Chapter 2: Least-squares Migration of Multisource Data with a Deblurring Filter

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.

With blended sources processing, many conventionally acquired shot gathers are phase-encoded and blended together to form supergathers to reduce the computational cost and I/O burden of migration. However, blended sources processing introduces crosstalk noise, which needs to be removed from the final migration images. Simultaneous sources acquisition shares some common ground with blended sources, as it reduces the acquisition cost, but introduces crosstalk noise also. In this chapter, a multisource least-squares migration algorithm is proposed to combine the strengths of least squares migration and blended sources processing to produce high quality images with low computational cost. The least-squares migration improves the image quality by suppressing migration artifacts, balancing reflector amplitudes and enhancing image resolution, and blended sources processing increases the computational efficiency. During the iterations of least-squares migration, the crosstalk noise introduced by blended sources is effectively reduced. The MLSM algorithm can be implemented with any migration method and the gain in efficiency depends on the migration method. My goal is to test the effectiveness of the MLSM algorithm with a Kirchhoff migration method.