Water-bottom and diffracted 2D multiple reflections in data space and image space

Water-bottom multiples from a dipping interface have the same kinematics in a Common Midpoint (CMP) gather as a primary from a reflector with twice the dip at twice the perpendicular depth at the CMP location. When migrated with the velocity of the primaries, these multiples are overmigrated just as primaries migrated with higher velocity, and their moveout is thus predictable in image space. Diffracted multiples, on the other hand, have an apex-shifted moveout in CMP gathers and a more complicated, also apex-shifted, residual moveout in image space when migrated with the velocity of the primaries. I illustrate the moveout of water-bottom and diffracted multiples in image space with a simple 2D synthetic dataset. INTRODUCTION Recently, the increased interest in exploration in areas with rough salt bodies, such as the Gulf of Mexico, has sparkled the interest in multiple attenuation methods that work in the image space (Sava and Guitton, 2003; Hargreaves and Wombell, 2004; Alvarez et al., 2004) as opposed to more traditional methods that work in the data space (Hampson, 1986) or Surface Related Multiple Elimination (SRME) methods (Verschuur et al., 1992; Verschuur and Berkhout, 1997) that require dense surface coverage of sources and receivers or demanding data interpolation and extrapolation. The main advantage of the image space is that most of the complexity of the propagation for the primary reflections is handled by prestack depth migration such that the primary reflections in Angle-Domain Common-Image Gathers (ADCIGs) are flat or nearly flat if the migration is done with the velocity of the primaries. It is not immediately obvious, however, what is the residual moveout of the migrated multiples in ADCIGs. A reasonable approximation is to consider that the residual moveout of the migrated multiples is the same as that of the primaries when migrated with the wrong (higher) velocity (Biondi and Symes, 2004). This approach leads, in 2D, to a relatively simple and effective algorithm for the attenuation of the multiples in the image space (Sava and Guitton, 2003) and, with some modifications, can 1email: [email protected] 365 366 Alvarez SEP–120 attenuate 2D diffracted multiples reasonably well (Alvarez et al., 2004). In this paper I present the equations for the image space coordinates of the water-bottom multiples in 2D ADCIGs and illustrate the migration of the multiples with a synthetic dataset. The next section presents the kinematics of water-bottom and diffracted multiples in data space. The following section presents the equations to map the multiples from data space to image space. The last section illustrates the mapping of the multiples in image space, both in common subsurface offset common-image gathers and angle-domain common-image gathers for the simple synthetic dataset. KINEMATICS OF MULTIPLES IN DATA SPACE FROM A 2D DIPPING INTERFACE Water-bottom multiples Consider a model with a dipping water-bottom in 2D. The raypath of the primary reflection can be easily computed using the concept of the image source as illustrated in Figure 1. The Figure 1: Construction of the primary reflection from a dipping interface. gabriel2-rayprim [CR] 0 50