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Equation 27 is a direct statement of the waveform
inversion procedure of Pratt and Worthington (1989) and Sirgue and Pratt (2004). However, the
use of one-way operators leads to the definition of a explicit
scattering operator and a slightly different gradient operator:
| |
(27) |

| (28) |

Note that the two approaches are similar: the wavefield residuals are
back-projected from the source point through the model and correlated
with the source Green's function. This approach, though, has the
scattering matrix chained between the source and receiver
Green's functions. This derives from the application of a
differential operator directly on the phase of the extrapolation
operator.

** Next:** Conclusion
** Up:** Waveform Inversion Problem
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Stanford Exploration Project

5/6/2007