Multidirectional slowness vector for computing angle gathers from reverse time migration

Angle gathers are important for true-amplitude migration, migration velocity analysis, and angle-dependent inversion. Among existing methods, calculating the t-x direction vector is efficient, but it can give only one direction per grid point and fails to give multiple directions for overlapping wavefields associated with multipaths and reflections. The slowness vectors (SVs) in t-x and omega-k can be connected by Fourier transforms (FTs); the forward FT from t-x to omega-k decomposes the wavefields into different vector components, and the inverse FT sums these components into a unique direction. Therefore, the SV has multiple directions in omega-k, but it has only one direction in t-x. Based on this relation, we have separated the computation of propagation direction into two steps: First, we used the forward FT, k/omega binning, and several inverse FTs to separate the wavefields into vector subsets with different approximate propagation angles, which contained much less wave overlapping; then, we computed t-x SVs for each separated wavefield, and the set of these single-direction SVs constituted a multidirectional SV (MSV). In this process, the FTs between t and omega domains required a large input/output (I/O) time. We prove the conjugate relation between the decomposition results using positive-and negative-frequency wavefields, and we use complex-valued modeling to obtain the positive-frequency wavefields. Thus, we did wavefield decomposition in t-k instead of omega-k, and avoided the huge I/O caused by the FT between the t and omega domains. Our tests demonstrated that the MSV can give multiple directions for overlapping wavefields and improve the quality of angle gathers.