Noise removal by filtering

Filtering is a common and effective method of removing noise, especially when the noise has a spectrum (1-D, 2-D, or 3-D) that is sufficiently different from the signal. In the work here, filters are derived from the data to be used as predictors. Predictive deconvolution is an example of this, where the signal is what remains after the predictable part of the trace is removed by the prediction-error filter. In contrast, f-x and t-x prediction treats the predictable part of the data as the signal, and the unpredictable part is considered noise.

Chapter  will compare the results of f-x and t-x predictions and extend the two-dimensional results into three dimensions. One of the main results of chapter  is that f-x prediction can be considered equivalent to a t-x prediction with a very long filter length in time. This long filter length allows more random noise to remain in the signal and may generate spurious events far from the original reflections. Another important result is that three-dimensional filtering provides important advantages over two-dimensional filtering, especially in areas of complex geology.

The advantage of filtering is that it is simple and easy to understand. The disadvantages of filtering, as shown in chapter , are that the filter response of the noise is left in the signal, and because the calculation of the filter is corrupted by the noise, spurious events may be generated and signal amplitudes reduced. To reduce these undesired effects, the signal and noise separation problem is posed as an inversion in the second part of this thesis.