The Shuey-Radon transform

Abstract

The traditional hyperbolic Radon transform (RT) decomposes seismic data into a sum of constant amplitude basis functions. This limits the performance of the transform when dealing with real data in which the reflection amplitudes include the amplitude variation with offset (AVO) variations. We adopted the Shuey-Radon transform as a combination of the RT and Shuey’s approximation of reflectivity to accurately model reflections including AVO effects. The new transform splits the seismic gather into three Radon panels: The first models the reflections at zero offset, and the other two panels add capability to model the AVO gradient and curvature. There are two main advantages of the Shuey-Radon transform over similar algorithms, which are based on a polynomial expansion of the AVO response. (1) It is able to model reflections more accurately. This leads to more focused coefficients in the transform domain and hence provides more accurate processing results. (2) Unlike polynomial-based approaches, the coefficients of the Shuey-Radon transform are directly connected to the classic AVO parameters (intercept, gradient, and curvature). Therefore, the resulting coefficients can further be used for interpretation purposes. The solution of the new transform is defined via an underdetermined linear system of equations. It is formulated as a sparsity-promoting optimization, and it is solved efficiently using an orthogonal matching pursuit algorithm. Applications to different numerical experiments indicate that the Shuey-Radon transform outperforms the polynomial and conventional RTs.