Although the convolution in equation (1) is commutative, the different spectra of and disallow us from using the same operator defined in equation (2) to retrieve the wavelet when the reflectivity sequence is completely known. However, if we start again from the ideal case of a sparse reflectivity sequence, it is possible to define an operator that retrieves the exact wavelet:

(12) |

(13) |

A similar approach to the one described for reflectivity estimation can be taken for the wavelet estimation in the case of a non-sparse known reflectivity sequence. The iterative process is then described by

(14) |

1/13/1998