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近年来,波动方程偏移都是用克莱鲍特和多尔蒂1972年及克莱鲍特1976年提出的有限差分法逼近抛物线微分波动方程来实现的[3,4].对波动方程的抛物线逼近[14]已经证明在波传播的很多领域都是成功的.塔珀特和哈丁1973年提出的长程声传播的分裂算法(“split-step”algorithm)对速度结构二维变化的介质是特别有效的方法[23].在这个算法中微分算子相继地被应用于它们相应的变换域,速度变化的影响可以分裂成以各个转换变数表示的相位移算子.因为微分算子能被应用于它们的变换域,与空间数值近似有关的误差就可消除.这个算法曾经成功地应用于在速度二维变化的介质中传播的长程声波.在地震资料中,这个方法也已成功地应用,并提供了一个作频率一波数偏移的高效率计算机方法.在速度结构剧烈变化的区域,实现这个方法将提供特殊的效果.
In recent years, the wave equation migration has been achieved by approximating the parabolic differential wave equation using the finite difference method proposed by Claybott and Doherty in 1972 and Claybottom in 1976 [3,4]. For wave equation The parabolic approximation [14] has proved successful in many areas of wave propagation. The medium that the split-step algorithm proposed by Tarpatt and Harding in 1973 for two-dimensional changes in velocity structures Is a particularly effective method [23], in which differential operators are successively applied to their corresponding transform domain and the effect of velocity variation can be split into phase shift operators expressed in terms of individual conversion variables. Since the differential operator can Is applied to their transform domain and the errors associated with the spatial numerical approximation can be eliminated.This algorithm has been successfully applied to long-range acoustic waves that propagate in two-dimensional media with varying velocities. This method has also been successfully applied to seismic data Application, and provides an efficient computer method for frequency-to-wavenumber migration. Implementing this method will provide special effects in areas where the speed structure changes dramatically.