Different versions of the Radon transform (RT) are widely used in seismic data processing to focus the recorded seismic events. Multiple separation, data interpolation, and noise attenuation are some of the RT applications in seismic processing workflows. Unfortunately, conventional RT methods cannot focus events perfectly in the RT domain. This problem arises due to the blurring effects of the source wavelet and the nonstationary nature of the seismic data. Sometimes, the distortion results in a big difference between the original data and its inverse transform. We have developed a nonstationary deconvolutive RT (DecRT) to handle these two issues. Our algorithm takes advantage of a nonstationary convolution technique that builds on the concept of block convolution and the overlap method, in which the convolution operation is defined separately for overlapping blocks. Therefore, it allows the Radon basis function to take arbitrary shapes in the time and space directions. In addition, we introduce a nonstationary wavelet estimation method to determine time-space-varying wavelets. The wavelets and the Radon panel are estimated simultaneously and in an alternating way. Numerical examples demonstrate that our nonstationary DecRT method can significantly improve the sparsity of Radon panels. Hence, inverse RT does not suffer from the distortion caused by unfocused seismic events.

中文翻译：

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非平稳解卷积 Radon 变换

不同版本的 Radon 变换 (RT) 广泛用于地震数据处理以聚焦记录的地震事件。多重分离、数据插值和噪声衰减是地震处理工作流程中的一些 RT 应用。不幸的是，传统的 RT 方法不能完美地将事件聚焦在 RT 域中。这个问题是由于源子波的模糊效应和地震数据的非平稳性而产生的。有时，失真会导致原始数据与其逆变换之间存在很大差异。我们开发了一个非平稳解卷积 RT (DecRT) 来处理这两个问题。我们的算法利用了基于块卷积概念和重叠方法的非平稳卷积技术，其中卷积操作是针对重叠块单独定义的。因此，它允许氡基函数在时间和空间方向上具有任意形状。此外，我们引入了一种非平稳小波估计方法来确定时空变化的小波。小波和氡气面板以交替方式同时估计。数值例子表明，我们的非平稳 DecRT 方法可以显着提高氡气面板的稀疏性。因此，逆 RT 不会受到未聚焦地震事件引起的失真的影响。小波和氡气面板以交替方式同时估计。数值例子表明，我们的非平稳 DecRT 方法可以显着提高氡气面板的稀疏性。因此，逆 RT 不会受到未聚焦地震事件引起的失真的影响。小波和氡气面板以交替方式同时估计。数值例子表明，我们的非平稳 DecRT 方法可以显着提高氡气面板的稀疏性。因此，逆 RT 不会受到未聚焦地震事件引起的失真的影响。