Recently Zeng et al. (1994) proposed a composite source model for convolution with synthetic Green's functions for computing strong ground motion due to a complex rupture process of a large earthquake. The composite source consists of sub-events with a distribution of sizes, distributed randomly on the fault. In this paper, we extend our discussion of the source by allowing subevent rake to vary within the positive strain quadrant and by including the effect of the random lateral heterogeneity of the earth by adding scattered waves into the Green's function computed from a layered elastic earth model. Both of these variations contribute towards equalizing different components of the high frequency waveform train. The random scattering has the stronger effect on increasing the amplitudes of the nodal components. The early part of these scattered coda waves also tends to elongate the strong shaking of the earthquake. ¿ American Geophysical Union 1995