oa Time series prediction using iterative phase estimation

For prediction, and particularly in predictive deconvolution, Weiner's approach has been used extensively in the seismic industry. In spite of the importance of phase in the prediction process (Urlych, 2008), approaches explicitly utilizing phase have received scant attention, due to the non-intuitive nature of phase.

An approach to seismic prediction has been developed which explicitly focuses on the phase of the predicted time series, without having to unwrap this phase. This technique assumes a slow temporal variation in the amplitude spectrum as a sampling window is advanced forward over the time series. By explicitly separating the amplitude and the phase, the non-linearity of the problem to predict phase component can be linearized using iterative least squares analysis.

Having calculated the phase, the amplitude component can be estimated - giving the predicted time series of the advanced window. Subtracting the predicted values from the observed data removes those components within this time series that are predictable, for example – the multiple reflection events.