Hurst指数与容量维在油气检测中的应用

Application of Hurst exponent and volume dimension to hydrocarbon prediction

本文首关论述了分数Brown运动是随机过程与分形理论相结合的产物，它可以刻画粒子的随机运动和揭示粒子振动位移增量与时间增量的标度性质；同时说明R／S分析表示由时间序列计算Hurst指数的算法与Hurst指数满足的经验幂律关系。文中指出，Hurst指数和容量线可作为油气检测的参数；并从理论上详细地描述了分数Brown运动的特性及Hurst指数的计算方法。文中给出的油气检测的应用实例表明，Hurst指数和容量维可作为油气检测中的一种有效参数。

Fractional Brown motion results from the combination of random process with fractal theory. It can describe random motion of particales and prove that both the displacement and time increments of particle vibration are of scale characteristic. R/S analysis (rescaled range analysis) means both the method for deriving Hurst ex-ponent from time sequence and the empiric power rules which Hurst exponent is satisfied for. Hurst exponent and volume dimension can be used as parameters for hydrocarbon prediction. We theoretically detail the characteristics of fractional Brown motion and the method for estimating Hurst exponent. lt is illustrated that Hurst exponent and volume dimension can be effective parameters in hydrocarbon prediction.