Asymptotic pseudounitary stacking operators |

I thank Jon Claerbout for helpful discussions and the sponsors of the Stanford Exploration Project for the financial support of this work. Comments from three anonymous reviewers helped to improve the paper.

This appendix exemplifies the application of adjoint operators by reviewing the analytical least-squares inversion of the classic Radon transform (slant stack operator).

Forming the product
for this case leads
to the double integral

Applying Fourier transform with respect to , we can rewrite equation (A-1) in the frequency domain as

where

(90) | |||

(91) |

The inner integral in equation (A-2) reduces to the -dimensional delta function:

(92) |

As follows from the properties of delta function,

Inverting (A-6) for , we conclude that

Substituting equation (A-7) into (13) produces the result precisely equivalent to Radon's inversion (4).

Asymptotic pseudounitary stacking operators |

2013-03-03