Fast linearized inversion with surface-related multiples with source estimation

In the well-known SRME relation, multiples are expressed as the multi-dimensional convolution between the subsurface Green’s function and the downgoing receiver wavefield. Therefore these multiples can be considered as the response of the subsurface to an "areal" source term given by the same downgoing receiver wavefield. This relation can be used to treat these multiples as signals instead of considering them as noise that must removed before seismic imaging. However, when we use conventional reverse-time migration to image these multiple events, it results in acausal imaging artifacts caused by cross-correlations between wrong pairs of up- and downgoing wavefields. We find that these artifacts can be removed by adopting a sparsity-promoting least-squares inversion approach. However, iterative inversions go at the expense of excessive computational costs. By combining the SRME relation and wave-equation based linearized modelling, we are able to significantly reduce the costs by avoiding the dense matrix-matrix multiplications of SRME and the number of wave-equation solves via source subsampling. As a result, we arrive at a method with a cost comparable to that of a single reverse-time migration with all shots.