Gabriel Alvarez

Image-space surface-related multiple prediction

A very important aspect of removing multiples from seismic data is accurate prediction of their kinematics. We cast the multiple prediction problem as an operation in the image space parallel to the conventional surface-related multiple-prediction methodology. Though developed in the image domain, the technique shares the data-driven strengths of data-domain surface-related multiple elimination (SRME) by being independent of the earth (velocity) model. Also, the data are used to predict the multiples exactly so that a Radon transform need not be designed to separate the two types of events. The cost of the prediction is approximately the same as that of data-space methods, though it can be computed during the course of migration. The additional cost is not significant compared to that incurred by shot-profile migration, though split-spread gathers must be used. Image-space multiple predictions are generated by autoconvolving the traces in each shot-gather at every depth level during the course of a shot-profile migration. The prediction in the image domain is equivalent to that produced by migrating the data-space convolutional prediction. Adaptive subtraction of the prediction from the image is required. Subtraction in the image domain, however, provides the advantages of focused energy in a smaller domain since extrapolation removes some of the imperfections of the input data.

Attenuation of specular and diffracted 2D multiples in image space

In complex areas, the 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. We present the equations that map, via wave-equation migration, 2D diffracted and specular water-bottom multiples from data space to image space. We show the equations for both subsurface-offset-domain common-image-gathers (SODCIGs) and angle-domain common-image-gathers (ADCIGs). We demonstrate that when migrated with sediment velocities, the over-migrated multiples map to predictable regions in both SODCIGs and ADCIGs. Specular multiples focus similarly to primaries, whereas diffracted multiples do not. In particular, the apex of the residual moveout curve of diffracted multiples in ADCIGs is not located at the zero aperture angle. We use our equation of 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, 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. We show the application of our 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 we show that we can successfully attenuate them, along with the specular multiples, in the image Radon domain.

Residual moveout of 2D multiples in angle‐domain common‐image gathers

I show that, for specularly-reflected multiples, the constant velocity straight-ray approximation of the residual moveout in Angle-Domain Common-Image Gathers (ADCIGs) is only appropriate for small aperture angles. The approximation is good for the primaries because the difference between the migration velocity and the true velocity is likely to be small. For the multiples, however, this difference may be large and correcting for ray bending produces a better approximation that leads to better focusing of the multiples in the Radon domain. This in turn allows a more accurate muting of the multiples. I show results with two ADCIGs, one synthetic and one real. INTRODUCTION When primary reflections are depth migrated with the exact velocity of the medium, their moveout in Angle-Domain Common-Image Gathers (ADCIGs) is flat (Biondi, 2005). When they are migrated with the wrong velocity, their residual moveout in ADCIGs can be approximated, to first order, by the equations given in Biondi and Symes (2004). For a flat reflector, their approximation reduces the residual moveout of the primaries as a function of aperture angle, to a tangent squared. Specularly-reflected multiples, when migrated with the velocity of the primaries, behave as primaries migrated with too slow velocity (Alvarez, 2005). The tangent-squared approximation can be used to design a Radon transform that focuses the energy of the primaries and the multiples in and ADCIG according to their residual curvature and so can be used to attenuate the multiples in image space (Sava and Guitton, 2003). This approximation is robust enough that it can even be used to approximate the residual moveout of diffracted multiples, provided that another dimension is added to the Radon transform to account for the shift of the apex of these multiples (Alvarez et al., 2004). Here I show that the approximation of Alvarez (2005) for the residual moveout of the multiples is better than the straight-ray approximation, because it takes into account the nonnegligible ray bending of the multiples at the water-bottom interface and by extension any interface in which the velocity of propagation of the primaries and the multiples is substantial, 67