Three-parameter Radon transform based on shifted hyperbolas

Abstract

The focusing power of the conventional hyperbolic Radon transform decreases for long-offset seismic data due to the nonhyperbolic behavior of moveout curves at far offsets. Furthermore, conventional Radon transforms are ineffective for processing data sets containing events of different shapes. The shifted hyperbola is a flexible three-parameter (zero-offset traveltime, slowness, and focusing-depth) function, which is capable of generating linear and hyperbolic shapes and improves the accuracy of the seismic traveltime approximation at far offsets. Radon transform based on shifted hyperbolas thus improves the focus of seismic events in the transform domain. We have developed a new method for effective decomposition of seismic data by using such three-parameter Radon transform. A very fast algorithm is constructed for high-resolution calculations of the new Radon transform using the recently proposed generalized Fourier slice theorem (GFST). The GFST establishes an analytic expression between the [Formula: see text] coefficients of the data and the [Formula: see text] coefficients of its Radon transform, with which a very fast switching between the model and data spaces is possible by means of interpolation procedures and fast Fourier transforms. High performance of the new algorithm is demonstrated on synthetic and real data sets for trace interpolation and linear (ground roll) noise attenuation.