In general, the synthetic data for one frequency, a shot positioned at and a receiver positioned at can be given by a linear operator acting on the full model space with ( in 2*D*) as

(6) |

In equation (6), we use two important properties Ehinger et al. (1996): first, the Green functions are computed by means of the one-way wave equation, and second, the extrapolation is performed by using the adequate paraxial wave equations (flux conservation) Bamberger et al. (1988).

The quadratic cost function is

(7) |

(8) |

Notice that computing in equation (8) needs only the precomputed Green functions at model points and . Thus, the size of the problem can be considerably reduced by computing the Green functions only at the target location , reducing equation (8) to

(9) |

5/3/2005