Time migration, as opposed to depth migration, suffers from two well-known shortcomings: (1) approximate equations are used for computing Green’s functions inside the imaging operator and (2) in case of lateral velocity variations, the transformation between the image-ray coordinates and the Cartesian coordinates is undefined in places where the image rays cross. We have found that the first limitation can be removed entirely by formulating time migration through wave propagation in image-ray coordinates. Our approach constructs a time-migrated image without relying on any kind of traveltime approximation by formulating an appropriate geometrically accurate acoustic wave equation in the time-migration domain. The advantage of this approach is that the propagation velocity in image-ray coordinates does not require expensive model building and can be approximated by quantities that are estimated in conventional time-domain processing. Synthetic and field data examples demonstrate the effectiveness of the proposed approach and show that the proposed imaging workflow leads to a significant uplift in terms of image quality and can bridge the gap between time and depth migrations. The image obtained by the proposed algorithm is correctly focused and mapped to depth coordinates; it is comparable to the image obtained by depth migration.

中文翻译：

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波方程时间偏移

与深度偏移相反，时间偏移具有两个众所周知的缺点：（1）近似方程式用于计算成像算子内部的格林函数，（2）在横向速度变化的情况下，即图像射线之间的转换影像光线交叉的地方，坐标和笛卡尔坐标是不确定的。我们已经发现，可以通过在图像射线坐标中通过波传播制定时间迁移来完全消除第一个限制。我们的方法通过在时移域中制定适当的几何精确声波方程，构建不依赖任何传播时间近似值的时移图像。该方法的优点在于，图像射线坐标中的传播速度不需要昂贵的模型构建，并且可以通过常规时域处理中估计的数量来近似。合成和现场数据示例证明了该方法的有效性，并表明，所提出的成像工作流程导致图像质量显着提升，并可以弥合时间和深度偏移之间的差距。通过提出的算法获得的图像被正确聚焦并映射到深度坐标；它与通过深度迁移获得的图像相当。合成和现场数据示例证明了该方法的有效性，并表明，所提出的成像工作流程导致图像质量显着提升，并可以弥合时间和深度偏移之间的差距。通过提出的算法获得的图像被正确聚焦并映射到深度坐标；它与通过深度迁移获得的图像相当。合成和现场数据示例证明了该方法的有效性，并表明，所提出的成像工作流程导致图像质量显着提升，并可以弥合时间和深度偏移之间的差距。通过提出的算法获得的图像被正确聚焦并映射到深度坐标；它与通过深度迁移获得的图像相当。