(1) | ||

(2) |

The modeled-data gathers are generated by extracting the wavefields values at the surface for all times and all surface locations as follows:

(3) | ||

(4) |

(5) | ||

(6) |

(7) | ||

(8) |

To illustrate the proposed modeling procedure I applied it to a SODCIG extracted from the prestack image of a simple synthetic data set. The data were modeled by using the two-way wave equation and by assuming a constant propagation velocity of 1 km/s and two reflectors: a flat reflector below a reflector dipping by 10 degrees. The complete data set comprises a total of 100 split-spread shot gathers. I migrated the data twice by source-receiver migration: once using the correct velocity and once using a velocity too slow by 10%. Figure , shows the zero-subsurface-offset sections obtained by migration with the correct velocity (Figure a), and a velocity too slow by 10% (Figure b).

Sections-overn
Zero-subsurface-offset sections
obtained by source-receiver migration:
a) with the correct velocity,
and b) a velocity too slow by 10%.
Figure 1 |

Figure shows snapshots of the wavefields obtained by extracting an individual SODCIG from the prestack image obtained using the correct velocity (Figure a). Panel a) shows the source wavefield and panel b) shows the receiver wavefield. Figure shows the data recorded at the surface by the aerial arrays corresponding to the wavefields shown in Figure . Notice that the source wavefield (panel a) is recorded at negative times, because it is propagated back in time. Figures - shows wavefields snapshots and the recorded data corresponding to the same SODCIG used to model the data shown in Figure , but assuming the reflectors to be dipping by 45 degrees, and imposing the initial conditions expressed in equations 5 and 6. Notice that, because of the assumed reflector dip, the wavefields shown in Figure are more asymmetric than the the wavefields shown in Figure , with the receiver wavefield (Figure b) tilted towards the right more than the source wavefield (Figure a).

Snaps-INF-overn
Snapshots of the source wavefield (panel a) and the receiver
wavefield (panel b) generated by modeling an isolated SODCIG
by imposing the initial conditions expressed
in equations 1 and 2.
Figure 2 |

Data-INF-overn
The data recorded at the surface by aerial arrays and corresponding
to the source wavefield (panel a) and the receiver wavefield (panel b)
shown in Figure .
Figure 3 |

Snaps-INF-DIP-overn
Snapshots of the source wavefield (panel a) and the receiver
wavefield (panel b) generated by modeling an isolated SODCIG
by imposing the initial conditions expressed
in equations 5 and 6
and
assuming a reflector dip of 45 degrees.
Figure 4 |

Data-INF-DIP-overn
The data recorded at the surface by aerial arrays and corresponding
to the source wavefield (panel a) and the receiver wavefield (panel b)
shown in Figure .
Figure 5 |

4/5/2006