Seismic migration in viscoacoustic vertical transversely isotropic media using a pure qP wave equation

Seismic anisotropic attenuation and anisotropic velocity exist widely in the earth's interior and have a great influence on the propagation of seismic waves. Ignoring the effects of attenuation anisotropy may lead to amplitude imbalance or noise in reflection seismic imaging, thus reducing the quality of the imaging results. In order to incorporate attenuation anisotropy into imaging methods and explore its effect on imaging, based on a novel two-way pure qP wave equation in viscoacoustic vertical transversely isotropy media, we propose the corresponding reverse time migration and least-squares reverse time migration method. Both imaging methods can accurately obtain subsurface structure information, especially the least-squares reverse time migration has the potential to compute accurate subsurface reflectivity. In this paper, we first introduce the pure qP wave equation in viscoacoustic vertical transversely isotropy media. As the equation is derived from the complex dispersion relation of P wave, wave propagation can be simulated without interference of SV wave and limitation of anisotropic parameters. Then, we derive the corresponding linearized wave equation and adjoint gradient for updating the imaging result. Finally, using two synthetic models, we demonstrate the effectiveness of the imaging method and discuss the effect of attenuation anisotropy on seismic imaging.