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Traditional source-receiver migration is based on the concept of survey sinking Claerbout (1985).
It sorts the recorded data into CMP gathers and
propagates the CMP gather to the subsurface with the Double Square Root (DSR) equation
| |
(6) |

where *x*_{s}=*x*-*h* is the shot location, *x*_{r}=*x*+*h* is the receiver location. The wavefield at each depth *z* is equivalent to the data that would have been recorded when the shots and
receivers were located at that depth. Source-receiver migration produces an image by
extracting the wavefield at zero subsurface offset , and stacking
over all frequencies. Correspondingly, the stack of along the
frequencies is its CIG.
Traditional source-receiver migration assumes that the source is an impulse function at the source location *x*_{s}.
But in fact, source-receiver migration works for arbitrary sources, such as wavelets, plane waves,
and primary reflections as well. For arbitrary sources, the surface wavefield is not
a simple CMP gather of the recorded data, but the stack of the cross-correlation between the source wavefield and the receiver
wavefield at the surface

| |
(7) |

Then is downward continued to the subsurface with the DSR equation (6)
and the image is formed by the same method as the traditional source-receiver migration.
In fact, traditional source-receiver migration is a special case of source-receiver migration when the source
is an impulse function at the source location, and the CMP gather of the recorded data at the surface is the cross-correlation
between the impulse function source and the receiver wavefield, which is the recorded data for each shot.

** Next:** Demonstration of equivalence
** Up:** Shan and Zhang: Migration
** Previous:** Shot-profile Migration
Stanford Exploration Project

7/8/2003