In the past, single trace deconvolution and NMO stacking have been the most effective noise attenuation advances. Single trace deconvolution can be thought of as removing the reverberation of the reflection, a coherent noise, from the data. NMO stacking is an effective noise attenuator of both coherent noise that does not follow the specified hyperbolic trajectory and of random noise. Even today, these two techniques provide the greatest improvement to our seismic records. Unfortunately, these techniques do not always provide sufficient noise attenuation.
When noise has properties that allow it to be distinguished from signal, it may be removed by taking advantage of these properties. Early noise-attenuation techniques were limited to the grouping of geophones to cancel coherent noise Dobrin and Savit (1988); Kanasewich (1990); Stone (1994), since sophisticated post-acquisition processing was unavailable. Later, along with digital data recording and processing, multichannel techniques such as velocity filters and F-K filteringYilmaz (1987) were used to eliminate noise such as ground roll and air blasts.
For attenuating random noise, a number of techniques involving filtering or mixing adjacent traces were used before the introduction of the prediction technique of Canales 1984. Canales divided the two-dimensional filtering problem into many one-dimensional filtering problems in space, one for each frequency. Canales' idea was further developed by Gulunay 1986 and was referred to as FX-decon. These techniques have been very successful. They were relatively easy to use, reliable, and did not harm reflected events. The f-x prediction techniques of Canales and Gulunay may also be implemented as t-x prediction process, as is done in chapter . A technique that is somewhat similar to the t-x prediction process shown here was presented by Hornbostel 1991, although the emphasis in his work was handling time- and space-varying signals. In this thesis, time- and space-varying signals are treated by windowing the seismic data into smaller sections as discussed in Claerbout 1992b. Unfortunately, these prediction techniques may be only partially successful in the presence of strong noise. Furthermore, these techniques can generate spurious events in seismic data, as I will show later in this thesis.
Bad traces in prestack seismic data may be manually removed or edited automatically Pokhriyal et al. (1991); Pokhriyal (1993). A similar approach to automatically removing samples with high-amplitude noise will be presented later in this thesis. Sinusoidal noise may be separated from signal without filtering out the signal of the same frequency Linville and Meek (1992). Various specialized methods are available to remove coherent noise from prestack data. Along with velocity filtering and F-K filtering, multiple attenuation, stacking, deconvolution, and dip filtering are all efforts to separate noise from signal.
In this thesis, I assume that the signals of interest are linear; that is, signals are lines in 2-D data and planes in 3-D data. For nonlinear events, the data are subdivided, or windowed, into smaller sections where the events of interest are approximately linear. While the human eye recognizes the continuity of nonlinear events, the mathematical tools available to us work best on linear problems. Windowing extends the applicability of the techniques discussed here to data in areas of complex geology and to prestack data. Complex geology requires that the windows be small enough to make the geology look linear within the window, although this requirement may be relaxed somewhat because of the smoothing effect of diffractions. Prestack data generally appears as a series of hyperbolas, which will be more linear at the far offsets than at the near. Once again, windowing these hyperbolas generally will allow them to be treated as linear events within the window.