As the most widely used subsurface imaging method in petroleum exploration, seismic migration attempts to place seismic reflection data into their correct spatial or temporal reflector positions. Similar to the echo sounding technique to fathom the water bottom from a boat, seismic migration maps the subsurface reflectors in two steps. Step one is to back-project the seismic data measured at the surface downwards using the wave equation and a velocity model, producing an extrapolated wavefield that is a function of space and time. Step two is to use an imaging condition to capture the positions of the subsurface reflectors from the extrapolated wavefield. These two steps are demonstrated by the three common seismic migration methods introduced in this chapter. First, Kirchhoff migration is the most intuitive and flexible migration method, and it uses the ray theory approximation in practice. Second, frequency domain migration is theoretically rigorous and made efficient by taking advantage of the Fourier transform, although it is less effective in the presence of strong lateral velocity variations. Like these two methods, most migrations simplify reality by assuming that the input data contain only primary reflections; hence some pre-processing procedures are necessary to suppress other seismic waves recorded. Third, reverse time migration is a full wave migration method that is capable of using both primary reflections and other waves such as refractions and multiple reflections.

Fundamentally, a velocity model is required for all seismic migration methods. A time migration uses layer-cake models without lateral velocity variations. In contrast, a depth migration may handle a significant level of lateral velocity variations in the velocity model. In the case of gently dipping reflectors, a post-stack migration may be sufficient, using post-NMO stacked traces to approximate zero-offset traces. In the presence of steeply dipping reflectors, a pre-stack migration is usually more suitable but takes many more computational resources. Depending on the complexity of the target structures, we may choose from a suite of migration methods, from the crude but fast post-stack time migration which is not sensitive to velocity variations, to the expensive pre-stack depth migration to handle steep reflector dips and strong lateral variations in the velocity models.