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To image the unknown source location at from the data
given in equation (3), we
simply identify the migration operator which when applied
to the above equation cancels the phase of the
term.
Such a migration operator is given by
| |
(2) |

where *s*' denotes the trial source-point location.
Application of this migration operator to the crosscorrelated data in
equation (3) will annihilate
the phase of the term
when the trial image point
coincides with the actual source location denoted by .The migration section is then given by summation over all geophone pairs
The migration operator in equation (5) is "tuned" to
image the source location so that as
, the term will
constructively interfere while the *all other terms* tend to
cancel.

**fig1
**

Figure 1
(Top) Direct ray and a (middle) scattered ray excited by
a specular free-surface reflection associated with a source at
*s* and a scatterer at *x*_{o}.
Bottom figure denotes the
rays associated with the migration operator
for free-surface reflections.

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Stanford Exploration Project

9/5/2000