The pyramid transform and its application to signal/noise separation

Yalei Sun and Shuki Ronen

yalei@sep.stanford.edu, shuki@gatwick.Geco-Prakla.slb.com

ABSTRACT

The ``pyramid transform'' is spatial-resampling of data in the frequency-space domain with frequency-dependent grids (FDG), in which the spatial-sampling interval is inversely proportional to the frequency. A cube in the F-X-Y domain is thus transformed to a pyramid. Wavefields do not contain high wavenumbers in low frequencies. Therefore, the pyramid transform is invertible when applied to wavefields. After pyramid transformation, the size of data has shunk dramatically. This feature can save many resources. However, the main benefit is that the low frequencies are not over-parameterized which makes frequency-dependent grids more suitable for inversion and interpolation. For example, spatial prediction filters become independent of the temporal frequency in the pyramid domain. This feature has a great potential in signal/noise separation and trace interpolation. In this paper, we investigate the possibility of applying the pyramid transform to noise suppression. Our results show the prediction filter estimated in the pyramid domain can remove the low temporal frequency random noise, which can not be handled by the prediction filter estimated from the common frequency-independent grids (FIG).