Three-dimensional wave-equation migration techniques are still quite expensive because of the huge matrices that need to be inverted. Several techniques have been proposed to reduce this cost by splitting the full 3D problem into a sequence of 2D problems. We compare the performance of splitting techniques for stable 3D Fourier finite-difference (FFD) migration techniques in terms of image quality and computational cost. The FFD methods are complex Padé FFD and FFD plus interpolation, and the compared splitting techniques are two- and four-way splitting as well as alternating four-way splitting, that is, splitting into the coordinate directions at one depth and the diagonal directions at the next depth level. From numerical examples in homogeneous and inhomogeneous media, we conclude that, though theoretically less accurate, alternate four-way splitting yields results of comparable quality as full four-way splitting at the cost of two-way splitting.

Three-dimensional wave-equation migration techniques are still quite expensive because of the huge matrices that need to be inverted. Several techniques have been proposed to reduce this cost by splitting the full 3D problem into a sequence of 2D problems. To reduce errors, the Li correction is applied at regular multiples of depth extrapolation increment. We compare the performance of splitting techniques in wave propagation for 3D finite-difference (FD) migration in terms of image quality and computational cost. We study the behaviour of the complex Padé approximation in combination with two- and alternating four-way splitting, that is, splitting into the coordinate directions at one depth and the diagonal directions at the next depth level. We also extend the Li correction for use with the complex Padé expansion and diagonal directions. From numerical examples in inhomogeneous media, we conclude that alternate four-way splitting is the most cost-effective strategy to reduce numerical anisotropy in complex Padé 3D FD migration.

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