角道集与偏移距道集在表象微分优化中的等价性

Equivalence of angle gather and offset gather in representation differential semblance optimization

(1.壳牌国际勘探和开发公司，美国德克萨斯休斯敦TX77025；2.Rice大学计算数学与应用数学系，美国德克萨斯休斯敦TX77005)

Shell International Exploration and Production, Houston, TX 77025, USA

在偏移速度分析中，地下散射角度共成像道集(简称角道集)有清晰的物理意义。地下偏移距共成像道集(简称偏移距道集)是角道集在逆Radon变换下的对偶量。从一次反射的正演模型入手，探讨了偏移距道集的物理意义，重点阐述了偏移距道集与角道集在表象微分优化中动力学上的等价性。这一等价性是偏移距域表象微分偏移速度分析的基础。

In migration velocity analysis, the common image gather in subsurface diffraction angle (angle gather) has clear physical meanings. The common image gather in migrated offset (offset gather) is the dual variable under the inverse Radon transform of angle gather. Starting from a single reflection forward model, we discussed the physical meanings of offset gathers and expounded the kinematical equivalence between angles and offset in representation differential semblance optimization. This equivalence is foundation for representation differential migration velocity analysis in the offset domain.