Ray-based reflection traveltime tomography using approximate stationary points

Reflection traveltime tomography has been used to describe subsurface velocity structures which, in practice, can be used as a background or initial model for pre-stack depth migration or full waveform inversion. Conventional reflection traveltime tomography is performed by solving an optimization problem based on a ray-tracing method. As a result, reflection traveltime tomography requires heavy computational efforts to carry out ray tracing and solve a large matrix equation. In addition, like most data-domain tomography methods, reflection traveltime tomography depends on initial guesses and suffers from non-uniqueness and uncertainty of solutions. In this research, we propose a deterministic ray-based reflection traveltime tomography method by applying seismic interferometry. This method does not suffer from the non-uniqueness problem and does not require a priori information on subsurface media. By adding a virtual layer (whose properties are known) on top of the real surface and applying convolution-type interferometry, we approximately determine the stationary points (i.e., incident raypaths in the virtual layer). Then, we generate reflection points for a range of assumed velocities and estimate the velocity by considering the number of reflection points and the traveltime difference between the observed and calculated data. The reflection surface can then be recovered by using the estimated velocity. Once the first target layer is resolved, we can recover the whole media by recursively applying the same method to the lower layers. Numerical examples using surface seismic profile data for homogeneous-layer (with a low-velocity layer) and inhomogeneous-layer models and real field data experiments on the Congo data set demonstrate that our method can successfully recover the velocities and depths of subsurface media without initial guesses. However, our method has some limitations for multi-layer models because the method does not have sufficient reflection points for the deeper layers.