Wavelet distortion

The previous examples show spurious events generated at widely spaced times because parallel events affect each other's predictions. These widely spaced events may be removed by shortening the filter length in time. Closely spaced parallel events will produce spurious events with little separation in time. These appear as distortions to the wavelet.

A single event that is extended in time, such as a reflection with a wavelet convolved with it, suffers distortions, as seen in Figures  to . Figure  shows an example of lateral prediction with a single event. The original event extending over three samples in time is shown in Figure . When a prediction filter was applied to the data, a trace from the noise-free side of the data was extracted and is shown in Figure . While Figure  shows the t-x prediction result, f-x prediction produces similar effects.

 

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Figure 4 An example of lateral prediction with a single event.

Notice that the event in Figure  appears similar to the event in Figure , but is extended in time. As the level of the noise is decreased, the spreading of the wavelet in time will decrease. There will be a trade-off between noise attenuation and resolution in time that will depend on the level of the noise. Normally this trade-off is well worth the small sacrifice of resolution, but the user should be aware that a trade-off is taking place.

 

smultspike Figure 5 The original trace before prediction filtering.

 

smultmda Figure 6 The trace after prediction filtering.