Conclusions

Since f-x prediction has been shown to be equivalent to a t-x prediction with a long time length, it may not be surprising that t-x prediction generally produces results similar to those of f-x prediction. Although both these techniques work equally well in low noise cases, t-x prediction provides better random noise reduction than the older f-x prediction technique in the presence of moderate- to high-amplitude noise. The t-x prediction also avoids the generation of false events in the presence of parallel events when using f-x prediction, at least for parallel events with spacings wider than the filter length in time. The advantages of t-x prediction are the result of its ability to control the length of the prediction filters in time. Because t-x prediction has a shorter effective filter length in time than f-x prediction, t-x prediction passes significantly less random noise than f-x prediction. While Gulunay's f-x prediction biases the prediction toward the traces nearest to the output point, allowing more noise to be passed, this bias appears unimportant when compared to the problem with the length of the effective filter in time.

3-dimensional prediction allows improved noise attenuation because more samples are used to make predictions. 3-dimensional prediction also relaxes the requirement that events be linear. Comparisons of one- and two-pass predictions on a land data set show that the one-pass results retain significantly more detail than the two-pass results. In both one- and two-pass predictions, the f-x prediction passes more random noise than the t-x prediction.

In the next chapter, the generation of spurious events is examined in more detail. In chapter , I will examine two more shortcomings of f-x and t-x prediction, that of the amplitude loss in the signal and that of the filter response to the noise being left in the signal. To avoid these difficulties, a method of extending t-x prediction is presented in chapter .