Time-migration velocity estimation using Fréchet derivatives based on nonlinear kinematic migration/demigration solvers

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.