Reflection traveltime tomography using approximate stationary points

Abstract

Reflection traveltime tomography has been used to describe subsurface velocity structures in practice, which can be used as a background or initial model for prestack 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 effort 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 study, I propose a deterministic ray-based reflection traveltime tomography method by applying seismic interferometry, and 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 on the top of the real surface (whose properties are known) and applying convolution-type interferometry, I approximately determine the stationary points (i.e., incident raypaths in the virtual layer). In the case that we already know the information on the first real layer, correlation-type interferometry also can be used to determine stationary points. Then, I generate reflection points for a range of assumed velocities and estimate the velocity by considering the number of reflection points and traveltime difference between the observed and calculated data instead of solving the conventional tomographic matrix. 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 and inhomogeneous models and real field data (Congo data set) demonstrate that the proposed method successfully recovers the velocity and depth of subsurface media without initial guesses. However, the proposed method has some limitations for multi-layer models because the method does not yield sufficient reflection points for the deeper layers.