For a long time free surface related multiple reflection were removed before further processing was done. Based on the recently developed Marchenko type redatuming theory a theory was developed that is able to remove surface related and internal multiples during the redatuming step. This requires some model information that is avoided by separating the redatuming step from the multiple elimination step. The iterative solution of this method does not always converge. I propose to use a conjugate algorithm to solve the problem. I also show that the problem can be cast in a form with a self-adjoint operator that allows a faster solution. The second feature that reduces the computational cost is to use the filters that have been computed for a certain travel time as initial estimate for a following travel time. I show with a one-dimensional example that exploiting these two new aspects reduces the computational cost dramatically.


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