Conventional migration (Claerbout, 1971) computes the reflectivity image by applying the adjoint operator to the data. Migration can also be interpreted as the first iteration of iterative inversion, where the Hessian of the misfit functional is approximated as a diagonal matrix. This approximation is violated when the data is incomplete (Nemeth et al., 1999) and the migration image will be obscured by migration artifacts.
It has been shown that least-squares migration (LSM) (Nemeth et al., 1999; Duquet et al., 2000) can improve the resolution of the migration image and suppress migration artifacts. However, one of the drawbacks of least-squares migration is its high computational cost. In this chapter, I propose to use a summation of phase encoded shot gathers as input data to reduce the computational burden of least-squares migration. The blended data is similar to that used in the blended sources method (Romero et al., 2000), but my proposed scheme of multisource least-squares migration (MLSM) aims to improve the image quality while reducing crosstalk noise. During the inversion, a deblurring filter is used as a preconditioner (Hu and Schuster, 2000; Guitton, 2004; Aoki and Schuster, 2009) to speed up the convergence.