Reflection waveform inversion (RWI) exploits reflected-wave information in seismic data to update the deep background velocity model. By alternately inverting for the migration and tomographic components, RWI not only improves the accuracy of deep velocity model updates but also alleviates the cycle-skipping problem to a certain degree. However, RWI generally requires seismic data with a high signal-to-noise ratio (SNR) and has so far achieved its most successful applications in marine environments. In contrast, land seismic data are often degraded by poor receiver coupling, rugged topography, environmental noise, and strong surface-wave interference, making it difficult to acquire continuous and high-SNR reflection waveforms, which severely limits the applicability of RWI to land data. To address these challenges, this study employs Kirchhoff pre-stack time migration to identify characteristic reflection layer and extract their corresponding common-image gathers (CIGs). The extracted events are then reverse migrated to reconstruct reflected-wave data with enhanced SNR. The reconstructed data are subsequently incorporated into RWI and validated using both synthetic and field data examples. The results demonstrate that the proposed method significantly improves the accuracy of deep background velocity model updates. Furthermore, the strong consistency between the migrated images and the corresponding CIGs confirms the reliability and effectiveness of the reconstructed reflection data for RWI applications. Overall, this method offers a new feasible solution for applying RWI to land seismic data.

P- and S-wave separation plays an important role in elastic reverse-time migration. It can reduce the artifacts caused by crosstalk between different modes and improve image quality. In addition, P- and S-wave separation can also be used to better understand and distinguish wave types in complex media. At present, the methods for separating wave modes in anisotropic media mainly include spatial non-stationary filtering, low-rank approximation, and vector Poisson equation. Most of these methods require multiple Fourier transforms or the calculation of large matrices, which require high computational costs for problems with large scale. In this paper, an efficient method is proposed to separate the wave mode for anisotropic media by using a scalar anisotropic Poisson operator in the spatial domain. For 2D problems, the computational complexity required by this method is 1/2 of the methods based on solving a vector Poisson equation. Therefore, compared with existing methods based on pseudo-Helmholtz decomposition operators, this method can significantly reduce the computational cost. Numerical examples also show that the P and S waves decomposed by this method not only have the correct amplitude and phase relative to the input wavefield but also can reduce the computational complexity significantly.