Removal of water-layer multiples and peg-legs is still one of the major processing problems in offshore exploration. The requirements on the optimal wave-equation approach for the suppression of such multiples are the following: 1) Without knowledge of the subsurface structure (except the approximate geometry of the water-bottom) it should correctly predict the kinematics of multiples. 2) The adaptive subtraction of the predicted multiples should be consistent with the data model (correct multiple suppression operator) and should involve as few parameters as possible. A long filter or time-varying filter used in the adaptive subtraction step changes the form of the predicted multiples, so that they fit not just the recorded multiples, but the sum of primaries and multiples. In our new wave-equation approach we try to fulfill the two essential requirements above. The approach is an extension of our data-consistent deconvolution Remul (Lokshtanov, 1999-A) for structures with strong inline lateral variations. If structural variations in the crossline direction are not severe and the main free-surface multiples are water-layer multiples and peg-legs, the new approach performs very well and is computationally efficient.
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