An analysis of deconvolution: Modeling reflectivity by fractionally integrated noise

Reflection coefficients are observed in nature to have stochastic behavior that departs significantly from the white-noise model. Conventional deconvo lution methods, however, assume reflectivity to be a white-noise process. I n this paper we analyze the deconvolution process, study the implications o f the assumption of white noise, and show that the conventional operator ca n recover only the white component of reflectivity. A new stochastic model, fractionally integrated noise, is proposed for modeling reflectivity-a mod el that more closely approximates its spectral character and that encompass es white noise as a special case. We discuss different techniques to genera lize the conventional deconvolution method based on the new model in order to handle reflectivity that is not white and compare the results of the con ventional and generalized filters using data derived from well logs.