Advanced seismic imaging and inversion are dependent on a velocity model that is sufficiently accurate to render reliable and meaningful results. For that reason, methods for extracting such velocity models from seismic data are always in high demand and are topics of active investigation. Velocity models can be obtained from both the time and depth domains. Relying on the former, time migration is an inexpensive, quick and robust process. In spite of its limitations, especially in the case of complex geologies, time migration can, in many instances (e.g. simple to moderate geological structures), produce image results compatible to the those required for the project at hand. An accurate time-velocity model can be of great use in the construction of an initial depth-velocity model, from which a high-quality depth image can be produced. Based on available explicit and analytical expressions that relate the kinematic attributes (namely, traveltimes and local slopes) of local events in the recording (demigration) and migrated domains, we revisit tomographic methodologies for velocity-model building, with a specific focus on the time domain, and on those that makes use of local slopes, as well as traveltimes, as key attributes for imaging. We also adopt the strategy of estimating local inclinations in the time-migrated domain (where we have less noise and better focus) and use demigration to estimate those inclinations in the recording domain. On the theoretical side, the main contributions of this work are twofold: 1) we base the velocity model estimation on kinematic migration/demigration techniques that are nonlinear (and therefore more accurate than simplistic linear approaches) and 2) the corresponding Fréchet derivatives take into account that the velocity model is laterally heterogeneous. In addition to providing the comprehensive mathematical algorithms involved, three proof-of-concept numerical examples are demonstrated, which confirm the potential of our methodology.

先进的地震成像和反演取决于速度模型，该速度模型足够准确，可以提供可靠且有意义的结果。因此，从地震数据中提取这种速度模型的方法一直是需求很高的，并且是积极研究的主题。速度模型可以从时域和深度域获得。依靠前者，时间迁移是一种廉价，快速且可靠的过程。尽管存在局限性，特别是在复杂的地质情况下，时间迁移在许多情况下（例如简单到中等的地质结构）仍可以产生与手头项目所需的图像结果兼容的图像结果。准确的时间-速度模型在初始深度-速度模型的构造中可能会非常有用，从中可以生成高质量的深度图像。基于可用的显式和解析表达式，它们与记录（迁移）域和迁移域中局部事件的运动学属性（即行进时间和局部坡度）相关，我们重新研究了用于速度模型构建的断层摄影方法，特别关注时间范围，以及那些利用局部坡度和旅行时间作为成像关键属性的区域。我们还采用了估计时间迁移域中局部倾斜度的策略（噪声较小且聚焦更好），并使用反偏移来估计记录域中的局部倾斜度。从理论上讲，这项工作的主要贡献是双重的：1）我们将速度模型估计基于非线性的运动学迁移/消解技术（因此比简单的线性方法更为准确）和2）相应的Fréchet导数考虑到速度模型在横向上是异质的。除了提供涉及的综合数学算法外，还演示了三个概念验证的数值示例，这证实了我们方法学的潜力。