The observed secondary microseismic wavefield is composed by Rayleigh and Love waves. While the presence and amount of Rayleigh waves is well understood, the generation of Love waves is still under debate. We investigate multiple scattering of surface waves as a possible mechanism that could be responsible for the generation of Love waves in the secondary microseism. We assume that the secondary microseism source generates mainly vertically polarized waves, and that the Love waves are produced during the propagation of the wavefield. To study this hypothesis, we model the wavefield in a highly heterogeneous 3-D half-space with a free surface. To understand the relationship between the surface wave types and the random medium properties, we perform a parameter study. We alter the model fluctuation strength, the correlation length and the layering structure of the medium. We find that the fluctuation strength has a major influence on the Love to Rayleigh ratio. We observe that the Love to Rayleigh ratio reaches a maximum value of 0.4 after approximately 4 scattering mean free paths. This value does not explain the observed Love to Rayleigh ratios in the secondary microseism, which lies between 0.6 and 1.2. Moreover, we would need an unrealistically strongly scattering medium to reach this value. Considering scattering properties similar to those encountered in oceanic crust for wavefields around 0.2 Hz, we obtain a Love to Rayleigh ratio of 0.1, which is significantly below the typically observed ratio of 0.6–1.2.