Automatic Velocity Analysis with the Two-way Wave Equation

Migration velocity analysis constructs a velocity model by focusing a migration image in terms of a redundant coordinate, for instance surface offset or a shift at depth between forward and time-reversed wavefield. The latter option is considered here in the context of two-way wave equation modelling with a frequency-domain finite-difference code. Gradient optimisation of a focusing cost functional automatically provides the velocity model. An experiment on multiple-free synthetic data confirms the validity of the method, as earlier demonstrated by other authors for one-way wave-equation propagators. In the presence of multiples, results may be less favourable. A variant is proposed that appears to give better results and can potentially be used to construct a starting model for more refined least-squares fitting of the measured seismic data.