In exploration seismics the objective is to image the subsurface structures from acoustic reflection measurements, in order to localize and monitor oil and gas reserves. The reflection measurements are usually carried out with sources and receivers positioned at the surface of the earth. Especially in the marine case the water-air interface acts as an almost perfect acoustic mirror, reflecting all upgoing energy back into the medium. As a result, the measurements suffer from multiple reflections that mask the desired primary reflections from the inhomogeneities in the earth. However, these surface multiples have a physical relationship with the primaries: each primary event will be followed by a sequence of multiple reflections. This relationship can be exploited to estimate the primary reflection response, i.e. the multiple-free transfer function of the subsurface. This is done by a full waveform inversion process, in which the primary transfer functions are parameterized by spikes and a sparseness constraint is used during the optimization process. Examples will be shown for synthetic and field data.
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