The reflectivity algorithm for laterally varying earth models is too slow to be practical for modeling refraction data when the vertical direction is the imbedding direction. However when the horizontal direction is made the direction of imbedding the cost of computation increase (at most) linearly with source-receiver offset. In general the horizontal propagator has a continuous spectrum and a point spectrum. The point spectrum is large and troublesome to locate at body-wave frequencies but the location of the continuous spectrum is always known. By adding a low-velocity lower half space to the model the continuous spectrum is enlarged at the expense of the point spectrum. We propose to treat lateral heterogeneity by coupling together the continuous spectra of adjacent vertical slices.
