Efficient 2.5-D true-amplitude migration

Kirchhoff depth migration is a widely used algorithm for imaging seismic data in both two and three dimensions. To perform the summation at the heart of the algorithm, standard Kirchhoff migration requires a traveltime map for 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 calculating the true-amplitude weight term in the summation. The increased input/output (I/O) and computational expense of including the true-amplitude weight term is often not justified by significant improvement in the final muted and stacked image. For this rea-son, some authors advocate neglecting the weight term in the Kirchhoff summation entirely for most everyday imaging purposes. We demonstrate that for nearly the same expense as ignoring the weight term, a much better solution is possible. We first approximate the true-amplitude weight term by the weight term for constant-velocity media; this eliminates the need for additional source and receiver maps. With one small additional approximation, the weight term can then be moved entirely outside the innermost loop of the summation. The resulting Kirchhoff method produces images that are almost as good as for exact true-amplitude Kirchhoff migration and at almost the same cost as standard methods that do not attempt to preserve amplitudes.