SCATTERING OF PLANE SH-WAVES BY A CYLINDRICAL ALLUVIAL VALLEY OF CIRCULAR-ARC CROSS-SECTION

A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical alluvial valley of circular-are cross-section in a h alf-space is presented using the wave functions expansion. The solutio n is reduced to solving a set of infinite linear algebraic equations u sing the exterior region form of Graf's addition theorem. Numerical so lutions are obtained by truncation of the infinite equations and their accuracies are demonstrated by convergence of the numerical results t o the exact boundary condition with the increasing of the truncation o rder. The present solution is compared with the existing one presented by Todorovska and Lee for the same problem and their differences are analyzed. complicated effects of the depth-to-width ratio of the alluv ia valley on surface ground motion are finally illustrated.