The amplitude of the Love–Rayleigh discrepancy created by small‐scale heterogeneities

Summary At global as well as at regional scale, the lithosphere appears faster to Love waves than to Rayleigh waves. This Love–Rayleigh discrepancy can be modelled by introducing transverse isotropy in the upper mantle. In some regions however, it is so large that the question arises as to whether part of it could be an artefact related to the presence of heterogeneities in the lithosphere. Using a multiple‐scattering scheme to model surface waves in 3‐D structures, we analyse the influence of small‐scale heterogeneities in the lithosphere on the Love–Rayleigh discrepancy in the period range 25 to 60 s. Small‐scale heterogeneities tend to lower the apparent phase velocity of the surface waves, and have a larger effect on the Love waves than on the Rayleigh waves. This is not due to mode‐coupling, which plays a negligible role here, but to the interference of the primary field with the one backscattered twice. For models with S ‐wave velocity variations of rms 2.5 per cent, and spatial correlations at distances of 20 to 100 km, we find that the Love waves are on average and at most 0.1 per cent slower than the Rayleigh waves. This apparent Love–Rayleigh discrepancy varies linearly with the variance of S ‐wave velocity variation in the structure. We conclude that small‐scale heterogeneities do not contribute significantly to the large Love–Rayleigh discrepancies of 4 to 9 per cent observed in some regions, since they produce an apparent discrepancy which is negligible in comparison, and which even has the opposite sign.