives us an estimate of the slope and intercept from which we can derive the Hubbert curve parameters: * the ''K'' parameter is the intercept with the vertical axis. * the line slope is equal to ''-K/URR'' from which we derive the ''URR'' value. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hubbert linearization」の詳細全文を読む スポンサード リンク
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