An approximate least squares reflectivity inversion in the presence of density

Traditional least-squares reverse time migration (LSRTM) often aims to improve the quality of seismic imaging, such as removing the acquisition footprint, suppressing migration artifacts and enhancing resolution. In this paper, we find that the conventional reflectivity defined in the LSRTM is related to the normal-incident reflection coefficient and the background velocity. Compared with the defined reflectivity, our inverted result is relatively “true”. With reflected data, LSRTM is mainly sensitive to impedance perturbations. According to an approximate relationship between them, we reformulate the perturbation related system into a reflection-coefficient related one. Then, we seek the inverted image through linearized iteration. Moreover, with the assumption that the density varies more gradually than the migration velocity, only the knowledge of the latter is required, although the reflected waves are produced at impedance discontinuities. We test our method using the 2D Marmousi synthetic dataset.