The problem of the propagation of Rayleigh waves in a double surface layer, although mathematically tractable, would involve very lengthy computations, scarcely justified by the rather inaccurate data available.
An approximate treatment by “Rayleigh's principle” gives, for any postulated ratio of the thicknesses of the layers, an overestimate of these thicknesses which needs reduction by 10 or 15 per cent. Applied to W. Rohrbach's data on the velocities of transmission (i.e., the group velocities) of Rayleigh waves of known period, this method yields values which are consistent with those previously obtained for Eurasia from Love waves.
For a single uniform granitic layer of thickness T1 resting on uniform ultrabasic material of great depth the Rayleigh-wave velocities from a track from the Kwen Lun Mountains to Göttingen give T1 = 39.4 km., without use of the Rayleigh approximation. This may be compared with the estimate of 34.6 km. obtained on slightly differing hypotheses from Love waves.
If the granitic layer is underlain by a uniform layer of basic rock of thickness T2, some hypothesis must, in our present state of knowledge, be made concerning the ratio T2: T1. For Rayleigh waves the Kwen Lun earthquake gives, on the two hypotheses T2 = T1 and T2 = 2T1, the values 27 km. and 19 km. respectively for T1. Reduced by, say, 15 per cent these values are 23 km. and 16 km., which may be compared with the estimates 22.1 km. and 17.6 km. derived on the same data from Love waves.
For a shock in Eastern Bengal the Rayleigh waves (both vertical and E-W components) give 30 km. and 25 km. on the two hypotheses, that is, “reduced values” of 25.5 km. and 21 km., which exceed the Love-wave estimates of 22.1 km. and 17.6 km. quoted above. However, these tracks cross the Himalayas and the excess values are not surprising.
There is evidently scope for further investigations along these lines.