Fast imaging with surface-related multiples by sparse inversion

When used correctly, surface-related multiples can provide extra illumination coverage compared with primaries. In this talk, I will discuss how to jointly image primaries and surface-related multiples in a computationally efficient fashion. We bring down the computational cost by two means. First we use wave-equation solvers to implicitly carry out the expensive dense matrix-matrix multiplications in the prediction of surface-related multiples. Second we bring down the simulation cost by subsampling the frequencies and monochromatic source experiments together with curvelet-domain sparsity-promoting and rerandomization. As a result, we obtain true-amplitude least-squares migrated seismic images with computational costs that are comparable to a single RTM with all the data. We demonstrate the efficacy of the proposed method using realistic synthetic examples.