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To image the unknown scatterer location and strength at , we
simply identify the migration operator which, when applied
to the crosscorrelated data in equation (4), cancels the
phase of the term.
Such a migration operator is given by
| |
(3) |

where *x* and *g*_{o} denote, respectively, the *trial* scatterer
and specular-reflector point locations respectively.
Application of this migration operator to equation (3)
will annihilate the phase term of the term in equation (3) when both
the trial image point, , coincides with the actual source
location denoted by , *and* the trial
specular-reflection point, , coincides with the actual
specular-reflection point, . In other words, we require
both
| |
(4) |

| (5) |

This can be understood more clearly by noting that
the migrated reflectivity section is given by summation of the
migrated crosscorrelation data over all geophone pairs
As and as , then it is clear that the above phase goes to zero, leading
to constructive interference at the scatterer's location.
In practice, these two conditions will be fulfilled if the
specular-reflection point is within the aperture of the recording
array and the geophone array is sufficiently dense.
**fig2
**

Figure 2
Ghost reflection rays associated with
a source at *s*, a trial image point
at *x*, and a scatterer at *x*_{o}.

**fig3
**

Figure 3
As *x* approaches *x*_{0} and *g*_{o} approaches *g*'' in
Figure 2, the dashed rays coincide with the solid
rays.
Thus the *Direct Ghost* correlation term will have zero phase,
leading to maximal constructive interference of the migration section
at the actual scatterer point.

** Next:** NUMERICAL RESULTS
** Up:** Theory of daylight imaging
** Previous:** Source location imaging
Stanford Exploration Project

9/5/2000