Transform Techniques Applied to the Attenuation of Long Period Multiples

In deep water areas, the interference at important target levels due to water layer multiples can be extremely troublesome. Conventional deconvolution approaches are ineffective, due to variation of the multiple period with time (non-stationarity) and poor statistical estimation due to the limited number of multiple contributions within the autocorrelation window.

Weighted stacking improves the attenuation of long period multiples, and in recent times the demultiple process based on the f-k transform has been routinely applied to supplement the response of CMP stack.

A serious weakness of the f-k technique is that the removal of multiple energy from the record is strongly dependent on offset, the slopes of primary and multiple events converging towards the near offsets, where the process is thus relatively ineffective. More recently, there has been increasing interest in applications of the general class of decompositions known as the Radon transform, which model the data as a set of projections on the zero offset axis along a number of possible geometrical trajectories. A well known example is the linear Radon transform, commonly known as slant-stack or the tau-p transform. Although, like the f-k transform, slant-stack results in a plane wave decomposition of the record, the representation in terms of zero offset intercept versus ray parameter is such that each trace in the transformed record is associated with a constant angle of emergence. Water layer multiples are then represented with constant reverberation periods within each trace, and may then be treated by a conventional statistical deconvolution.

A further example of the general class is the parabolic Radon transform, which models the record as a set of parabolic alignments. With prior application of approximate NMO correction, this transformation can provide a well focused mapping of multiple reflections, enabling them to be identified and isolated for inverse transformation. The predicted multiple is then removed by subtraction from the original record. This method is not dependent on the accuracy of a statistical model and provides effective demultiple on near as well as far offsets.

Merits and disadvantages of these methods are discussed and performances are compared on data from a typical deep water area. Results show that the parabolic Radon transform enables a far more accurate modelling of long period multiples than the other methods considered, thus achieving a more effective demultiple process.