Summary

In complex areas, attenuation of specular and diffracted multiples in image space is an attractive alternative to surface-related multiple elimination (SRME) and to data space Radon filtering. In this chapter I present the equations that map, via wave-equation migration, 2D diffracted and specular water-bottom multiples from data space to image space. I show the equations for both subsurface-offset-domain common-image-gathers (SODCIGs) and angle-domain common-image-gathers (ADCIGs). I demonstrate that when migrated with sediment velocities, the over-migrated multiples map to predictable regions in both SODCIGs and ADCIGs. Specular multiples migrate as primaries whereas diffracted multiples do not. In particular, the apex of the residual moveout curve of diffracted multiples in ADCIGs is not located at zero aperture angle.

I use the equation I derive for the residual moveout of the multiples in ADCIGs to design an apex-shifted Radon transform that maps the 2D ADCIGs into a 3D model space cube whose dimensions are depth, residual moveout curvature and apex-shift distance. Well-corrected primaries map to or near the zero curvature plane and specularly-reflected multiples map to or near the zero apex-shift plane. Diffracted multiples map elsewhere in the cube according to their curvature and apex-shift distance. Thus, specularly reflected as well as diffracted multiples can be attenuated simultaneously. I show the application of the apex-shifted Radon transform to a 2D seismic line from the Gulf of Mexico. Diffracted multiples originate at the edges of the salt body and I show that I can successfully attenuate them, along with the specular multiples, in the image Radon domain.