The phase-shift method of migration
begins with a two-dimensional Fourier transform (2D-FT) of the dataset.
(See chapter .)
This transformed data is downward continued
with and subsequently evaluated
at *t*=0 (where the reflectors explode).
Of all migration methods,
the phase-shift method
most easily incorporates depth variation in velocity.
The phase angle and obliquity function are correctly included,
automatically.
Unlike Kirchhoff methods,
with the phase-shift method there is no danger of aliasing the operator.
(Aliasing the data, however, remains a danger.)

Equation (14) referred to upcoming waves. However in the reflection experiment, we also need to think about downgoing waves. With the exploding-reflector concept of a zero-offset section, the downgoing ray goes along the same path as the upgoing ray, so both suffer the same delay. The most straightforward way of converting one-way propagation to two-way propagation is to multiply time everywhere by two. Instead, it is customary to divide velocity everywhere by two. Thus the Fourier transformed data values, are downward continued to a depth by multiplying by

(15) |

(16) |

- Pseudocode to working code
- Kirchhoff versus phase-shift migration
- Damped square root
- Adjointness and ordinary differential equations
- Vertical exaggeration example
- Vertical and horizontal resolution
- Field data migration

12/26/2000