On the Parametrization of Slope Tomography: Its Implication on the Velocity-position Coupling
Résumé
Seismic tomography seeks to reconstruct the subsurface parameters, mainly wavespeeds. In reflection/diffraction tomography, an additional parameter class is inherently introduced: the scattering positions. The underlying inverse problem is awkward due to the ill-famed velocity-position coupling. We review different optimization strategies in the frame of slope tomography, namely tomographic approaches based on locally coherent seismic events associated with reflection/diffraction from small reflector segments/diffractors. The latter are described by their two-way traveltimes and slopes, the horizontal component of slowness vector at the source and receiver positions). Three plausible inversion strategies exist to address this multi-variate problem: the first consists of alternating between scattering position and wavespeed updates to bypass the coupling issue. The second jointly updates both sought parameters with the risk of ill-posedness. The third one relies on the projection of the model subspace spanned by scattering positions onto the model subspace spanned by velocities leading to a mono-variate reduced-space inversion. This projection is implemented in the adjoint-state method by using two focusing equations satisfied by two observables (one slope and two-way traveltimes) as constraints. Assessing these strategies on synthetic and real cases shows that the reduced-space approach exhibits superior performance while not needing any scaling of the data and model spaces.