Fast hyperbolic Radon transform using chirp-z transform

Abstract

The hyperbolic Radon transform plays an important role in seismic data processing for its ability to focus seismic events in the transform domain. Traditional algorithms based on direct implementations, however, are inefficient with limited applications for processing large data sets. A new algorithm is presented for fast computation of the hyperbolic Radon transform and its sparse calculations. It uses interpolation procedures to stretch the data along time axis and efficiently computes the summation paths in the new coordinates via the chirp-z transform which is carried out by fast Fourier transform (FFT). The proposed fast algorithm is then used within the deconvolutive form of the Radon transform and iterative sparse algorithms for effective decomposition of CMP gathers with an improved temporal resolution, compared to the traditional Radon transforms. The effectiveness of the new algorithm are confirmed on sparse velocity-stack inversion, primary and multiple separation, high-quality stacking, and automatic velocity model building. The tests show that sparse velocity-stack inversion using the new algorithm is even more efficient than the traditional velocity scan, both in resolution and speed. Furthermore, numerical tests show the superiority of the proposed algorithm over the state-of-the-art fast algorithms, based on butterfly scheme and log-polar convolutions, demanding less computational complexity.