Because the velocity errors are inevitable in field data applications, direct implementation of conventional least-squares reverse time migration (LSRTM) would generate defocused migration images. Extending the model domain has the potential to preserve the data information, and reducing the extended model could provide a final image with more continuous subsurface structures for geologic interpretation. However, the computational cost and the memory requirement would be increased significantly compared to conventional LSRTM. To obtain an inversion image with better quality than conventional LSRTM, while maintaining the same computational cost and memory requirement, we have introduced random space shifts in LSRTM. The key point is to perform implicit model extension and immediate model reduction within each iteration of the inversion procedure. To be robust against the random noise during the random sampling process, we formulate the inverse problem based on a correlation objective function. Numerical examples on a simple layered model, the Marmousi model, and the SEAM model demonstrate that even when the bulk velocity errors are up to 10%, we still obtain reasonable results for subsurface geologic interpretation.

中文翻译：

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最小二乘法扩展了反向时间迁移，具有随机采样的空间移位

由于速度误差在现场数据应用中是不可避免的，因此传统的最小二乘反向时间偏移（LSRTM）的直接实现将生成散焦的偏移图像。扩展模型域具有保存数据信息的潜力，而减少扩展模型可以为最终图像提供具有更连续地下结构的地质解释。但是，与传统的LSRTM相比，计算成本和存储需求将大大增加。为了获得比传统LSRTM更好的质量的反转图像，同时保持相同的计算成本和内存要求，我们在LSRTM中引入了随机空间移位。关键是在反演过程的每次迭代中执行隐式模型扩展和立即模型简化。为了在随机采样过程中抵抗随机噪声，我们基于相关目标函数来构造反问题。简单分层模型，Marmousi模型和SEAM模型上的数值示例表明，即使当体速度误差高达10％时，我们仍然可以获得合理的地下地质解释结果。