The simple fitting goals seen in a previous section () do not reflect what must be done to use RIP in practice. The seismic imaging results in this thesis are obtained using these fitting goals:

55#55 | (25) | |

(26) |

56#56 is a mask that allows us to pad the offsets and frequencies. 57#57 is weighting operator that allows us to apply the Jacobian and mask out angles beyond the critical angle. 58#58 is a user-defined mask that can be used to further limit the ray parameters, generally to smooth in depth the effect of masking beyond the critical angle. 43#43 now has two possible definitions. It can be the inverse of the geophysical regularization operator 50#50 or it can be the inverse of the cascade of the geophysical regularization operator and the geological regularization operator 54#54.

In practice, the downward continuation migration operator 59#59 needs to be modified. First, to reduce artifacts, I have included absorbing boundaries to reduce edge effects. Second, to reduce the computational cost of the inversion, I have designed the migration operator so that it has a variable depth step option so that the inversion can take one step through the whole water column.

10/31/2005