Efficient 2.5-D true-amplitude migration

Kirchhoff depth migration is a widely used algorithm for imaging seismic da ta in both two and three dimensions. To perform the summation at the heart of the algorithm, standard Kirchhoff migration requires a traveltime map fo r each source and receiver. True-amplitude Kirchhoff migration in 2.5-D v(x , z) media additionally requires maps of amplitudes, out-of-plane spreading factors, and takeoff angles; these quantities are necessary for calculatin g the true-amplitude weight term in the summation. The increased input/outp ut (I/O) and computational expense of including the true-amplitude weight t erm is often not justified by significant improvement in the final muted an d stacked image. For this rea-son, some authors advocate neglecting the wei ght term in the Kirchhoff summation entirely for most everyday imaging purp oses. We demonstrate that for nearly the same expense as ignoring the weight term , a much better solution is possible. We first approximate the true-amplitu de weight term by the weight term for constant-velocity media; this elimina tes the need for additional source and receiver maps. With one small additi onal approximation, the weight term can then be moved entirely outside the innermost loop of the summation. The resulting Kirchhoff method produces im ages that are almost as good as for exact true-amplitude Kirchhoff migratio n and at almost the same cost as standard methods that do not attempt to pr eserve amplitudes.