In the previous chapter, the generation of spurious events by t-x and f-x prediction was shown to occur when a signal occured in a background of noise. Soubaras 1994 also pointed out that the amplitudes of signals may be reduced by these prediction-filtering techniques. Both these effects are examples of how t-x and f-x prediction-filtering methods may break down in the presence of noise. These breakdowns are partially caused by the corruption of the prediction filter by noise. It may also be seen that the response of the filter to the noise can also contribute to these breakdowns when it overwhelms weak reflections.
These problems can be overcome by posing the noise removal as an inversion problem. This inversion removes the filter response from the calculated noise; plus, the inversion allows the filter to be recalculated without the noise corruption. The recalculated filter allows improved signal prediction.
In this chapter, I will show how the noise removal may be posed as an inversion problem and how the noise estimate from prediction filtering is used to increase the accuracy and speed of the solver. The combination of the inversion and the recalculation of the filter will be shown to preserve the amplitude of reflectors and to reduce spurious events generated by the prediction filteringAbma (1994). The process is demonstrated on synthetic and real data.