Summary
If the migration frequency is high (e.g., 50 Hz), reverse time migration (RTM) can be computationally very expensive and hardware demanding for large 3D data sets with large apertures. For this reason, while the vertical wave-propagation grid is chosen to be dense enough to hold the highest frequency content, a sparser than needed horizontal wave-propagation grid is often used to make high-frequency RTM affordable. As a result, the theoretically alias-free RTM operator suffers from aliasing issues when applied to high-frequency data with steep surface angles. To solve this aliasing issue, we propose first decomposing the input shot gathers of the common-shot RTM into the plane-wave domain using sparse inversion and then applying surface-angle-dependent anti-aliasing filters to individual plane-wave coefficients before transforming them back to the spatial domain. Using 2D synthetic and 3D field data examples, we demonstrate that our method allows RTM to migrate data with a frequency higher than the Nyquist frequency imposed by the horizontal wave-propagation grid without much suffering from aliasing problems.
Introduction
Aliasing in seismic processing can be broadly classified into three types: data aliasing, migration operator aliasing, and imaging aliasing. We focused on migration operator aliasing and data aliasing. Aliasing issues in a Kirchhoff migration operator can be solved either by interpolating input data to a denser grid or applying anti-aliasing filters during the migration (Gray, 1992; Lumley et al., 1994; Abma et al., 2005; Zhang et al., 2001).
RTM is performed in the frequency domain either explicitly (Larson, 1999) or implicitly (Zhang et al., 2007) and thus is alias-free when the wave-propagation grid in all three spatial directions is dense enough to hold the highest frequency content in the input data (Gray, 2013).
If the migration frequency is high (e.g., 50 Hz), RTM is computationally very expensive and hardware demanding for large 3D data sets with large apertures. To make highfrequency RTM affordable or possible at all, one commonly-adopted strategy is to use an uneven spatial grid in RTM wave propagation: the vertical grid is dense enough (e.g., <10 m) to hold the highest frequency content in the input data, whereas the horizontal grid is chosen to be coarser (e.g., 50 m × 50 m). By doing this, the computational cost and memory usage can be significantly reduced, and the majority of the high-frequency events with small surface angles can still be correctly propagated and migrated despite the sparse horizontal grid. However, highfrequency reflection data with steep surface angles will suffer from aliasing issues that degrade the RTM images.
