Abstract In this study, based on the exact dispersion relationship between qP and qSV waves in VTI media, the circular frequency of qSV-waves in the corresponding HTI dispersion relation was set to zero after vector rotation. This step enables us to derive a first-order velocity-stress wave equation specifically for qP-waves in HTI media. Building on this foundation, we developed and applied an explicit Q-viscous theory to anisotropic media, establishing an approximate acoustic first-order velocity-stress wave equation for qP-waves that incorporates the quality factor Q in viscous HTI media while maintaining computational accuracy and efficiency. Forward numerical experiments confirm that all newly derived equations represent pure qP-wave equations, free from constraints imposed by the anisotropic parameters ε and δ. Furthermore, the study examines how subsurface viscosity and anisotropy influence seismic-wave amplitude and phase characteristics. For migration imaging, an optimized cross-correlation imaging condition based on seismic-wave propagation paths and the Q factor is proposed to achieve energy compensation, improve illumination across image sections, and suppress shallow cross-correlation noise. Through migration imaging using seven distinct methods, the effects of subsurface media viscosity and anisotropy on image profiles are comparatively analyzed. The results demonstrate the advantages of the proposed migration-imaging method in terms of signal-to-noise ratio and overall image accuracy.
Zhu et al. (Thu,) studied this question.