Abstract: The invention is a method for processing seismic data to eliminate the coherent noise arising from multiple seismic reflections. A decomposition procedure is applied to decompose along N directions of decomposition seismic data into a set of N components. At least one model of multiple reflections is decomposed according to the same decomposition procedure and along the same N directions. For each direction of decomposition, a relative concentration between the component of the model of multiples and the component of the data in the direction concerned is calculated. Next a procedure of adaptive filtering of the multiple reflections is applied to each of the seismic components. The filtered seismic components are recombined with the recombination being weighted by a weighting dependent on the relative concentrations calculated for each direction of decomposition.