An Efficient Amplitude-Preserving Radon Transform With Frequency-Dependent Curvature for Multiple Attenuation

The parabolic Radon transform (PRT) is one of the commonly used demultiple methods and can be efficiently realized in the frequency domain. To avoid aliasing, its curvature range (CR) and curvature sampling interval (CSI) are usually set according to the highest frequency sampling standard. Thus, the CR and CSI are identical for all frequencies. However, the CR and CSI are indeed dependent on frequency. The frequency-independent sampling will lead to amplitude loss, resulting in inaccurate estimation of multiples. For this problem, in this article, the sampling theories of CR and CSI are rederived based on the ${f}$ - ${k}$ spectrum. The result shows that the maximum CR and CSI are inversely proportional to frequency. This frequency-dependent sampling will lead to nonuniform CSI for each frequency, which causes inconvenient multiple attenuation. Therefore, a variable CSI is further designed to attenuate multiples flexibly. In the overlap region of multiples and primaries, the CSI is identical for all frequencies and follows the maximum CSI of the highest frequency. For other regions, the CSI still depends on frequency. Finally, an amplitude-preserving PRT with frequency-dependent CR and CSI is developed. Compared with the conventional PRT, this method can estimate amplitude more accurately due to the extended CR. Compared with the amplitude-preserving high-order PRT, this method has a lower computational cost due to fewer Radon coefficients to be inverted. Multiple attenuation experiments demonstrate the amplitude-preserving performance and efficiency of the proposed PRT.