oa Seismic data processing using the pyramid transform

The pyramid transform is a resampling of data in the f-x-y domain (Fourier transform over time but not over space) which generates frequency-dependent spatial grids with a spatial sampling interval that is inversely proportional to frequency. The pyramid transform is reversible and has the important feature that f-x-y prediction filters in the pyramid domain are independent of frequency. This then allows prediction filters to be estimated from a range of frequencies that have high signal-to-noise ratio. The resulting filters are therefore more reliable and can then be applied across the whole frequency range to perform prediction filtering.

We demonstrate how prediction filtering in the pyramid domain can be used in seismic data processing for trace interpolation, data regularisation and infilling missing traces. Using synthetic and field data examples, we show that prediction filters estimated in the pyramid domain are more robust against noise, aliased events and conflicting dips than ones estimated in the conventional f-x-y domain.