The velocity model quality is assessed through common-image gathers computed by TTI Kirchhoff prestack-depth migration. The slope tomography is finally applied to real broadband towed-streamer data to build the vertical velocity and the scatterers, while anisotropic parameters ϵ and δ are used as background parameters. A more realistic synthetic example indicates the feasibility of the joint update of the vertical wavespeed and ϵ. A toy synthetic example allows for a first assessment of the crosstalk between anisotropic parameters and scatterer coordinates. This new formulation of slope tomography is extended to tilted transverse isotropic (TTI) acoustic media, in which the model space is parameterized by four anisotropic parameters (e.g., vertical wavespeed, Thomson’s parameter δ, ϵ, and tilt angle) and the coordinates of the scatterers. Moreover, a matrix-free inverse problem can be implemented with the adjoint-state method for the estimation of the data-misfit gradient. Alternatively, slope tomography can be implemented with eikonal solvers, which compute efficiently finely sampled traveltime maps from the sources and receivers, whereas slopes are estimated by finite differences of the traveltime maps. The inverse problem relies on the explicit building of the sensitivity matrix to update the velocity model by local optimization. Slope tomography conventionally relies on ray tracing for traveltimes and slopes computation, where rays are traced from scatterers in depth to sources and receivers. These models can be further used as background/initial models for depth migration or full-waveform inversion. Locally coherent events by opposition to continuous reflections are suitable for semiautomatic and dense picking, which is conducive to better resolved tomographic models. Slope tomography uses traveltimes, source, and receiver slopes of locally coherent events to build subsurface velocity models.

The matrix free