Wavefield decomposition can be used to extract effective information in reverse time migration and full-waveform inversion. The wavefield decomposition methods based on the Hilbert transform (HTWD) and the Poynting vector (PVWD) are the most commonly used. The HTWD needs to save the wavefields at all time steps or introduce additional numerical simulation, which increases the computational cost. PVWD cannot handle multiwave arrivals, and its performance is poor in complex situations. We have developed an efficient wavefield decomposition method based on the Hilbert transform (EHTWD). EHTWD constructs two wavefields to replace the original wavefield and the wavefield after the Hilbert transform. The first wavefield is obtained by using the dispersion relation to modify the frequency components. The other wavefield is obtained by time difference approximation. Therefore, there is a 90° phase change between the two wavefields. In EHTWD, we only need two wavefields at different moments, which avoids the need for additional numerical simulation. EHTWD is also suitable for wavefield decomposition in arbitrary directions. Compared to HTWD, the computational complexity can be greatly reduced with the decrease of the number of imaging time slices. The numerical examples of wavefield decomposition demonstrate that our method can realize wavefield decomposition in any direction. The examples of imaging decomposition and real data also indicate that EHTWD suppresses imaging noise effectively.

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基于希尔伯特变换的高效波场分解方法

波场分解可用于提取逆时偏移和全波形反演中的有效信息。最常用的是基于希尔伯特变换（HTWD）和坡印廷矢量（PVWD）的波场分解方法。HTWD需要在所有时间步长保存波场或引入额外的数值模拟，这会增加计算成本。PVWD无法处理多波到达，并且在复杂情况下其性能很差。我们已经开发了一种基于希尔伯特变换（EHTWD）的有效波场分解方法。EHTWD构造两个波场以替换原始波场和希尔伯特变换后的波场。通过使用色散关系修改频率分量来获得第一波场。通过时差近似获得另一个波场。因此，两个波场之间存在90°的相位变化。在EHTWD中，我们仅在不同时刻需要两个波场，从而避免了额外的数值模拟。EHTWD也适用于任意方向的波场分解。与HTWD相比，随着成像时间片数量的减少，计算复杂度可以大大降低。波场分解的数值例子表明，我们的方法可以实现任何方向的波场分解。成像分解和实际数据的示例还表明，EHTWD有效地抑制了成像噪声。这样就无需进行额外的数值模拟。EHTWD也适用于任意方向的波场分解。与HTWD相比，随着成像时间片数量的减少，计算复杂度可以大大降低。波场分解的数值例子表明，我们的方法可以实现任何方向的波场分解。成像分解和实际数据的示例还表明，EHTWD有效地抑制了成像噪声。这样就无需进行额外的数值模拟。EHTWD也适用于任意方向的波场分解。与HTWD相比，随着成像时间片数量的减少，计算复杂度可以大大降低。波场分解的数值例子表明，我们的方法可以实现任何方向的波场分解。成像分解和实际数据的示例还表明，EHTWD有效地抑制了成像噪声。波场分解的数值例子表明，我们的方法可以实现任何方向的波场分解。成像分解和实际数据的示例还表明，EHTWD有效地抑制了成像噪声。波场分解的数值例子表明，我们的方法可以实现任何方向的波场分解。成像分解和实际数据的示例还表明，EHTWD有效地抑制了成像噪声。