Kinematically consistent slope tomography using eikonal solvers and the adjoint-state method : Theory and applications to velocity model building and event location

Velocity model building is a key step of seismic imaging since inferring high-resolution subsurface model by migration or full waveform inversion (FWI) is highly dependent on the kinematic accuracy of the retrieved velocity model. Stereotomography, a slope tomographic method that exploits well the density of the data, was proposed as an alternative to conventional reflection traveltime tomography. The latter is based on interpretive tracking of laterally-continuous reflections in the data volume whereas stereotomography relies on automated picking of locally coherent events. The densely picked attributes, namely the traveltimes and their spatial derivatives with respect to the source and receiver positions, are tied to scatterers in depth. More recently, a slope tomography variant was proposed under a framework based on eikonal solvers as an alternative to ray tracing and the adjoint-state method instead of Fréchet-derivative matrix inversion. This revamped stereotomography provides a scalable and flexible framework for large-scale applications. On the other hand, similarly to previous works, the scatterer positions and the subsurface parameters are updated jointly. In this thesis, I propose a new formulation of slope tomography that handles more effectively the ill-famed velocity-position coupling inherently present in reflection tomography. Through a kinematic migration, the scatterer position sub-problem is solved and projected into the main sub-problem for wavespeed estimation. Enforcing the kinematic consistency between the two kinds of variable, that is not guaranteed in the joint inversion, mitigates the ill-posedness generated by the velocity-position coupling. This variable projection leads to a reduced-parametrization inversion where the residuals of a single data class being a slope are minimized to update the subsurface parameters.I introduce this parsimonious strategy in the framework of eikonal solvers and the adjoint-state method for tilted transversely isotropic (TTI) media. I benchmark the method against the Marmousi model and present a field data case study previously tackled with the joint inversion strategy. Both case studies confirm that the parsimonious approach leads to a better-posed problem, with an improved robustness to the initial guess and convergence speed.Slope tomography is mainly used for streamer data due to the requirement of finely-sampled sources and receivers. To exploit cutting-edge long-offset datasets, I involve in the inversion first arrivals extracted from streamer or ocean bottom seismometer data. Before showing the complementarity between reflections and first arrivals, I examine the added value of introducing slopes in first-arrival traveltime tomography (FATT). Using a FWI workflow for quality control, I show with the Overthrust benchmark and a real data case study from the Nankai trough (Japan) how the joint inversion of slopes and traveltimes mitigates the ill-posedness of FATT. I also examine with the BP Salt model the limits of FATT to build an initial model for FWI in complex media. The results show how tomography suffers even with proper undershooting of the imaging targets due to the poor illumination of the subsalt area. On a crustal-scale benchmark, I first show the limits of reflection slope tomography induced by the limited streamer length before highlighting the added-value of the joint inversion of first-arrival and reflection picks.Finally, I introduce the same variable projection technique to tackle the velocity-hypocenter problem, which finds application in earthquake seismology and microseismic imaging. I propose a formulation where the hypocenter is located through the inversion of subsurface parameters and an origin time correction, both of them being used as a proxy and validate the proof of concept on two synthetic examples.