中文摘要：

基于常规双曲Radon变换进行叠前地震数据重建时，即使分辨率很高也难以得到准确的中远偏移距数据，因为地震信号同相轴在偏移距较远时已经不再满足双曲线假设。提出基于各向异性Radon变换，即由偏移距、慢度、非椭圆率三参数控制的各向异性Radon变换进行叠前地震数据重建的方法，考虑了偏移距较远时地震数据的非双曲线同相轴，通过稀疏约束控制Radon变换提高了地震数据的重建精度。针对时变Radon变换耗时较长的问题，在算子求解过程中采用快速迭代软阈值算法（Fast iterative shrinkage-thresholding algorithm，FISTA）加快了收敛速度，提高了计算效率。模拟数据和实际数据的应用结果表明，各向异性Radon变换方法在提高数据重建准确度和计算效率方面效果良好。

英文摘要：

Although the conventional hyperbolic Radon transform owns high resolution to reconstruct seismic data, it is diffi- cult to reconstruct the far-offset seismic data, because the event of far-offset seismic signals is no longer satisfied with the hy- perbolic assumption. Therefore,we proposed a prestack seismic data reconstruction method by anisotropie Radon transform to consider the effect of far-offset factor. The formula of anisotropic Radon transform is controlled by offset, slowness and anelliptieity. The travel-time curve of horizontal layer can be accurately described for far-offset by the anisotropic anellipticity parameter of the non-hyperbolic moveout formula. We also use sparsity constraint to improve the accuracy of reconstruction. During the procedure of operator solving, fast iterative shrinkage-thresholding algorithm （FISTA） is used to speed up the convergence and reduce the calculation time. The results of theoretical model and field data demonstrate that anisotropic Ra- don transform has good effect on the reconstruction accuracy and calculation efficiency.