Multiple attenuation using λ-f domain high-order and high-resolution Radon transform based on SL0 norm

Abstract

Radon transform is to use the speed difference between primary wave and multiple wave to focus the difference on different “points” or “lines” in Radon domain, so as to suppress multiple wave. However, the limited migration aperture, discrete sampling, and AVO characteristics of seismic data all will weaken the focusing characteristics of Radon transform. In addition, the traditional Radon transform does not take into account the AVO characteristics of seismic data, and uses L1 Norm, the approximate form of L0 Norm, to improve the focusing characteristics of Radon domain, which requires a lot of computation. In this paper, we combine orthogonal polynomials with the parabolic Radon transform (PRT) and find that the AVO characteristics of seismic data can be fitted with orthogonal polynomial coefficients. This allows the problem to be transformed into the frequency domain by Fourier transform and introduces a new variable, lambda, combining frequency and curvature. Through overall sampling of lambda, the PRT operator only needs to be calculated once for each frequency, yielding higher computational efficiency. The sparse solution of PRT under the constraints of the smoothed L0 Norm (SL0) obtained by the steepest descent method and the gradient projection principle. Synthetic and real examples are given to demonstrate that the proposed method has This method has advantages in improving the Radon focusing characteristics than does the PRT based on L1 norm.