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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。
This paper first discusses that the fractional Brownian motion is a product of the combination of stochastic processes and fractal theory. It can characterize the random motion of particles and reveal the scaling properties of incremental and temporal increments of particle vibration. At the same time, Time-series calculation Hurst index algorithm and Hurst exponent satisfaction power-law relationship. It is pointed out that Hurst exponent and capacitance line can be used as parameters for oil and gas detection. The characteristics of fractional Brownian motion and the calculation method of Hurst exponent are described in detail in theory. The application examples of oil and gas detection given in this paper show that the Hurst exponent and the capacity dimension can be used as effective parameters in oil and gas detection.