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有限差分算法的时间偏移精度随反射面倾角的增大而变差。通常,偏移,特别是有限差分法的一些性质,给出了一种改善用有限差分算法偏移陡倾角的精度。第一个性质是,用过低的速度偏移时虽然会产生偏移不足,但通过对其结果再次做偏移,会得到正确的结果。实际上,只要各级偏移步骤的偏移速度平方和等于正确偏移速度的平方值,那么,对偏移不足数据做多次偏移将得到正确的结果。第二个性质是,偏移处理感受到的反射面的空间视倾角不仅仅是未偏移反射的时间倾角的函数,而且也是用于偏移的速度的函数。在多步低速偏移过程中,每个偏移步骤感受到的空间视倾角比真倾角小得多。这样,由于对小空间倾角有限差分偏移是精确的,所以串联偏移产生的结果精度要高于单步偏移结果。另外,每个偏移步骤使用了低的速度,所以深度步长可以大些,因此,不需要增加计算工作量。在速度随深度增加的介质中,不损害该方法的精度(实际上得到了改善)。此外,在速度横向变化不太严重的情况下,串联方法受到的影响不会大于其它时间偏移方法。在该方法用于墨西哥湾叠加剖面的例子中,近于垂直的盐丘侧翼经偏移后,其精度可与经频率—波数域偏移方法的结果相比拟。
The accuracy of the time-shift of the finite difference algorithm deteriorates with the increase of the inclination of the reflecting surface. In general, some properties of offsets, and in particular of finite difference methods, give an approach to improve the accuracy of offsetting steep dips using finite difference algorithms. The first one is that with too low a speed offset, there will be less than enough offset, but by offsetting the result again, you get the correct result. In fact, as long as the sum of squares of the offset velocities at all stages of the offset equals the square of the correct offset velocities, multiple offsets to the offset less data will yield the correct result. The second property is that the spatial apparent dip of the reflecting surface experienced by the offset process is not only a function of the temporal dip of the undamped reflection but also a function of the velocity used for the offset. During multi-step low-speed excursions, the spatial apparent dip experienced by each offset step is much smaller than the true dip. In this way, the tandem offset produces higher accuracy than the one-step offset due to the finite difference offset of the small spatial dip is accurate. In addition, each offset step uses a low speed, so the depth step can be larger, so there is no need to increase the computational effort. In media with increased speed with depth, the accuracy of the method is not compromised (actually improved). In addition, the tandem method is not affected more than other time-shift methods when lateral changes in velocity are less severe. In the case of this method for the Gulf of Mexico superimposed profile, the accuracy of the near-normal salt dome flanks, after offsetting them, can be compared with the results of the frequency-to-wave number domain offset method.