Least-squares migration was originally implemented with KM method (Duquet et al., 2000; Nemeth et al., 1999), but was later developed for phase shift migration algorithms (Huang and Schuster, 2012a; Kaplan et al., 2010). In this dissertation, I propose to implement LSM with RTM (Whitmore, 1983; Baysal et al., 1983; McMechan, 1983), where the Green's functions are calculated by finite-difference solution to the full wave equation instead of asymtotic Green's function in Kirchhoff migration (Bleistein, 1987), or one-way solution in one-way wave equation migration (Claerbout, 1985). The advantages include: (1) there is no high-frequency approximation; (2) it has no dip limitations; (3) once the known boundaries, e.g., a salt boundary, are embedded in the migration velocity model, RTM can correctly migrate multiples such as prism waves (Lu et al., 2008; Jones et al., 2007; Malcolm et al., 2009); and (4) phase shifts associated with caustics are taken into account when solving the two-way wave equation.
However, least-squares migration is usually considered to be too expensive for practical use. In this dissertation, I propose a new algorithm to combine the blended sources processing technique with LSRTM to increase its computational efficiency. To adapt this method for data recorded with a marine streamer geometry, frequency-selection encoding can be used instead of random time-shift encoding. In the following chapters, the multisource least-squares reverse time migration algorithm is tested with synthetic and real data examples to illustrate its advantages.