Attenuation of multiples in image space

In complex subsurface areas, attenuation of 3D specular and diffracted multiples in data space is difficult and inaccurate. In those areas, image space is an attractive alternative. There are several reasons: (1) migration increases the signal-to-noise ratio of the data; (2) primaries are mapped to coherent events in Subsurface Offset Domain Common Image Gathers (SODCIGs) or Angle Domain Common Image Gathers (ADCIGs); (3) image space is regular and smaller; (4) attenuating the multiples in data space leaves holes in the frequency-Wavenumber space that generate artifacts after migration.; I develop a new equation for the residual moveout of specular multiples in ADCIGs and use it for the kernel of an apex-shifted Radon transform to focus and separate the primaries from specular and diffracted multiples. Because of small amplitude, phase and kinematic errors in the multiple estimate, we need adaptive matching and subtraction to estimate the primaries. I pose this problem as an iterative least-squares inversion that simultaneously matches the estimates of primaries and multiples to the data. Standard methods match only the estimate of the multiples. I demonstrate with real and synthetic data that the method produces primaries and multiples with little cross-talk.; In 3D, the multiples exhibit residual moveout in SODCIGs in in-line and cross-line offsets. They map away from zero subsurface offsets when migrated with the faster velocity of the primaries. In ADCIGs the residual moveout of the primaries as a function of the aperture angle, for a given azimuth, is flat for those angles that illuminate the reflector. The multiples have residual moveout towards increasing depth for increasing aperture angles at all azimuths. As a function of azimuth, the primaries have better azimuth resolution than the multiples at larger aperture angles. I show, with a real 3D dataset, that even below salt, where illumination is poor, the multiples are well attenuated in ADCIGs with the new Radon transform in planes of azimuth-stacked ADCIGs. The angle stacks of the estimated primaries show little residual multiple energy.