The seislet transform is a waveletlike 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 the 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, the 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 adopted a new velocity-dependent (VD) formulation of the seislet transform, in which the normal moveout equation served as a bridge between local slope patterns and conventional moveout parameters in the common-midpoint domain. The VD slope has better resistance to strong random noise, which indicated the potential of VD seislets for random noise attenuation under 1D earth assumption. Different slope patterns for primaries and multiples further enabled a VD-seislet frame to separate primaries from multiples when the velocity models of primaries and multiples were well disjoint. We evaluated the results by applying the method to synthetic and field-data examples in which the VD-seislet transform helped in eliminating strong random noise. We performed synthetic and field-data tests that showed the effectiveness of the VD-seislet frame for separation of primaries and peg-leg multiples of different orders.

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