Towards the seislet transform

I introduce a digital wavelet-like transform tailored specifically for representing seismic data. The transform provides a multiscale orthogonal basis with basis functions aligned along seismic event slopes in the input data. It is defined with the help of the wavelet lifting scheme combined with local plane-wave destruction. The main objective of the new “seislet” transform is an optimal seismic data compression for designing efficient algorithms. Traditional signal processing tasks such as noise removal and trace interpolation are simply defined in the seislet domain and realizable with optimally efficient O(N) algorithms. 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.