We develop a numerical simulation method that can efficiently model the combined effects of large-scale structural variations and small-scale heterogeneities (e.g. random media) on Lg-wave propagation at far regional distances. The approach is based on the generalized screen propagator (GSP) method, which has previously been used to simulate SHLg waves in complex crustal waveguides. In this paper, we extend the GSP method to treat complex crustal models with irregular or rough topography by incorporating surface flattening transformation into the method. The transformation converts surface perturbations into modified volume perturbations. In this way the range-dependent boundary condition becomes a stress release boundary condition on a flat surface in the new coordinate system where the half-space GSP can be applied.
To demonstrate the accuracy and efficiency of the extended GSP method, synthetic seismograms are generated for various crustal waveguides, including uniform crusts, a Gaussian hill half-space, and crustal models with mild and moderately rough surfaces. The results are compared with those generated by the exact boundary element method. It is shown that the screen method is efficient for modelling the effect of surface topography on Lg waves. The comparison of synthetic seismograms generated by the screen method and the traditional parabolic equation method shows that the screen method can handle wider-angle waves as well as rougher topography than the parabolic equation method. Finally, we apply the method to complex crustal waveguides with both small-scale heterogeneities (random media) and random rough surfaces for Lg propagation to far regional distances. The influence of random heterogeneities and rough surfaces on Lg attenuation is significant.