大步长波场深度延拓的理论

Theory of large-step wavefield depth extrapolation

波场延拓是地震偏移成像的基础.快速进行目标区波场延拓对石油勘探中急需发展的深部地震勘探和无组合海量地震数据的成像有重要意义.在目标区成像中,目前已有的波场延拓方法,包括基于走时计算的Dix方法和射线追踪方法,以及基于小步长波场递推的方法,在适应复杂介质、计算精度和计算效率的某一方面还不能完全满足实际需要.本文提出一种基于“算子相位”李代数积分的快速计算延拓算子的方法,称为大步长波场延拓方法.在该方法中,指向目标区的波场延拓算子象征的复相位被表示成波数的线性组合.线性组合的系数是层速度函数及其导数的深度积分,计算和存储较为方便.波场延拓算子通过相移算子加校正的方法,利用快速Fourier变换在空间域和波数域予以实现.利用动力学等价关系导出了便于计算的表达式.本文比较了算子主象征函数用一步法展开和用两步法展开的精度,从而说明大步长方法的精度要高于递推方法.在横向和纵向线性变化介质中,将大步长方法的脉冲响应与递推法做了比较,说明大步长延拓算子的走时精度主要取决于相移因子中的横向变速校正项;且在各种近似下,大步长算子发生的频散都非常小.

Wavefield extrapolation object oriented wavefield extrapolati is the foundation of seismic migration imaging. Finding a way of quick and on is significant not only for deep seismic exploration but also for imaging with super-tremendous seismic data acquired from non-combination receivers, both highly needed to develop in petroleum prospecting. To image target zones, as far as all present wavefield extrapolation methods are concerned, including travel-time based Dix-formula methods, ray tracing, small-step depth recursion, etc., the adaptability to complex media, precision and computing efficiency are not satisfying for practical needs in some respects. In this paper, a new technique （so-called large-step wavefield depth extrapolation method）, that is based on the Lie algebraic integral of operator＇ s phase to compute depth extrapolation operator efficiently, is ~ In the method, the complex phase of object oriented wavefield extrapolation operator＇ s symbol is expressed as a linear combination of wavenumbers, and the coefficients of linear combination are all in the form of the integral of interval velocity functions and their derivatives over depth. Moreover, the computation is convenient and needs less storage space. With phase shift plus correction, the wavefield extrapolation operator is implemented using equivalent relationship FFT （Fast Fourier Transform） in spatial and wavenumber domains. Here, the kinetic is resorted to derive the expression convenient for computation. We compare the precision of one-step scheme with that of two-step scheme for expanding an operator＇s primary symbol function, which illustrates the large-step scheme is more accurate than its recursive counterpart. Besides, in a linearly variant medium laterally and vertically, the point source pulse response of the large-step method is compared with that of depth recursion methods. The numerical examples indicate that travel-time precision of the large-step extrapolation operator mainly depends on the lateral velocity variation modifcafion items in phase shift operator. In addition, in different approximation cases, the dispersion caused by the large-step operator is rather small.