Multiple Attenuation With A Modified Parabolic Radon Transform

We present a fast and efficient frequency-domain implementation of a modified parabolic Radon transform (modified PRT) based on a singular value decomposition with applications to multiple removal. With a change of variable, the problem is transformed into a complex linear system involving a single operator after merging the curvature-frequency parameters into a new variable. A complex singular value decomposition (SVD) can be applied to this operator and the forward modified parabolic Radon transform is computed for all frequency components within the signal bandwidth by means of complex back-substitution only.<br>The standard PRT can be obtained by interpolation in the modified transform domain. The method is also able to resolve the multiple energy from the primaries when they interfere in a small time interval and resists well to AVO effects in the data. The proposed modified PRT was successfully applied to a deep-water seismic line at the Gulf of Mexico to attenuate water-bottom multiples and subsequent peg-legs originating from multiple paths in the water column.