OC-seislet: seislet transform construction with differential offset continuation

Conclusions

We have introduced the OC-seislet transform, a new domain for analyzing prestack reflection data in offset, midpoint, and time coordinates. Thanks to its physical basis, the new transform is able to characterize and compress structurally complex seismic data better than either the 3-D Fourier transform or the PWD-seislet transform. The offset-continuation operator serves as a transformational bridge between different offsets, which allows the OC-seislet transform to compress all predictable reflections and diffractions into small scales. In the new transform domain, random noise spreads over different scales while the predictable reflection seismic events get compressed to large coefficients at small scales. Therefore, a thresholding approach is successful in separating seismic signal and noise. Reconstructing missing seismic data is a more difficult task, where iterative thresholding is required to help the proposed OC-seislet transform recover the missing seismic traces. Tests using both synthetic and field data demonstrate that the proposed transform can succeed in handling structurally complex data even in the presence of strong random noise.

OC-seislet: seislet transform construction with differential offset continuation