High-order seislet transform and its application of random noise attenuation

The seislet transform is a wavelet-like transform that analyzes seismic data by following variable slopes of seismic events across different scales. It generalizes the discrete wavelet transform (DWT) in the sense that DWT in the lateral direction is simply the seislet transform with zero slopes. An earlier work used low-order versions of DWT to construct the seislet transform. In this work, we extend this approach to a higher order, using the Cohen-Daubechies-Feauveau 9/7 biorthogonal wavelet transform (the basis for the JPEG2000 compression scheme) as a template. Using synthetic and field-data examples, we demonstrate that the new transform can provide a better compression rate for seismic events than the Fourier transform, DWT, or the low-order seislet transform. Therefore, the high-order seislet transform can be more suitable for data processing tasks such as data regularization and noise attenuation.