Abstract
The author considers the propagation of surface Love waves in a random layered elastic medium. The material parameters in the model are stochastic functions of the vertical coordinates chi 3: this includes the general case when the wave propagates through a statistically inhomogeneous layer. The author applies the averaging method for stochastic equations. The method essentially involves approximating the expectation of the solution with averages formed by integrating various moments of the random coefficients over 'long' times (long relative to the correlation time). This method provides higher-order corrections to the purely asymptotic approximations which are often used to solve equations of this type. It is shown that the mean wave amplitude always attenuates exponentially on the depth scale in 2 chi 3 where in is the fluctuation parameter. The author analyses the dispersion relation for a statistically homogeneous layer and finds a criterion which determines whether the mean phase velocity is decreased by the fluctuations.
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