Viscoacoustic least squares reverse time migration with attenuation estimation using alternating directions

Seismic imaging in attenuating media requires accurate compensation for amplitude decay and phase dispersion. Conventional least-squares reverse time migration (LSRTM) methods are sensitive to this phenomenon, as the lack of compensation for dispersion and absorption can lead to low-resolution images with distorted and blurred amplitudes. A common way to overcome this problem is by applying viscoacoustic modeling based on an independent estimate of the quality factor Q (Q-LSRTM). An alternative procedure is to incorporate the attenuation estimation into Q-LSRTM in a multiparameter approach, estimating reflectivity and attenuation models within the same iterative procedure. This procedure was carried out using alternating directions (AD-Q-LSRTM). The idea was to alternate between estimating reflectivity and attenuation, iterating this process until both parameters converged. The approach was validated through numerical experiments on three synthetic models: a layered model with an attenuation anomaly, the Marmousi-II model, and a part of the BP gas reservoir model. The results demonstrated that the proposed method improved the delineation of subsurface structures, particularly in highly attenuating regions, while reducing imaging artifacts. AD-Q-LSRTM allowed the attenuation model to account for transmission losses, multiple scattering effects, and illumination variations, leading to enhanced reflectivity images. Whereas conventional Q-LSRTM relies on an a priori attenuation model (typically assuming a constant Q), this method provided a more robust solution by jointly refining both the reflectivity image and the Q model. Although challenges remain in fully recovering an accurate attenuation model due to inherent trade-offs, the proposed framework achieved significant improvements in seismic image resolution and amplitude fidelity. These findings highlight the potential of AD-Q-LSRTM as a robust tool for imaging complex subsurface environments.