Sparsity-promoting Migration with Surface-related Multiples

Multiples, especially the surface-related multiples, form a significant part of the total up-going wavefield. If not properly dealt with, they can lead to false reflectors in the final image. So conventionally practitioners remove them prior to migration. Recently research has revealed that multiples can actually provide extra illumination so different methods are proposed to address the issue that how to use multiples in seismic imaging, but with various kinds of limitations. In this abstract, we combine primary estimation and sparsity-promoting migration into one convex-optimization process to include information from multiples. Synthetic examples show that multiples do make active contributions to seismic migration. Also by this combination, we can benefit from better recoveries of the Green's function by using sparsity-promoting algorithms since reflectivity is sparser than the Green's function.