中文摘要：

针对高分辨率Radon变换无法较好地保持地震波振幅变化信息问题,在高阶Radon变换和3D Radon变换基础上,根据地震波传播的横向连续性提出高阶3D Radon变换。该方法首先将正交多项式拟合延拓至正交多项式面拟合,模拟平面波沿不同传播方向的振幅变化特性。与3D Radon变换结合,实现地震波在不同传播路径下的正交多项式面拟合,构成高阶3D Radon变换。该方法既考虑了地震波的传播路径,又考虑了地震波传播振幅变化,因此具有保幅以及高分辨率的特点。应用于地震数据重建表明,该方法具有良好的重建效果,并具有一定的抗噪性,且能够较好地保留地震波在不同方向上的振幅变化特性。

英文摘要：

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.