Simultaneous correction of near-surface statics and trace interpolation is constructed from a Fourier integral representation of wavefield extrapolation and implemented in a least-squares sense. Synthetic examples based on extreme velocity variation and extreme elevation change are used to demonstrate individually and together the aspects of interpolation and of the full statics-application-plus-interpolation (STAPPI). The Husky 2D dataset is used to to demonstrate that this approach interpolates missing traces and applies nearsurface statics in a real setting with extreme near surface variation in velocity and elevation.
The method is found to be computationally intensive, and an approximation based on expansion of the Hessian matrix is derived and implemented. A four term implementation of the expansion of the Hessian is developed and tested against the exact operator. The approximate method is found to return comparable data to that of the exact method for all but the most extreme cases. Though computational efficiency is improved by only a scalar relative to the exact algorithm, this work provides an analytic and numerical platform upon which to build an accurate operator that reduces the order associated with computational cost.
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