A Vertical Seismic Profiling Wavefield Separating Method Based on the Frequency-Wavenumber Vector.

The separation of up-going and down-going wavefields is a significant step in vertical seismic profiling (VSP) data processing. The traditional frequency-wavenumber (FK) transform method maps the VSP signal from the time-space domain to the FK domain for separation. However, the FK transform method cannot separate the wavefields well near the reflecting surface. In this letter, we propose a novel method called FK vector classification (FKVC) to separate up-going and down-going wavefields from 2-D VSP data. First, we use the curvelet transform (CT) to extract the direction information of the VSP signal. CT is a tight frame and has multi-direction characteristics, so it can sparsely represent the signal in the curvelet domain. Although the shape of the curvelet window will cause some energy diffusion, synchrosqueezed CT (SSCT) can reassign the curvelet coefficients at the 2-D reference instantaneous frequency (IF) to improve the resolution. Then we extract the FK vector (FKV) of the up-going and down-going wavefields respectively based on SSCT. Finally, the up-going and down-going wavefields can be separated by the angular difference of FKV. Both the synthetic example and real zero-offset VSP data example demonstrate the effectiveness of the proposed method. Compared with the FK transform method, the FKVC has a better separation result.