ARMA formulation of FX prediction error filters and projection filters

Random noise attenuation of seismic sections is commonly implemented using linear prediction error filters in the f-x domain. Linear prediction filter ing assumes that the signal can be described via an autoregressive (AR) mod el. In autoregressive modeling the noise sequence enters into the problem a s an innovation rather than as additive signal. This leads to a model that is inconsistent with the standard assumption of additive white noise made i n f-x random noise attenuation methods. An autoregressive/moving-average (ARMA) model provides an alternative repre sentation of the signal that satisfies the aforementioned assumptions. The ARMA structure of the signal leads, in the stationary approximation, to an eigenvalue problem. The prediction error filter is obtained from the eigen- decomposition of the correlation matrix of the noisy signal. In our algorit hm the prediction error filter is applied to the noisy data and finally, an estimate of the additive noise sequence is obtained by self-deconvolving t he prediction error filter from the filtered data. This procedure is equiva lent to the projection filtering technique proposed by Soubaras (1994, 1995 ).