Although first-arrival tomography provides an effective way to estimate near-surface velocities and static corrections, the undulation of velocity interfaces such as the base of the weathered zone may not be easily determined by this method. The main reason is that first arrivals are insensitive to small geometric changes in velocity interfaces because their raypaths tend to traverse along those interfaces. To improve the solution of interface geometry, we developed a deformable layer tomostatics method that approximates the near-surface velocity field as several layers of constant velocity and variable thickness that can be inverted for the geometry of the velocity interfaces. We use a multiscale model parameterization in the inversion for interface geometry. Synthetic and field data tests showed that the method can determine the interface geometry. Constraining the depth range of the basal boundary of the weathered zone increases the convergence rate of the iterative inversion process. Tests on field data showed greater reflection coherency in a stacked section based on constrained static corrections than in one from unconstrained static corrections. The method yielded a better match with statics computed from sand-dune curves than does a match obtained by using two commercial grid tomography packages.

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