Elastic wave scattering by a rough free surface of solids is analyzed. The analysis is based on the concept of scattering amplitude (SA) and perturbation approximation. The SA method is very convenient for rough surface scattering problems. By solving the boundary equations, the first and the second order solutions of approximate scattering amplitude are obtained. The general solutions are used for, as an example, the wave scattering by rough surfaces with Gaussian distribution. The mean field and variance are given. Finally, an experiment is designed to verifv the theoretical predications.
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