Least-squares reverse time migration based on the viscoacoustic VTI pure qP-wave equation

With the deepening of oil and gas exploration and the increasing complexity of exploration targets, the influence of anisotropy and anelasticity of subsurface media on seismic imaging cannot be ignored. The least-squares reverse time migration is developed on the idea of linear inversion, which can effectively solve the amplitude imbalance, low resolution, and serious imaging noise problems of RTM. In this paper, based on the viscoacoustic pure qP-wave equation, the corresponding demigration operator, adjoint operator, and gradient-sensitive kernel are derived, and the least-square reverse time migration imaging algorithm of viscoacoustic pure qP-wave in VTI medium is proposed. During iterative inversion, the inverse of Hessian is approximately solved to achieve stable attenuation compensation. Finally, we verify the effectiveness and applicability of the proposed viscoacoustic VTI least-squares reverse time migration imaging algorithm through the model tests and field data. The numerical results show that the method can compensate for the amplitude loss and phase distortion caused by attenuation, and correct the anisotropy-induced misalignment of the reflection interfaces, which improves the accuracy and resolution of the imaging profile.