Preconditioning least-squares RTM in viscoacoustic media by Q-compensated RTM

Reverse-time de-migration (RTDM) is formulated as the ad-joint operator of reverse-time migration (RTM). In acoustic medium, RTM provides a good approximation to the inverse of RTDM, and can be used to iteratively invert for the reflectivity image in least-squares RTM (LSRTM). In viscoelastic medium, however, the adjoint of the RTDM operator is far from its inverse because of amplitude attenuation during both forward and backward wave propagation. As a result, LSRTM in attenuating medium may suffer from a slow convergence rate due to the ill-conditioned wave-equation Hessian. To improve the convergence rate, we propose preconditioning LSRTM by replacing the original RTM operator with a better approximate inverse to the RTDM operator, namely the Q-compensated RTM (Q-RTM). Since the inverted matrix is numerically non-Hermitian, we use the Generalized Minimum Residual (GMRES) method instead of the Conjugate Gradient (CG) method as the iterative method. Numerical tests demonstrate that the proposed Q-LSRTM approach converges significantly faster than LSRTM, and is capable of producing high-quality attenuation-compensated images within the first few iterations.