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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.

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2007-10-24