SCATTERING OF PLANE SH-WAVES BY A CYLINDRICAL CANYON OF ARBITRARY SHAPE IN ANISOTROPIC MEDIA

The scattering and diffraction of plane SH-waves by an arbitrary-shaped cylindrical canyon in anisotropic media is formulated here. Analytical solutions are obtained via the complex function theory, using the orthogonal property of the Hermite functions to solve the resulting set of infinite algebraic equations. Expressions for scattered displacements and scattered stresses are given. Three cross-sectional profile types are used in the numerical simulation of the two-dimensional canyon topography: (a) a semi-circular profile, (b) a semi-elliptical profile and (c) a triangular profile. The results obtained in (a) and (b) are consistent with known solutions computed by Trifunac and his co-workers [1, 3] using a different method. As the exact solution for (c) is not known to exist, the result given here is believed to be new and would therefore serve as a useful check for numerical analysts working in this area.