A unified framework for the deconvolution of traces of nonwhite reflectivity

One of the fundamental assumptions of conventional deconvolution methods is that reflection coefficients follow the white-noise model. However, analys is of well logs in various regions of the world confirms that in the majori ty of cases, reflectivity tends to depart from the white-noise behavior. Th e assumption of white noise leads to a conventional deconvolution operator that can recover only the white component of reflectivity, thus yielding a distorted representation of the desired output. Various alternative process es have been suggested to model reflection coefficients. In this paper, we will examine some of these processes, apply them, contrast their stochastic properties, and critique their use for modeling reflectivity. These proces ses include autoregressive moving average (ARMA), scaling Gaussian noise, f ractional Brownian motion, fractional Gaussian noise, and fractionally inte grated noise. We then present a consistent framework to generalize the conv entional deconvolution procedure to handle reflection coefficients that do not follow the white-noise model. This framework represents a unified appro ach to the problem of deconvolving signals of nonwhite reflectivity and des cribes how higher-order solutions to the deconvolution problem can be reali zed. We test generalized filters based on the various stochastic models and analyze their output. Because these models approximate the stochastic prop erties of reflection coefficients to a much better degree than white noise, they yield generalized deconvolution filters that deliver a significant im provement on the accuracy of seismic deconvolution over the conventional op erator.