Using the definition of data-space pseudo inverse, Chemingui and Biondi (1997) presented a new technique to invert for reflectivity models while correcting for the effects of irregular sampling. The final reflectivity model is a two step solution where the data is equalized in a first stage with an inverse filter and an imaging operator is then applied to the equalized data to invert for a model.

We start from the definition for the data-space inverse solution

(6) |

(7) |

(8) |

where is AMO from input offset *h*_{i} to output offset *h*_{j}
and, is the identity operator (mapping from *h*_{i} to *h*_{i}). Conforming
to the definition of AMO Biondi et al. (1996),
is the adjoint of ;
therefore, the filter is Hermitian
with diagonal elements being the identity and off-diagonal elements being
AMO transforms.

7/5/1998