3D ray+Born migration/inversion -: Part 1:: Theory

Prestack ray+Born migration/inversion can be split in two steps : the computation of common image gathers (CIGs) and their weighted stack (the migration stack). The choice of the domain for the CIGs (shot, offset, angle, etc.) has a direct impact on the resolution of the migration stack. This resolution can be studied easily in the frame of ray+Born migration/inversion theory resulting into improved migration/inversion formulas according to the acquisition geometry. This paper is devoted to this analysis in the cases of a simple 2D acquisition and of a 3D swath acquisition, both corresponding to classical data sets from the SEG/EAGE 3D overthrust experiment. We show that the migration formula originally designed for 3D marine acquisition is not adaptable to the 3D swath acquisition. Finally, we propose a new formula for this specific acquisition, which improves the resolution of the final migrated image. The relevance of this new formula is illustrated in the frame of the SEG/EAGE experiment in the companion paper.