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The imaging condition for shot-profile migration
Claerbout (1971) is
| |
(1) |

where the image, *I*, is a function of surface location, ,and depth, *z*, and geophone and source wavefields, *P*^{g,s}, are
functions of location, depth and frequency, . I hypothesized that
the correlation in the imaging condition would satisfy that in the
passive seismic conjecture and make calculating the correlations prior
to processing unnecessary. Further, we could rely on the dispersion
relation to handle the unknown phase characteristics of the ambient
noise-field rather than hoping that the correlations will collapse
these wave-trains into a well-behaved wavelet.
Therefore, without making the intermediate processing step of
correlating all traces with each other, we can downward continue the
receiver wavefield, *P*^{g}, from every location back into the
earth. This means we are migrating the entire dataset as one large
shot gather. Remembering the cartoon in Figure 1, we can
comfortably accept the same wavefield for *P*^{s} since the
source wavefield is recorded by each receiver as it reflects
from the free surface. Setting *P*^{g} = *P*^{s}, I then migrate the data
with a modified shot-profile algorithm similar to that presented in
Guitton (2002).

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Stanford Exploration Project

11/11/2002