A variational principle for Love waves propagating in a layer with varying thickness overlying a half-space is formulated. By an averaging procedure, the wave modulation due to gradual variation of the thickness of the upper layer is found. The case of long-period Love waves is particularly examined and the wave number and amplitude modulation both for a monochromatic wave and for a transient wave train due to an impulsive source are determined. Moreover, the travel time for a certain phase in the wave train is determined. It is found that for well-dispersed wave trains the travel time is given by the phase velocity corresponding to the mean depth of the upper layer.

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