The diffraction-stack (Kirchhoff) migration method is widely used in industry for depth imaging. For migrating a single event on a single trace, it smears the event energy to all possible subsurface reflection points in the model space. After smearing and summation of all samples on all traces into the earth model, a diffraction-stack migration image is obtained. This migration method is computationally inexpensive, easily adaptable to different filtering strategies such as obliquity factors, first-arrival restrictions, angle-dependent truncation of data aperture, and antialiasing filters. However, it is subject to the high-frequency approximation of ray tracing, and therefore it has difficulty in complex velocity models which preclude the accurate use of ray tracing or the modeling of multiple scattered arrivals.
As a more accurate alternative, the reverse-time migration (RTM) method is a well established imaging method that uses finite-difference solutions to the wave equation to accurately propagate seismic energy through complex models. The key benefits of RTM compared to diffraction-stack migration method are that, if the velocity model is accurate enough, it can correctly image any dipping structure, can account for multiple arrivals, and has the capability of providing much higher resolution in the reflectivity image. But the price we pay is a computationally expensive algorithm that appears inflexible to efficiency improvements, or operator filtering strategies used in diffraction-stack migration.
To overcome the inability to filter unwanted noise in the RTM operator, I reformulate the equation of reverse-time migration into that of generalized diffraction-stack migration (GDM), where GDM is interpreted as summing data along a series of hyperbola-like curves, each one representing a different type of event such as a reflection or multiple. This is a generalization of the familiar diffraction-stack algorithm where the migration image at a point is computed by the sum of trace amplitudes along an appropriate hyperbola-like curve. Instead of summing along the curve associated with the primary reflection, the sum is over all scattering events and so this method is named generalized diffraction-stack migration (GDM). The GDM formulation is equivalent to RTM but it leads to filters that can be applied to the GDM operator to mitigate migration artifacts due to aliasing, crosstalk, and multiples.