Abstract
Propagation of elastic waves in heterogeneous linear 1-D media is considered. The scalar wave equation is transformed by the Liouville substitution and the Dyson integral equation is applied for a statistically homogeneous field of heterogeneities. The result is the mean wave field which is analysed in detail for the exponential correlation functions. The general case of the random elastic medium with an arbitrary heterogeneity of small scale is considered and simple closed form expressions for the mean field and attenuation are derived.
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