Water bottom multiple attenuation by Kirchhoff extrapolation

Despite being less general than 3D-SRME, multiple prediction based on wavefield extrapolation can still be of interest, because it is less CPU and I/O demanding than 3D-SRME and moreover it does not require any prior data regularization. Here we propose a fast implementation of water bottom multiple prediction that uses the Kirchhoff formulation of wavefield extrapolation. With wavefield extrapolation the multiple prediction is usually obtained through the cascade of two extrapolation steps. Actually by applying the Fermat's principle (i.e. minimum reflection traveltime) we show that the cascade of two operators can be replaced by a single approximated extrapolation step. The approximation holds as long as the water bottom is not too complex. Indeed the proposed approach has proved to work well on synthetic and field data when the water bottom is such that wavefront triplications are negligible, as it happens in many practical situations.