Fast image-domain target-oriented least-squares reverse time migration

We have developed a fast image-domain target-oriented least-squares reverse time migration (LSRTM) method based on applying the inverse or pseudoinverse of a target-oriented Hessian matrix to a migrated image. The image and the target-oriented Hessian matrix are constructed using plane-wave Green's functions that are computed by solving the two-way wave equation. Because the number of required plane-wave Green's functions is small, the proposed method is highly efficient. We exploit the sparsity of the Hessian matrix by computing only a couple of off-diagonal terms for the target-oriented Hessian, which further improves the computational efficiency. We examined the proposed LSRTM method using the 2D Marmousi model. We demonstrated that our method correctly recovers the reflectivity model, and the retrieved results have more balanced illumination and higher spatial resolution than traditional images. Because of the low cost of computing the target-oriented Hessian matrix, the proposed method has the potential to be applied to large-scale problems.