Reflection tomography: How to handle multiple arrivals?

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Applications of reflection tomography for the determination of complex geologic structures calls for the generalization of this method so that it can take triplications and other multiple arrivals into account. In this way, we propose a new formulation of travel time inversion. It relies on the choice of an adequate parametric representation of travel time information: the parameters we have chosen for this representation are the receiver location and the ray parameter at the receiver, some quantities directly measured from seismic data. The forward problem involved in the solution of this new inverse problem consists in shooting rays from a receiver according to the measured values of the ray parameter at the receiver. We can thus predict for a given model the emergence point of the reflected ray (i.e., the shot location) and the associated reflection arrival time. The least squares formulation of the inverse problem consists in minimizing an objective function that measures the mismatch between predicted and actual shot locations on one side and predicted and actual reflection arrival times on the other side, for the considered receiver locations and the associated measured ray parameters. However, inversion of noise corrupted kinematic data calls for a realistic definition of the uncertainties associated with the data. In particular, those uncertainties should take into account the sensitivity of reflection arrival times and shot locations to an error in the measurement of the ray parameter at the receiver. The objective function to minimize being chosen, the solution of the inverse problem is performed by a Gauss‐Newton method, the Jacobian of the forward modeling operator being computed by the adjoint state technique. It is interesting to note that no two‐point ray tracing is required in our method which is therefore cheaper than classical reflection tomography. The effectiveness of this approach is illustrated on a difficult synthetic example with large lateral velocity variations and strongly noise corrupted data.