Linear uncorrelated noise attenuation
Random noise uncorrelated from trace to trace abounds in recorded data and retains its presence at almost all steps in a processing sequence. CMP stacking reduces the uncorrelated noise in the data significantly (basic data processing sequence). Noise that remains in the stacked data can have adverse effect on reflection continuity.
While time-variant filtering (the 1-D Fourier transform) reduces noise in the temporal direction, it does not necessarily attenuate the noise uncorrelated from trace to trace. Although a number of multichannel signal enhancement techniques has been practiced, the one that best preserves relative amplitudes and retains the signal character without amplitude distortion is based on spatial prediction filtering invented by Canales . Mathematical details of this uncorrelated noise attenuation technique is provided in Section F.5.
To understand the conceptual basis for spatial prediction filtering, first, recall from optimum wiener filters the prediction filtering in the temporal direction. A recorded seismic trace is represented by a time series with two components — a predictable part that relates to the multiple reflections and an unpredictable part that relates to the primary reflections. The prediction process involves estimating some future value of the input series defined by the prediction lag from the past values of the input series. For the prediction process to work on a seismic trace, strictly, it must represent a zero-offset seismogram recorded over a horizontally layered earth so as to preserve periodicity of multiples. Assuming this to be the case, another fundamental assumption in predictive deconvolution is that the reflectivity series that contains the primaries is random. Hence, a prediction filter, when applied to the recorded seismic trace produces an estimate of the predictable part — the multiple reflections. The error in the prediction process then represents the random reflectivity series — the primary reflections.
Now consider the prediction process in the spatial direction. A spatial prediction filter, when applied to a stacked section, produces an estimate of the predictable part — the coherent signal. The error in the prediction process represents the noise uncorrelated from trace to trace. Whereas, the prediction lag for the temporal prediction filter is specified according to the period of the multiples, for the spatial application, a unit prediction lag is used. Since predictive deconvolution with a unit prediction lag is equivalent to spiking deconvolution, a spatial prediction filter is of the form of a spiking deconvolution operator.
- Canales (1984), Canales, L., 1984, Random noise reduction: 54th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 525.
- Introduction to noise and multiple attenuation
- Multiple attenuation in the CMP domain
- Frequency-wavenumber filtering
- The slant-stack transform
- The radon transform
- Multichannel filtering techniques for noise and multiple attenuation