Three dimensional wave equation depth migration by a direct solution method

We propose a new method for wave equation depth migration which is carried out by depth stepping in the space-temporal frequency domain. The propagation of the solution is based on a rational expansion of the formal solution to the acoustic wave equation. The expansion coefficients are calculated by a filter design approach. The method is not based on one way wave equations or on perturbations to constant velocity solutions to the wave equation, but rather it uses the constant density variable velocity wave equation as the basis. The method has a good steep dip response and can handle strong lateral variations in the subsurface velocity. The new method is tested against the Sigsbee data set and the 3D SEG salt model.