Seislet transform and seislet frame

Published as Geophysics, 75, no. 3, V25-V38, (2010)

Seislet transform and seislet frame

Sergey Fomel and Yang Liu

Bureau of Economic Geology
John A. and Katherine G. Jackson School of Geosciences
The University of Texas at Austin
University Station, Box X
Austin, TX 78713-8924

Abstract:

We introduce a digital wavelet-like transform, which is tailored specifically for representing seismic data. The transform provides a multiscale orthogonal basis with basis functions aligned along seismic events in the input data. It is defined with the help of the wavelet lifting scheme combined with local plane-wave destruction. In the 1-D case, the seislet transform is designed to follow locally sinusoidal components. In the 2-D case, it is designed to follow local plane wave components with smoothly variable slopes. If more than one component is present, the transform turns into an overcomplete representation or a tight frame. In these terms, the classic digital wavelet transform is simply a seislet transform for a zero frequency (in 1-D) or zero slope (in 2-D).

The main objective of the new transform is an effective seismic data compression for designing efficient data analysis algorithms. Traditional signal processing tasks such as noise attenuation and trace interpolation become simply defined in the seislet domain. When applied in the offset direction on common midpoint or common image point gathers, the seislet transform finds an additional application in optimal stacking of seismic records.

Seislet transform and seislet frame