Mapping of water-bottom and diffracted 2D multiple reflections to image space

Wave-equation migration with the velocity of the primaries maps non-diffracted waterbottom multiples to an hyperbola in subsurface-offset-domain-common-image-gathers. Furthermore, for positive surface offsets, the multiples are mapped to non-positive subsurface offsets if sediment velocity is faster than water. The larger the offset in the data space, the larger the subsurface offset and the shallower the image point. When migrated with the velocity of the water, the multiples are mapped to zero subsurface offset just as primaries migrated with the exact velocity. Diffracted multiples, on the other hand, map to positive or negative subsurface offsets depending on the relative position of the diffractor with respect to the common-midpoint. I present the equations of the image point coordinates in terms of the data space coordinates for diffracted and non-diffracted multiples from flat or dipping water-bottom in both subsurface-offset-domain commonimage-gathers and angle-domain common-image-gathers. I illustrate the results with simple synthetic models. INTRODUCTION Attenuation of multiples in the image space is attractive because prestack wave-equation migration accurately handles the complex wave propagation of primaries. In subsurface-offsetdomain common-image-gathers (SODCIG) the primaries are imaged at zero subsurface offset at the depth of the reflector if migrated with the correct velocity. Correspondingly, in angledomain common-image-gathers (ADCIG) the primaries are imaged with flat moveout. Attenuation of multiples in image space depends on the difference in residual moveout between the primaries and the multiples, either in SODCIGs or ADCIGs (Sava and Guitton, 2003; Hargreaves et al., 2003; Alvarez et al., 2004). Understanding how wave-equation migration maps the multiples into SODCIGs and ADCIGs is therefore of paramount importance in order to design a proper strategy to attenuate the multiples in the image space. Non-diffracted water-bottom multiples from a flat or dipping water-bottom are imaged as primaries. Thus, if the migration velocity is that of the water, they are mapped to zero 1email: [email protected] 129