Comparative analysis of three approaches to propagation of stochastic one-dimensional elastic waves

Abstract

Three approaches to the problem of 1-D wave propagation in media with random elastic and mass properties are studied, i.e. the method of integral spectral decomposition, the Fokker-Planck-Kolmogorov equation and the Dyson integral equation. Advantages and disadvantages of each approach are discussed. The approaches are shown to cover actually all possible problems of the harmonic wave propagation in heterogeneous or stochastic media. Hence, one can choose an appropriate strategy for solving a particular problem by means of a preliminary analysis of the problem and advantages of each approach.