Introduction

The goal of seismic imaging is to find out underground structures based on seismic data observed on the surface or within borehores, given a migration velocity (Claerbout, 1971). Mathematically, the problem can be thought as finding an reflectivity model to explain the observed data with a forward modeling operator. The forward modeling operator is built based on the wave equation and the given velocity model. However, it is prohibitively expensive to solve the problem directly for real data examples. Therefore, conventional migration applies the adjoint of the forward modeling operator to the observed data to produce an image, where the Hessian of the problem is approximated to be an identity matrix. In reality, the conventional migration image usually contains migration artifacts caused by a limited recording aperture and/or coarse source and receiver sampling. To improve the image quality, Nemeth et al. (1999) proposed to solve the problem by an iterative method and named the method LSM, and it has been shown to have the following advantages: (1) it can reduce migration artifacts; (2) it can balance the amplitudes of the reflectors; and (3) it can improve the resolution of the migration images.

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.