Discussion and Conclusions

Increasing the focusing power of the Radon transform is critical in real situations in which the primaries and the multiples may map close together in the Radon domain. Therefore, taking into account the ray bending of the multiples, at least to first order, is an improvement. The cost of the new transform is essentially the same and no additional information is required. Although the new transform explicitly depends on the ratio ($\rho$) between the multiple velocity and the migration velocity, in practice this ratio can be fixed to something reasonable like 1.5 and the results are good. The new transform may also be advantageous in the implementation of the apex-shifted Radon transform for the attenuation of diffracted multiples Alvarez et al. (2004).

Taking into account the ray bending of the multiple raypaths at the multiple generating interface improves the focusing power of the Radon transform when applied to ADCIGs. This in turn improves our ability to separate the primaries from the multiples and, therefore, allows a better estimate of the multiple model to be computed. The new transform can be implemented at essentially no extra cost compared with the tangent-squared approximation designed to treat the primaries ignoring ray bending.