Signal and noise separation in prestack seismic data using velocity-dependent seislet transform |

**Yang Liu ^{}, Sergey Fomel^{}, Cai Liu^{}**

^{}College of Geo-exploration Science and Technology,

Jilin University

No.938 Xi minzhu street,

Changchun, China, 130026
^{}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, USA, 78713-8924

The seislet transform is a wavelet-like transform that analyzes
seismic data by following varying slopes of seismic events across
different scales and provides a multiscale orthogonal basis for
seismic data. It generalizes the discrete wavelet transform (DWT) in
the sense that DWT in the lateral direction is simply the seislet
transform with a zero slope. Our earlier work used plane-wave
destruction (PWD) to estimate smoothly varying slopes. However, PWD
operator can be sensitive to strong noise interference, which makes
the seislet transform based on PWD (PWD-seislet transform)
occasionally fail in providing a sparse multiscale representation for
seismic field data. We adopt a new velocity-dependent (VD) formulation
of the seislet transform, where the normal moveout equation serves as
a bridge between local slope patterns and conventional moveout
parameters in the common-midpoint (CMP) domain. The velocity-dependent
(VD) slope has better resistance to strong random noise, which
indicates the potential of VD seislets for random noise attenuation
under 1D earth assumption. Different slope patterns for primaries and
multiples further enable a VD-seislet frame to separate primaries from
multiples when the velocity models of primaries and multiples are well
disjoint. Results of applying the method to synthetic and field-data
examples demonstrate that the VD-seislet transform can help in
eliminating strong random noise. Synthetic and field-data tests also
show the effectiveness of the VD-seislet frame for separation of
primaries and pegleg multiples of different orders.

- Introduction
- Theory
- Review of seislets
- VD-slope pattern for primary reflections
- VD-slope pattern for pegleg multiples
- Separation of primaries and pegleg multiples using VD-seislet frame

- Synthetic Data Examples
- Validation of slope estimation and random noise elimination
- Separation of primaries and pegleg multiples

- Field Data Examples
- Discussion
- Conclusions
- Acknowledgments
- Appendix: The lifting scheme for DWT
- Bibliography
- About this document ...

Signal and noise separation in prestack seismic data using velocity-dependent seislet transform |

2015-10-24