In reverse time migration (RTM), wavefield decomposition can play an important role in addressing the issue of migration noise, especially low-frequency noise. The complete wavefield decomposition based on the Hilbert transform is a commonly used method in RTM, but it is accompanied by extra wavefield simulation and wavefield storage. We have developed three distinct methods. The first is a convenient method for wavefield decomposition, which is based on Poynting vectors. Only the unit vector in one direction is needed to realize the wavefield decomposition in an arbitrary direction by this method. It breaks through the limitation that the Hilbert transform-based method is applicable only to the up- and downgoing wave or left- and right-going wave decomposition, and the calculation cost is negligible compared with RTM. The second is a method based on the instantaneous wavenumber, which we developed for calculating the wave propagation direction. On the basis of wavefield decomposition, the imaging angle gather from the new method performs better than that of the Poynting vector method. Meanwhile, it also is used for generating the incident angle gather and dip angle gather. The latter expresses the dip angle of underground strata. More importantly, the above methods allow us to control the wavefield decomposition direction and three angles at any position underground. The third adopts a stratigraphic imaging condition method, and we briefly analyze the relationship between the new method and the inverse-scattering imaging condition. The stratigraphic imaging condition maps the results to the dip angle of the stratum through a spatial gradient wavefield, which can enhance the effective imaging information. The above three kinds of angle gathers also can be constructed by the stratigraphic imaging condition. Numerical experiments demonstrate that the imaging results and the angle gathers obtained by our proposed method have higher accuracy and resolution.

中文翻译：

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基于地层倾角的任意方向波场分解和成像条件

在逆时偏移（RTM）中，波场分解在解决偏移噪声（尤其是低频噪声）问题方面可以发挥重要作用。基于希尔伯特变换的完整波场分解是RTM中常用的方法，但伴随着额外的波场模拟和波场存储。我们开发了三种不同的方法。第一种是基于Poynting矢量的便捷波场分解方法。通过该方法，仅需要一个方向上的单位矢量即可实现任意方向上的波场分解。它克服了基于希尔伯特变换的方法仅适用于上下波分解或左右波分解的局限性，与RTM相比，计算成本可忽略不计。第二种是基于瞬时波数的方法，该方法是我们为计算波传播方向而开发的。在波场分解的基础上，新方法采集的成像角比Poynting矢量法的成像角更好。同时，它也用于生成入射角聚集和倾角聚集。后者表示地下岩层的倾角。更重要的是，上述方法允许我们控制地下任何位置的波场分解方向和三个角度。第三种采用地层成像条件方法，并简要分析了新方法与反散射成像条件之间的关系。地层成像条件通过空间梯度波场将结果映射到地层的倾角，可以增强有效的成像信息。通过地层成像条件也可以构造以上三种角度集。数值实验表明，该方法获得的成像结果和角度集具有较高的精度和分辨率。