The importance of including density in elastic least-squares reverse time migration: multiparameter crosstalk and convergence
Time-domain elastic least-squares reverse time migration (LSRTM) can provide higher spatial resolution images with fewer artefacts and a superior balance of amplitudes than elastic reverse time migration (RTM). More important, it can mitigate the crosstalk between P- and S-wave images. In previously proposed elastic LSRTM algorithms, density is either assumed to be constant or known. In other words, the density perturbation is not part of the least-squares inversion formulation. Neglecting density in elastic LSRTM may lead to crosstalk artefacts in the P- and S-wave images. In this paper, we propose a time-domain three-parameter elastic LSRTM algorithm to simultaneously invert for density, P- and S-wave velocity perturbation images. We derive the elastic Born approximation and elastic RTM operators using the continuous adjoint-state method. We carefully discretize the two operators to assure that they pass the dot-product test. This allows us to use the conjugate gradient least-squares method to solve the least-squares migration problem. We evaluate the proposed algorithm on two synthetic examples. We show that our proposed three-parameter elastic LSRTM can suppress the multiparameter crosstalk among density, P- and S-wave velocity perturbation images. Moreover, including density image in the elastic LSRTM inversion can improve the convergence of the least-squares inversion.