The great advantages of one-way propagation methods, such as the generalized screen propagators (GSP) method, are the fast speed of computation, often several orders of magnitude faster than the full-wave finite difference and finite element methods, and the huge savings in internal memory. In this article, a half-space GSP is formulated for the SH half-space problem. Two versions of the half-space GSP are derived: the wide-angle pseudo-screen and the phase-screen. The Moho discontinuity is treated as parameter perturbations from the crustal background. The validity and limitations of this treatment are discussed. It is shown that half-space screen propagators can accurately propagate guided crustal waves that are composed of small-angle waves with respect to the horizontal direction. Comparisons of numerical results with a wavenumber integration method for flat crustal models and a finite difference algorithm for heterogeneous models show excellent agreements. For a model with propagation distance of 250 km, dominant frequency at 0.5 Hz, the GSP method is about 300 times faster than a finite difference algorithm with a similar accuracy. These comparisons demonstrate the accuracy and efficiency of the method. We apply our method to simulate regional wave propagation in different types of complex crustal waveguides including those with small-scale random heterogeneities. The influence of these heterogeneities on Lg amplitude attenuation and Lg coda formation is significant.