标题： 快速方位各向异性三维Radon变换的广义Fourier Slice定理 显示英文标题

标题： Fast Azimuthally Anisotropic 3D Radon Transform by Generalized Fourier Slice Theorem

摘要： 昂贵的常规稀疏拉东变换计算限制了其用于有效转换三维各向异性地震数据立方体。 我们介绍了一种快速算法，用于方位各向异性三维拉东变换，并带有稀疏性约束，允许对任意各向异性非均匀介质对应的地震体数据进行有效变换。 特别是，一个时间与偏移坐标组成的三维数据（CMP）立方体被转换为截距时间、慢度和方位角的三维立方体。 最近提出的广义 傅里叶切片定理被用于非常快速地计算三维逆变换及其伴随，这些随后通过前向后向分裂算法用于有效的稀疏变换实现。 新的各向异性变换提高了所得地震数据的时间分辨率。 此外，拉东变换系数允许在任何水平面上构造方位相关的NMO速度曲线，该曲线可以用来反演介质的各向异性参数。 使用合成数据集的数值例子展示了所提出的各向异性方法相比传统的各向同性方法在提高地震处理结果方面的有效性。 显示英文摘要

摘要： Expensive computation of the conventional sparse Radon transform limits its use for effective transformation of 3D anisotropic seismic data cubes. We introduce a fast algorithm for azimuthally anisotropic 3D Radon transform with sparsity constraints, allowing effective transformation of seismic volumes corresponding to arbitrary anisotropic inhomogeneous media. In particular, a 3D data (CMP) cube of time and offset coordinates is transformed to a 3D cube of intercept time, slowness, and azimuth. The recently proposed generalized Fourier slice theorem is employed for very fast calculation of the 3D inverse transformation and its adjoint, which are subsequently used for efficient implementation of the sparse transform via a forward-backward splitting algorithm. The new anisotropic transform improves the temporal resolution of the resulting seismic data. Furthermore, the Radon transform coefficients allows constructing azimuthally dependent NMO velocity curve at any horizontal plane, which can be inverted for the medium anisotropic parameters. Numerical examples using synthetic data sets are presented showing the effectiveness of the proposed anisotropic method in improving seismic processing results compared with conventional isotropic counterpart.