运用分形方法模拟地震勘探中的三维随机介质

Simulation of 3-D random medium in seismic prospecting using fractal method

实际的地震勘探遇到的是复杂随机介质,常规层状介质地震波场理论已经不能适应于高精度地震工作,需要进一步发展非均匀介质地震波场理论.本文首次给出了运用分形方法建立三维随机介质的具体算法;其次引入了三维锥形函数来压制建模时产生的离散误差;最后,通过建立几种三维随机介质模型来讨论尺度系数和豪斯特指数对模拟结果的影响,并且简单构建了区域多尺度随机介质模型.模拟的结果表明,分形方法可以更方便、灵活地模拟三维随机介质.针对南海某地区生物礁储层非均质性强的特点,在建立生物礁速度模型时,对目标区充填了多尺度的分形随机介质,波动方程正演模拟结果表明,分形随机介质可以用来描述生物礁等非均质性储层.

The actual seismic exploration encountered complex random medium,the conventional layered medium seismic wave field theory has been unable to adapt to the high-precision seismic work,we need further develop the non-homogeneous medium seismic wave-field theory. Firstly,the specific algorithm of 3-D random medium with fractal is given in this paper.Secondly,to suppress discrete modeling errors,a 3-D tapering function is introduced. Finally, through the establishment of several 3-D random medium models,we discuss the impact of scale coefficients and Hurst exponent on the simulation results,and simply construct regionalized multiscale random medium model.The results show that simulating3-D random medium with fractal is more convenient and flexible.The reef reservoir has very strong heterogeneity in some area in south of China,when we establish reef velocity model,the target area is filled with multi-scale fractal random medium,the result of seismic wave equation forward modeling shows that fractal random media can be used to describe reef and other heterogeneous reservoirs.