A high-efficiency wavefield decomposition method based on the Hilbert transform

Abstract

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.