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High order 3D Radon transform and its application in data reconstruction
XUE Yaru, CHEN Jiansheng, QIAN Buren
(College of Geophysics and Information Engineering in China University of Petroleum,Beijing 102249,China)
Abstract:
The high resolution Radon transform cannot preserve the event amplitude information due to the incompleteness of the transform basis functions. Based on high order 2D Radon transform and 3D Radon transform, a high order 3D Radon transform is proposed to keep the amplitude information continuously along both inline and crossline directions. The method first expands the orthogonal polynomial transform to 2 dimensions and then embeds it to 3D Radon transform to construct high order 3D Radon transform. The proposed method integrates the gradient and curvature information in the event amplitude variations into the 3D Radon transform. With these additional properties, the directional variations in the events amplitude can be modeled continuously in the transformation, which improves the resolution of Radon transform. The experiments of synthetic and field data show robust results in denoising and reconstruction.
Key words:  Radon transform  orthogonal polynomial transform  amplitude-preservation  data reconstruction