Wave-mode separation can be achieved by projecting elastic wavefields onto mutually orthogonal polarization directions. In isotropic media, because the P-wave’s polarization vectors are consistent with wave vectors, the isotropic separation operators are represented by divergence and curl operators, which are easy to realize. In anisotropic media, polarization vectors deviate from wave vectors based on local anisotropic strength and separation operators lose their simplicity. Conventionally, anisotropic wave-mode separation is implemented either by direct filtering in the wavenumber domain or nonstationary filtering in the space domain, which are computationally expensive. Moreover, in conventional anisotropic separation, correcting for amplitude and phase changes of waveforms by applying separation operators is also more difficult than in an isotropic case. We have developed new operators for efficient wave-mode separation in vertical transversely isotropic (VTI) media. Our separation operators are constructed by local rotation of wave vectors to directions where the quasi-P (qP) wave is polarized. The deviation angles between the wave vectors and the qP-wave’s polarization vectors are explicitly estimated using the Poynting vectors. Obtaining polarization directions by rotating wave vectors yields separation operators in VTI media with the same forms as divergence and curl operators, except that the spatial derivatives are now rotated to implement wavefield projections in accurate polarization directions. The main increase in computational cost relative to isotropic separation operators is the estimation of the Poynting vectors, which is relatively small within elastic-wave extrapolation. As a result, applying the proposed operators is efficient. In the meantime, the waveforms corrections for divergence and curl operators can be directly extended for our new operators due to the similarities between these operators. By numerical exercises, we have determined that wave modes can be well-separated with small numerical cost using the present separation operators. The conservation of energy in wave-mode separation by applying waveform corrections was also verified.

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Angle‐domain common‐image gathers are an important tool in the post‐processing of seismic images and for reservoir characterization. The generation of angle gathers is a very important issue when dealing with angle‐domain images. Efficiency and robustness are the main concerns in the generation of angle gathers. In this paper, we propose two methods for producing angle gathers based on the implementation of a reverse‐time migration. In the hybrid method, we adopt the local‐plane‐wave decomposition method to extract the local plane waves and obtain two possible opposite propagation directions in the time‐wavenumber domain. Then, Poynting vectors are used to determine the correct propagation direction. The hybrid method achieves a satisfactory balance between robustness and computational efficiency. Furthermore, in the improved hybrid method, additional computational acceleration is obtained by separating the overlapping and non‐overlapping wavefield areas. The hybrid method is only applied in these areas with overlapping wave fronts, and the Poynting‐vector‐based method is adopted in the other areas. The location of the overlapping events is determined using the eigenvalues of the structural tensor. Finally, the two‐dimensional synthetic and field examples demonstrate the effectiveness of both methods.

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