Wave Field Separation Technology Research Based On High-resolution Radon Transform

Radon transform has been used to separate wave field early in seismic data processing, seismic event identification, and wave filed separation, multiple suppression, velocity analysis etc, and it has a good effect. Compared with Fourier transform, wavelet transform and the other, the Radon transform operator is not orthogonal. This result in energy error in forward and inverse Radon transform. Many methods have been used to improve the results, among which the most popular method is inversion method.In the paper, all types and fundamental principles of Radon transform are summarized systematacially. This paper starts from the general linear Radon transform, and then researches how to use the damped least square method to find the solution of the forward transform. However, the least squares smoothing effect will lead to a certain degree of trails in the data of Radon domain, which led to the application's limitations. After that the implementation in Radon domain and relative merits of linear Radon transform, parabolic Radon transform and polynomial Radon transform which have time invariance are introduced, the conjugate gradient method that can solve numerical solution is also given. And then the high resolution Randon transform is discussed, it introduces the regularization theory and Bayes principle into inversion, which successfully remove the negative affect caused by discrete Radon transform. Finally, we introduce the optimal weighting similar coefficient Radon transform, which adapt to the time variant quality of hyperbolic Radon transform. High resolution Radon transform makes Radon domain data appear in the form of energy group, this greatly improves the resolution of data and makes wave-field separation more easily in Radon domain. Simultaneously, the end point effect, truncated effect, space alias and other questions of Radon transform is discussed, the method that take the high resolution Radon transform and similarity function to press truncated effect is presented. Meanwhile,we also discuss how to avoid space alias by selecting parameters. In order to display the advantage of Radon transform, the paper also studies f-k wave field separation, and compared with Radon transform through a simple linear model.The application of model and practical results shows that: compared to typical Radon transform, high resolution Radon transform completely suppresses the so-called smoothing effect, greatly improves the resolution, and enable data inversion recovery, all these demonstrates its superiority.