Correlative least-squares reverse time migration in viscoelastic media

Abstract Standard elastic least-squares reverse time migration (LSRTM) generally ignores the subsurface attenuation effects which can lead to blurred and unfocused migration images. To correct these attenuation effects, we develop a correlative Q-LSRTM approach in viscoelastic media. We use the viscoelastic wave equation based on the standard linear solid model to simulate the subsurface attenuation. The Born modeling and adjoint state equations in viscoelastic media can be derived by the Born approximation and adjoint state method, respectively. Instead of the conventional amplitude-matching misfit function, the proposed Q-LSRTM approach utilizes the normalized zero-lag crosscorrelation misfit function to emphasize the phase measure between the predicted and observed data. The gradients of the crosscorrelation misfit function with regard to reflectivity images of P- and S-wave impedance are estimated by a zero-lag crosscorrelation between the forward background wavefields and the reversal adjoint wavefields. In view of computational efficiency, we also derive an analytical step-length formula for the correlative Q-LSRTM approach, which only requires to solve the Born modeling operator once. Numerical examples using several 2D models have determined that the proposed Q-LSRTM can improve better image quality, compared with the standard elastic LSRTM approach. Furthermore, the crosscorrelation misfit function is less sensitive to amplitude errors.