Seislet transform and seislet frame |

We have introduced a new digital transform named *seislet
transform* because of its ability to characterize and compress seismic
data in the manner similar to that of digital wavelet transforms. We
define the seislet transform by combining the wavelet lifting scheme
with local plane-wave destruction. In 1-D, the seislet transform
follows sinusoidal components. In 2-D, it follows locally plane
events. When more than one sinusoid or more than one local slope are
applied for the analysis, the transform turns into an overcomplete
representation or a frame. The seislet transform and seislet frame can
achieve a better compression ratio than either the digital Fourier
transform (DFT) or the digital wavelet transform (DWT).

The seislet transform provides a convenient orthogonal basis with the basis functions spanning different scales analogously to those of the digital wavelet transform but aligned along the dominant seismic events. Traditional signal analysis operations such as denoising and trace interpolation become simply defined in the seislet domain and allow for efficient algorithms. Seismic stacking also has a simple meaning of the zeroth-order seislet coefficient computed in an optimally efficient manner by recursive partial stacking and thus avoiding the usual problems with wavelet stretch and nonhyperbolic moveouts.

Seislet transform and seislet frame |

2013-07-26