Fast imaging with surface-related multiples

Surface-related multiples, which are waves that bounce more than once between the water surface and the subsurface reflectors, constitute a significant part of the data acquired in marine seismic surveys. If left untreated, they can lead to misplaced phantom reflectors in the image, and result in erroneous interpretations of the subsurface structure. As a result, these multiples are removed before the imaging procedure in conventional seismic data processing. However, because they interact more with the subsurface medium, they may carry extra information that is not present in the primaries. Therefore instead of removing these multiples, a more desirable alternative is to make active use of them. We derive from the well-established "Surface-Related Multiple Elimination" relation, and arrive at a linearized expression of the wave-equation based modelling that incorporates the surface- related multiples. We then present a computationally efficient approach to iteratively invert this expression to obtain an image of the subsurface from data that contain multiples. We achieve the computational efficiency inside each iteration by (i) using the wave-equation solver to implicitly carry out the expensive multiple prediction; and (ii) reducing the number of wave-equation solves during data simulation by subsampling the monochromatic source experiments. We show that, compared with directly applying the cross-correlation/deconvolutional imaging conditions, the presented approach can suppress the coherent imaging artifacts from multiples more effectively. We also show that, by curvelet-domain sparsity promoting and occasionally drawing new data samples during the inversion, the proposed inversion method gains improved robustness to velocity errors in the background model, as well as modelling errors incurred during linearization of the wave-equation. To combine the information encoded in both the primaries and the multiples, we then propose a highly accurate source estimation method to jointly invert the total upgoing wavefield. We show with field data examples that we can reap benefits from both the relative noise-free primaries and the extra illumination coverage of the multiples. We also demonstrate that the inclusion of multiples help mitigate the amplitude ambiguity during source estimation. We conclude the thesis with an outlook for future research directions, as well as potential extensions of the proposed work.