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

Gabriel Alvarez

gabriel@sep.stanford.edu

ABSTRACT

Wave-equation migration with the velocity of the primaries maps non-diffracted water-bottom 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 common-image-gathers and angle-domain common-image-gathers. I illustrate the results with simple synthetic models.