Time migration is an important tool to provide a subsurface image because it is faster and less sensitive to velocity errors than depth migration. However, a reliable and focused time migration image is achievable only with well-determined time-migration velocities. As an alternative of prestack time migration, equivalent offset migration (EOM) provides intermediate common scatterpoint (CSP) gathers that have higher fold and larger offset range than common midpoint (CMP) gathers, which enables precise focusing of the velocity semblance and accurate velocity analysis. However, direct implementation of EOM might introduce coherent mapping noise, which smears the velocity spectra and decreases the resolution of the final stacked image. We reformulate the EOM as a linear operator that maps CMP gathers to CSP gathers and then propose least-squares equivalent offset migration (LS-EOM) method that inverts for optimal CSP gathers by minimising the misfit between simulated and observed CMP gathers. Compared with the EOM method, LS-EOM provides noise-free CSP gathers, leading to better focusing of the velocity semblance and higher resolution of the final stacked image. Both synthetic and field data tests demonstrate the effectiveness of our proposed method.

时间迁移是提供地下图像的重要工具，因为它比深度迁移更快速且对速度误差不敏感。但是，只有确定的时间迁移速度才能获得可靠且集中的时间迁移图像。作为叠前时间偏移的替代方法，等效偏移偏移（EOM）提供的中间公共散射点（CSP）褶皱比普通中点（CMP）褶皱具有更高的折叠度和更大的偏移范围，从而可以精确聚焦速度相似度并进行准确的速度分析。但是，直接实施EOM可能会引入相干映射噪声，这会涂抹速度谱并降低最终堆叠图像的分辨率。我们将EOM重新构造为将CMP收集映射到CSP收集的线性算子，然后提出最小二乘等效偏移迁移（LS-EOM）方法，该方法通过最小化模拟和观察到的CMP收集之间的不匹配性来反转最佳CSP收集。与EOM方法相比，LS-EOM提供了无噪声的CSP聚集，从而使速度相似性更好地聚焦并且最终堆叠图像的分辨率更高。综合和现场数据测试都证明了我们提出的方法的有效性。