Seismic data processing in terms of locally supported wavelets

We develop a mathematical tool which is used for the regularization of a singular integral representation of the Helmholtz equation in a region with non-smooth boundaries with a constant parameter, i.e. in a medium with a constant velocity. The classical perturbation approach is then applied in order to calculate the Helmholtz equation with a variable parameter. Moreover, for media with strong variation in a velocity field, the combination with a solution of the eikonal equation can be used. Because such approach consider only waves with the shortest travel times, we apply it for a filtering, e.g. for the separating of down-going and up-going waves.