Elastic up/down going wavefields separation and imaging condition analysis

Multi-component seismic data contain shear wave information, which can supply more information about the underground. But, for get a good PP and PS image, we'd better use elastic reverse time migration. Elastic reverse time migration can handle diving-wave and without dip-angle limitation. But in the elastic reverse time migration, the up/down going wave mixed together. They will generate noise from up-up, down-down crosscorrelation. So, we use Hilbert transform to separate up/down going wave to overcome migration noise. Hilbert method requires less computation resource than traditional frequency-wavenumber domain method. In elastic media, P- and S-wave mixed together too. We use vector based decomposition method to separate them. This method can maintain the amplitude and phase information versus Helmholtz decomposition. But the separated P- and S-wave both are vectors. We should use a new imaging condition. In this paper, we introduce P-wave Poynting vector to get a scalar PP image result. We separate the PS image in two parts: sign and energy. The sign is computed by dot multiply from source P wave and receiver S wave. The energy is computed by the crosscorrelation between source P wave's amplitude and receiver S wave's. This imaging condition don't exist polarity inverse phenomenon.