Abstract: τ-p transform is a classic projection transform method, which is widely used in seismic data processing such as signal-noise separation, seismic trace interpolation, and plane wave decomposition based on different ray parameters. However, the precision and resolution of τ-p transform are limited by mathematical inverse problems, and it is necessary to study the methods to accelerate the calculation speed of τ-p transform or to design relevant filter, while maintaining high precision. We propose two τ-p transform methods based on radial trace transform and slope decomposition respectively. In this paper,we demonstrate the fundamental theory of the two methods and compare them with conventional τ-p transform. Using fast Fourier transform and radial trace transform, the τ-p transform method can efficiently reduce the time consumption. Utilizing stable slope decomposition algorithm, the τ-p transform method can perform high resolution τ-p transform,and provide redundant transformation dimension (τ-x-p domain),which enable the design of filter operator more flexible. The numerical experiments show that these two proposed methods are superior to the conventional τ-p transform in calculation speed and reconstruction accuracy. The field-data examples for ground-roll noise suppression confirm that the two methods can provide more effective and flexible implementations for seismic data processing.

Key words: τ-p transform, projection-slice theorem, radial trace transform, slope decomposition