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对于常速介质.Stolt 的频率—波数(f-k)方法在计算上是有效率的,且对倾角精度没有限制。虽然 f-k 方法可以处理适中的垂向速度变化.但当这种变化很大时,对于陡倾角情况.误差将变得难以接受。本文阐述了一种推广后的 f-k 方法,该方法消除了对垂向速度变化的限制.且仅需用少量的计算时间,就可以达到与相移法偏移相当的精度。f-k 方法的推广是以速度场的剖分为基础.就象串联有限差分偏移那样,执行若干级 f-k偏移。在每一级中.偏移速度场较之常规偏移方法中的速度场而言更接近于常数,这时的 f-k 偏移很理想。经验结果和误差分析表明,对于任何一个实际的垂向非均匀速度场而言,最多只需要四级串联 f-k 偏移就可以达到与相移法相同的精度。对给定的精度和效率.串联 f-k偏移成为一种可供选择的方法,用来做二维、两次三维和一次三维时间偏移。
For constant media, Stolt’s frequency-wavenumber (f-k) method is computationally efficient and has no limit to the accuracy of the dip. Although the f-k method can handle modest vertical velocity changes, when this change is large, the error will become unacceptable for steep dip angles. In this paper, a generalized f-k method is introduced, which eliminates the limitation of the vertical velocity and only achieves the accuracy of the phase shift method with a small amount of computation time. The generalization of the f-k method is based on the velocity field splitting, which performs several stages of f-k offsets, just as serial finite difference offsets do. In each stage, the offset velocity field is closer to constant than the velocity field in the conventional migration method, and the f-k offset at this time is ideal. Empirical results and error analysis show that for any actual vertical inhomogeneous velocity field, only up to four stages of series f-k offsets are required to achieve the same accuracy as the phase shift method. For a given accuracy and efficiency, series f-k offsets become an alternative method for making two-dimensional, two-dimensional, and three-dimensional time offsets.