A new modification of scalar ray-Kirchhoff algorithms for 2- and 3-D seismic modeling in laterally inhomogeneous media with regular and irregular interfaces is suggested. The method removes limitations of the ray theory in singular regions of ray field and gives a uniform high-frequency approximation of wavefield including effects of single and multiple scattering on irregular interfaces. Its crucial point is the double superposition principle when the total wavefield is represented in the form of finite superposition of some elementary body waves which are decomposed into a set of wave beams spreading from the integral surface. These wave beams are constructed on the basis of uniform fundamental solutions of wave equations combining most of the existing particular solutions like Gaussian beams, edge waves, etc. Their special phase and amplitude approximations produce computationally convenient analytical expressions. They are regular everywhere and can be combined with other asymptotic methods owing to a quite general form of Green's function. Numerical estimation of accuracy and stability of resulting computational algorithm are made by the calculation of some canonical integrals and also by comparison of synthetics with finite differences. The results show that the method can be applied to seismic modeling in real geological structures of composite type.
